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@book{Bryson1975,
author = {Bryson, Arthus E. and Ho, Yu-Chi},
publisher = {Taylor {\&} Francis},
title = {{Applied Optimal Control}},
year = {1975}
}
@article{Dorn2015a,
author = {Dorn, Tim W. and Wang, Jack M. and Hicks, Jennifer L. and Delp, Scott L.},
doi = {10.1371/journal.pone.0121407},
file = {:home/matt/Documents/Mendeley Desktop//Dorn et al. - 2015 - Predictive Simulation Generates Human Adaptations during Loaded and Inclined Walking.pdf:pdf},
issn = {1932-6203},
journal = {Plos One},
number = {4},
pages = {e0121407},
title = {{Predictive Simulation Generates Human Adaptations during Loaded and Inclined Walking}},
url = {http://dx.plos.org/10.1371/journal.pone.0121407},
volume = {10},
year = {2015}
}
@article{Schoellig2012,
abstract = {Current control systems regulate the behavior of dynamic systems by reacting to noise and unexpected disturbances as they occur. To improve the performance of such control systems, experience from iterative executions can be used to anticipate recurring disturbances and proactively compensate for them. This paper presents an algorithm that exploits data from previous repetitions in order to learn to precisely follow a predefined trajectory. We adapt the feed-forward input signal to the system with the goal of achieving high tracking performance—even under the presence of model errors and other recurring disturbances. The approach is based on a dynamics model that captures the essential features of the system and that explicitly takes system input and state constraints into account. We combine traditional optimal filtering methods with state-of-the-art optimization techniques in order to obtain an effective and computationally efficient learning strategy that updates the feed-forward input signal according to a customizable learning objective. It is possible to define a termination condition that stops an execution early if the deviation from the nominal trajectory exceeds a given bound. This allows for a safe learning that gradually extends the time horizon of the trajectory. We developed a framework for generating arbitrary flight trajectories and for applying the algorithm to highly maneuverable autonomous quadrotor vehicles in the ETH Flying Machine Arena testbed. Experimental results are discussed for selected trajectories and different learning algorithm parameters.},
author = {Schoellig, Angela P. and Mueller, Fabian L. and D'Andrea, Raffaello},
doi = {10.1007/s10514-012-9283-2},
file = {:home/matt/Documents/Mendeley Desktop/art{\%}3A10.1007{\%}2Fs10514-012-9283-2.pdf:pdf},
issn = {09295593},
journal = {Autonomous Robots},
keywords = {Aerial robotics,Convex optimization,Input and state constraints,Kalman filtering,Learning,Motion planning and control,Quadrocopter control,Trajectory tracking},
number = {1-2},
pages = {103--127},
title = {{Optimization-based iterative learning for precise quadrocopter trajectory tracking}},
volume = {33},
year = {2012}
}
@article{Mayne1966,
abstract = {ABSTRACT A second-order method of successively improving a control sequence for a non-linear discrete-time system is derived. One step convergence is obtained for linear systems with quadratic performance functions. Although the results are of interest in their own right, a second-order method for continuous-time systems is obtained by formally allowing the sampling interval to approach zero. The equations so obtained differ slightly, because of the method of derivation, from results already obtained using the calculus of variations approach. The difference, which is an advantage of the method described in this paper, is that one vector differential equation less has to be integrated. The approach used in the derivation is motivated by dynamic programming and facilitates the application of gradient methods to stochastic problems which will be the subject of a future paper.},
annote = {Differential Dynamic Programming (DDP)},
author = {Mayne, David},
doi = {10.1080/00207176608921369},
file = {:home/matt/Documents/Mendeley Desktop/00207176608921369.pdf:pdf},
isbn = {0020717660892},
issn = {0020-7179},
journal = {International Journal of Control},
keywords = {Differential Dynamic Programming},
mendeley-tags = {Differential Dynamic Programming},
number = {1},
pages = {85--95},
title = {{A Second-order Gradient Method for Determining Optimal Trajectories of Non-linear Discrete-time Systems}},
volume = {3},
year = {1966}
}
@article{Elnagar1995,
abstract = {This paper presents a computational technique for opti- mal control problems including state and control inequality constraints. The technique is based on spectral collocation methods used in the solution of differential equations. The system dynamics are collocated at LegendMauss-Lohatto points. The derivative z(t) of the state z(t) is approximated by the analytic derivative of the corresponding interpolating polynomial. State and control inequality constraints are collocated at LegendMauss-Lohatto nodes. The integral involved in the definition of the performance index is discretized based on Gauss-Lobatto quadrature rule. The optimal control problem is thereby converted into a mathematical programming program. Thus existing, well-developed optimization algorithms may be used to solve the transformed problem. The method is easy to implement, capable of handling various types of constraints, and yields very accurate results. Illustrative examples are included to demonstrate the capability of the proposed method, and a comparison is made with existing metbods in the literature.},
author = {Elnagar, Gamal and Kazemi, Mohammad A. and Razzaghi, Mohsen},
file = {:home/matt/Documents/Mendeley Desktop//Elnagar, Kazemi, Razzaghi - 1995 - The Pseudospectral Legendre Method for Discretizing Optimal Control Problems.pdf:pdf},
journal = {IEEE},
number = {October},
pages = {1793--1796},
title = {{The Pseudospectral Legendre Method for Discretizing Optimal Control Problems}},
volume = {40},
year = {1995}
}
@inproceedings{NPeng2015,
abstract = {The locomotion skills developed for physics-based characters most often target flat terrain. However, much of their potential lies with the creation of dynamic, momentum-based motions across more complex terrains. In this paper, we learn controllers that allow simulated characters to traverse terrains with gaps, steps, and walls using highly dynamic gaits. This is achieved using reinforcement learning, with careful attention given to the action representation, non-parametric approximation of both the value function and the policy; epsilon-greedy exploration; and the learning of a good state distance metric. The methods enable a 21-link planar dog and a 7-link planar biped to navigate challenging sequences of terrain using bounding and running gaits. We evaluate the impact of the key features of our skill learning pipeline on the resulting performance.},
author = {NPeng, Xue Bin and Berseth, Glen and van de Panne, Michiel},
booktitle = {SIGGRAPH},
file = {:home/matt/Documents/Mendeley Desktop/NPeng, Berseth, Panne - 2015 - Dynamic Terrain Traversal Skills Using Reinforcement Learning.pdf:pdf},
keywords = {across challenging terrains that,and steps,computer animation,contain gaps,expand the capabilities of,figures by learning control,in this paper we,motions,physics simulation,simulated articulated,strategies for highly dynamic,walls},
title = {{Dynamic Terrain Traversal Skills Using Reinforcement Learning}},
url = {http://www.cs.ubc.ca/{~}van/papers/2015-TOG-terrainRL/index.html},
year = {2015}
}
@article{Mellinger2011,
abstract = {We address the controller design and the trajectory generation for a quadrotor maneuvering in three dimensions in a tightly constrained setting typical of indoor environments. In such settings, it is necessary to allow for significant excursions of the attitude from the hover state and small angle approximations cannot be justified for the roll and pitch. We develop an algorithm that enables the real-time generation of optimal trajectories through a sequence of 3-D positions and yaw angles, while ensuring safe passage through specified corridors and satisfying constraints on velocities, accelerations and inputs. A nonlinear controller ensures the faithful tracking of these trajectories. Experimental results illustrate the application of the method to fast motion (5{\&}{\#}x2013;10 body lengths/second) in three-dimensional slalom courses.},
author = {Mellinger, Daniel and Kumar, Vijay},
doi = {10.1109/ICRA.2011.5980409},
file = {:home/matt/Documents/Mendeley Desktop/Mellinger, Kumar - 2011 - Minimum snap trajectory generation and control for quadrotors.pdf:pdf},
isbn = {9781612843865},
issn = {10504729},
journal = {Proceedings - IEEE International Conference on Robotics and Automation},
pages = {2520--2525},
title = {{Minimum snap trajectory generation and control for quadrotors}},
year = {2011}
}
@article{Romberg1965,
author = {Romberg, Method O F},
file = {:home/matt/Documents/Mendeley Desktop/out (2).pdf:pdf},
journal = {J. SIAM Numer. Anal.},
number = {2},
pages = {250--259},
title = {{On the Method of Romberg Quadrature}},
volume = {2},
year = {1965}
}
@techreport{Finn2004,
author = {Finn, David L},
file = {:home/matt/Documents/Mendeley Desktop/quinticHermite.pdf:pdf},
institution = {Rose-Hulman},
title = {{MA 323 Geometric Modelling Course Notes : Day 09 Quintic Hermite Interpolation}},
url = {https://www.rose-hulman.edu/{~}finn/CCLI/Notes/day09.pdf},
year = {2004}
}
@article{Pratt2001,
author = {Pratt, J.},
doi = {10.1177/02783640122067309},
file = {:home/matt/Documents/Mendeley Desktop/Pratt - 2001 - Virtual Model Control An Intuitive Approach for Bipedal Locomotion.pdf:pdf},
isbn = {0278364012},
issn = {0278-3649},
journal = {The International Journal of Robotics Research},
month = {feb},
number = {2},
pages = {129--143},
title = {{Virtual Model Control: An Intuitive Approach for Bipedal Locomotion}},
url = {http://ijr.sagepub.com/cgi/doi/10.1177/02783640122067309},
volume = {20},
year = {2001}
}
@article{Saglama,
author = {Saglam, Cenk Oguz and Byl, Katie},
file = {:home/matt/Documents/Mendeley Desktop/Saglam, Byl - Unknown - Robust Policies via Meshing for Metastable Rough Terrain Walking.pdf:pdf},
title = {{Robust Policies via Meshing for Metastable Rough Terrain Walking}}
}
@misc{Weisstein,
author = {Weisstein, Eric W.},
booktitle = {MathWorld--A Wolfram Web Resource.},
title = {{Smooth Function}},
url = {http://mathworld.wolfram.com/SmoothFunction.html},
urldate = {2015-12-10}
}
@article{Maleki2010,
annote = {These authors clearly don't know what they are doing. Their introduction is full of mistakes. Obvious ones.},
author = {Maleki, Mohammad and Hadi-Vencheh, Abdollah},
doi = {10.1080/00207160802524754},
file = {:home/matt/Documents/Mendeley Desktop/Maleki, Hadi-Vencheh - 2010 - Combination of non-classical pseudospectral and direct methods for the solution of brachistochrone problem.pdf:pdf},
issn = {0020-7160},
journal = {International Journal of Computer Mathematics},
keywords = {brachistochrone problem,direct method,non-classical pseudospectral method,quadratic},
number = {8},
pages = {1847--1856},
title = {{Combination of non-classical pseudospectral and direct methods for the solution of brachistochrone problem}},
url = {http://www.tandfonline.com/doi/abs/10.1080/00207160802524754},
volume = {87},
year = {2010}
}
@article{Westervelt2003,
abstract = { Planar, underactuated, biped walkers form an important domain of applications for hybrid dynamical systems. This paper presents the design of exponentially stable walking controllers for general planar bipedal systems that have one degree-of-freedom greater than the number of available actuators. The within-step control action creates an attracting invariant set - a two-dimensional zero dynamics submanifold of the full hybrid model {\$}whose restriction dynamics admits a scalar linear time-invariant return map. Exponentially stable periodic orbits of the zero dynamics correspond to exponentially stabilizable orbits of the full model. A convenient parameterization of the hybrid zero dynamics is imposed through the choice of a class of output functions. Parameter optimization is used to tune the hybrid zero dynamics in order to achieve closed-loop, exponentially stable walking with low energy consumption, while meeting natural kinematic and dynamic constraints. The general theory developed in the paper is illustrated on a five link walker, consisting of a torso and two legs with knees.},
author = {Westervelt, E. R. and Grizzle, J. W. and Koditschek, D. E.},
doi = {10.1109/TAC.2002.806653},
file = {:home/matt/Documents/Mendeley Desktop//Westervelt, Grizzle, Koditschek - 2003 - Hybrid zero dynamics of planar biped walkers.pdf:pdf},
isbn = {0018-9286},
issn = {00189286},
journal = {IEEE Transactions on Automatic Control},
keywords = {Bipeds,Hybrid systems,Poincar{\'{e}} sections,Under-actuated system,Zero dynamics},
number = {1},
pages = {42--56},
title = {{Hybrid zero dynamics of planar biped walkers}},
volume = {48},
year = {2003}
}
@misc{PSOPT_Becerra,
author = {Becerra, Victor M},
publisher = {University of Reading, School of Systems Engineering},
title = {{PSOPT Optimal Control Solver User Manual}},
url = {http://www.psopt.org/},
year = {2011}
}
@article{Eaton1992,
author = {Eaton, W},
file = {:home/matt/Documents/Mendeley Desktop/1-s2.0-000925099280263C-main.pdf:pdf},
journal = {Engineering},
number = {4},
pages = {705--720},
title = {{MODEL-PREDICTIVE CONTROL PROCESSES Q ( Ov + UT}},
volume = {47},
year = {1992}
}
@article{Trefethen2006,
author = {Trefethen, Lloyd N},
file = {:home/matt/Documents/Mendeley Desktop/out.pdf:pdf},
keywords = {adaptive grid points,barycentric interpola-,blow-up problem,chebyshev,complex singularities,e approximation,pad,rational spectral collocation method,the burgers,tion formula},
number = {5},
pages = {1798--1811},
title = {{A rational spectral collocation method with adaptively transformed chebyshev grid points ∗}},
volume = {28},
year = {2006}
}
@article{Milam2000,
author = {Milam, M.B. B and Mushambi, K. and Murray, R.M. M},
doi = {10.1109/CDC.2000.912875},
file = {:home/matt/Documents/Mendeley Desktop/Milam, Mushambi, Murray - 2000 - A new computational approach to real-time trajectory generation for constrained mechanical systems.pdf:pdf},
isbn = {0-7803-6638-7},
issn = {01912216},
journal = {Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187)},
keywords = {constrained trajectory genera-,design,nonlinear control,optimal control,real-time optimization},
pages = {845--851},
title = {{A new computational approach to real-time trajectory generation for constrained mechanical systems}},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=912875},
year = {2000}
}
@article{Wang2012,
author = {Wang, Haiyong and Xiang, Shuhuang},
file = {:home/matt/Documents/Mendeley Desktop/Wang, Xiang - 2015 - of Legendre Approximation.pdf:pdf},
journal = {Mathematics of Computation},
keywords = {11071260,and phrases,barycen-,bernstein ellipse,by the nsf of,c 2011 american mathematical,chebyshev expansion,china,legendre expansion,no,society,this work was supported,tric lagrange interpolation},
number = {278},
pages = {861--877},
title = {{On the Convergence Rate of Legendre Approximation}},
volume = {81},
year = {2011}
}
@phdthesis{Benson2005,
abstract = {A pseudospectral method for solving nonlinear optimal control problems is proposed in this thesis. The method is a direct transcription that transcribes the continuous optimal control problem into a discrete nonlinear programming problem (NLP), which can be solved by well-developed algorithms. The method is based on using global polynomial approximations to the dynamic equations at a set of Gauss collocation points. The optimality conditions of the NLP have been found to be equivalent to the discretized optimality conditions of the continuous control problem, which is not true of other pseudospectral methods. This result indicates that the method can take advantage of the properties of both direct and indirect formulations, and allows for the costates to be estimated directly from the Lagrange multipliers of the NLP. The method has been shown empirically to have very fast convergence (exponential) in the states, controls, and costates, for problems with analytic solutions. This convergence rate of the proposed method is significantly faster than traditional finite difference methods, and has been demonstrated with many example problems. The initial costate estimate from the proposed method can be used to define an optimal feedback law for real time optimal control of nonlinear problems. The application and effectiveness of this approach has been demonstrated with the simulated trajectory optimization of a launch vehicle.},
archivePrefix = {arXiv},
arxivId = {arXiv:1011.1669v3},
author = {Benson, David},
booktitle = {MIT Libraries},
doi = {10.1073/pnas.0703993104},
eprint = {arXiv:1011.1669v3},
file = {:home/matt/Documents/Mendeley Desktop//Benson - 2005 - A gauss Pseudospectral Transcription for Optimal Control.pdf:pdf},
isbn = {9781604138795},
issn = {1098-6596},
keywords = {Aeuronautics and Astronautics},
pmid = {25246403},
school = {MIT},
title = {{A gauss Pseudospectral Transcription for Optimal Control}},
year = {2005}
}
@article{Programming1954,
author = {Bellman, Richard},
file = {:home/matt/Documents/Mendeley Desktop/pnas00731-0009.pdf:pdf},
pages = {231--235},
title = {{Dynamic programming and a new formalism in the calculus of variations}},
volume = {40},
year = {1954}
}
@article{Hargraves1987,
author = {Hargraves, C R and Hargraves, C R and Paris, S W and Paris, S W and Margraves, C R and Paris, S W},
file = {:home/matt/Documents/Mendeley Desktop//Margraves, Paris - 1987 - Direct Trajectory Optimization Using Nonlinear Programming and Collocation.pdf:pdf;:home/matt/Documents/Mendeley Desktop//Hargraves et al. - 1987 - Direct trajectory optimization using nonlinear programming and collocation.pdf:pdf},
journal = {AIAA J. Guidance},
number = {4},
pages = {338--342},
title = {{Direct Trajectory Optimization Using Nonlinear Programming and Collocation}},
volume = {10},
year = {1987}
}
@article{Wang2010,
abstract = {A widely recognized shortcoming of model predictive control (MPC) is that it can usually only be used in applications with slow dynamics, where the sample time is measured in seconds or minutes. A well-known technique for implementing fast MPC is to compute the entire control law offline, in which case the online controller can be implemented as a lookup table. This method works well for systems with small state and input dimensions (say, no more than five), few constraints, and short time horizons. In this paper, we describe a collection of methods for improving the speed of MPC, using online optimization. These custom methods, which exploit the particular structure of the MPC problem, can compute the control action on the order of 100 times faster than a method that uses a generic optimizer. As an example, our method computes the control actions for a problem with 12 states, 3 controls, and horizon of 30 time steps (which entails solving a quadratic program with 450 variables and 1284 constraints) in around 5 ms, allowing MPC to be carried out at 200 Hz.},
author = {Wang, Yang and Boyd, Stephen},
doi = {10.1109/TCST.2009.2017934},
file = {:home/matt/Documents/Mendeley Desktop/05153127.pdf:pdf},
isbn = {1063-6536},
issn = {10636536},
journal = {IEEE Transactions on Control Systems Technology},
keywords = {Model predictive control (MPC),Real-time convex optimization},
number = {2},
pages = {267--278},
pmid = {18494040},
title = {{Fast model predictive control using online optimization}},
volume = {18},
year = {2010}
}
@article{Grizzle2009,
abstract = {This paper introduces MABEL, a new platform for the study of bipedal locomotion in robots. One of the purposes of building the mechanism is to explore a novel powertrain design that incorporates compliance, with the objective of improving the power efficiency of the robot, both in steady state operation and in responding to disturbances. A second purpose is to inspire the development of new feedback control algorithms for running on level surfaces and walking on rough terrain. A third motivation for building the robot is science and technology outreach; indeed, it is already included in tours when K-through-12 students visit the College of Engineering at the University of Michigan. MABEL is currently walking at 1.1 m/s on a level surface, and a related mono-pod at Carnegie Mellon is hopping well, establishing that the testbed has the potential to realize its many objectives.},
author = {Grizzle, J. W. and Hurst, Jonathan and Morris, Benjamin and Park, Hae Won and Sreenath, Koushil},
doi = {10.1109/ACC.2009.5160550},
file = {:home/matt/Documents/Mendeley Desktop/Grizzle et al. - 2009 - MABEL, a new robotic bipedal walker and runner.pdf:pdf},
isbn = {9781424445240},
issn = {07431619},
journal = {Proceedings of the American Control Conference},
pages = {2030--2036},
title = {{MABEL, a new robotic bipedal walker and runner}},
year = {2009}
}
@article{Bertsekas2015,
author = {Bertsekas, Dimitri P},
file = {:home/matt/Documents/Mendeley Desktop/Det{\_}Opt{\_}Control{\_}Lewis{\_}Vol.pdf:pdf},
journal = {MIT LIDS Report},
number = {May},
pages = {1--15},
title = {{Value and Policy Iteration in Optimal Control and Adaptive Dynamic Programming}},
year = {2015}
}
@incollection{Kuindersman2016,
author = {Pierre-Brice and Tedrake, Russ and {Scott Kuindersma} and Wieber, Pierre-Brice},
booktitle = {Handbook of Robotics},
edition = {2},
file = {:home/matt/Documents/Mendeley Desktop/Pierre-Brice, Tedrake, Scott Kuindersma - Unknown - Modeling and Control of Legged Robots.pdf:pdf},
pages = {1--53},
publisher = {Springer},
title = {{Modeling and Control of Legged Robots}},
url = {http://groups.csail.mit.edu/robotics-center/public{\_}papers/Wieber15.pdf},
year = {2016}
}
@article{Kyriakopoulos1988,
abstract = {A simple method of trajectory generation of robot manipulators is presented. It is based on an optimal control problem formulation. The jerk, the third derivative of position, of the desired trajectory, adversely affect the efficiency of the control algorithms and therefore should be minimized. assuming joint position, velocity and acceleration to be constrained, a cost criterion containing jerk is considered. Initially, the simple environment without obstacles and constrained by the physical limitations of the joint angles only is examined. For practical reasons, the free execution time has been used to handle the velocity and acceleration constraints instead of the complete bounded state variable formulation. The problem of minimizing the jerk along an arbitrary Cartesian trajectory is formulated and given analytical solution, making this method useful for real-world environments containing obstacles},
author = {Kyriakopoulos, Konstantinos J and Saridis, George N},
doi = {10.1109/ROBOT.1988.12075},
file = {:home/matt/Documents/Mendeley Desktop/00012075.pdf:pdf},
isbn = {0-8186-0852-8},
journal = {Robotics and Automation, 1988. Proceedings., 1988 IEEE International Conference on},
pages = {364--369},
title = {{Minimum jerk path generation}},
year = {1988}
}
@inproceedings{Moore2014,
author = {Moore, Joseph and Tedrake, Russ},
booktitle = {American Controls Conference},
file = {:home/matt/Documents/Mendeley Desktop/Moore, Tedrake - 2014 - Adaptive Control Design for Underactuated Systems using SUms-of-Squares Optimization.pdf:pdf},
title = {{Adaptive Control Design for Underactuated Systems using SUms-of-Squares Optimization}},
year = {2014}
}
@article{Akbari2014,
author = {Akbari, Kaveh and Jessy, Hamed},
file = {:home/matt/Documents/Mendeley Desktop/Akbari, Jessy - 2014 - Iterative Robust Stabilization Algorithm for Periodic Orbits of Hybrid Dynamical Systems Application to Bipedal.pdf:pdf},
journal = {International Federation of Automatic Control},
keywords = {hybrid periodic orbits,robust orbital stability,underactuated bipedal running},
title = {{Iterative Robust Stabilization Algorithm for Periodic Orbits of Hybrid Dynamical Systems : Application to Bipedal Running}},
year = {2014}
}
@article{Hull1997,
author = {Hull, David G.},
doi = {10.1007/s13398-014-0173-7.2},
file = {:home/matt/Documents/Mendeley Desktop/Hull - 1997 - n of Optimal Control Problems into Parameter Optimization Problems.pdf:pdf},
isbn = {9780874216561},
journal = {1Journal of Guidance, Control, and Dynamics},
number = {1},
title = {{n of Optimal Control Problems into Parameter Optimization Problems}},
volume = {20},
year = {1997}
}
@misc{MatlabSymbolicToolbox2014,
author = {Mathworks},
publisher = {Mathworks},
title = {{Matlab Symbolic Toolbox}},
url = {http://www.mathworks.com/products/symbolic},
year = {2014}
}
@book{Wachter2006,
abstract = {We present a primal-dual interior-point algorithm with a filter line-search method for nonlinear programming. Local and global convergence properties of this method were analyzed in previous work. Here we provide a comprehensive description of the algorithm, including the feasibility restoration phase for the filter method, second-order corrections, and inertia correction of the KKT matrix. Heuristics are also considered that allow faster performance. This method has been implemented in the IPOPT code, which we demonstrate in a detailed numerical study based on 954 problems from the CUTEr test set. An evaluation is made of several line-search options, and a comparison is provided with two state-of-the-art interior-point codes for nonlinear programming.},
author = {W{\"{a}}chter, Andreas and Biegler, Lorenz T.},
booktitle = {Mathematical Programming},
doi = {10.1007/s10107-004-0559-y},
file = {:home/matt/Documents/Mendeley Desktop//W{\"{a}}chter, Biegler - 2006 - On the implementation of primal-dual interior point filter line search algorithm for large-scale nonlinear(2).pdf:pdf},
isbn = {1010700405},
issn = {00255610},
keywords = {Barrier method,Filter method,IPOPT,Interior-point method,Line search,Nonconvex constrained optimization,Nonlinear programming,barrier method,filter method,interior-point method,line search,nonconvex constrained optimization,nonlinear programming},
mendeley-tags = {IPOPT},
number = {1},
pages = {25--57},
title = {{On the implementation of primal-dual interior point filter line search algorithm for large-scale nonlinear programming}},
url = {http://dx.doi.org/10.1007/s10107-004-0559-y},
volume = {106},
year = {2006}
}
@article{Benson2006,
abstract = {A pseudospectral method, called the Gauss pseudospectral method, for solving nonlinear op- timal control problems is presented. In the method presented here, orthogonal collocation of the dynamics is performed at the Legendre-Gauss points. This form of orthogonal collocation leads a nonlinear programming problem (NLP) whose Karush-Kuhn-Tucker (KKT) multipliers can be mapped to the costates of the continuous-time optimal control problem. In particular the Legendre-Gauss collocation leads to a costate mapping at the boundary points. The method is demonstrated on an example problem where it is shown that highly accurate costates are ob- tained. The results presented in this paper show that the Gauss pseudospectral method is a viable apprach for direct trajectory optimization and costate estimation.},
author = {Benson, David a. and Huntington, Geoffrey T. and Thorvaldsen, Tom P. and Rao, Anil V.},
doi = {10.2514/1.20478},
file = {:home/matt/Documents/Mendeley Desktop//Benson et al. - 2006 - Direct Trajectory Optimization and Costate Estimation via an Orthogonal Collocation Method.pdf:pdf},
isbn = {1563478196},
issn = {0731-5090},
journal = {Journal of Guidance, Control, and Dynamics},
number = {6},
pages = {1435--1440},
pmid = {15739559},
title = {{Direct Trajectory Optimization and Costate Estimation via an Orthogonal Collocation Method}},
volume = {29},
year = {2006}
}
@techreport{Lambers2009,
author = {Lambers, Jim},
file = {:home/matt/Documents/Mendeley Desktop/lecture29.pdf:pdf},
institution = {University of Southern Mississippi},
isbn = {5000000013},
title = {{Romberg Integration}},
url = {http://www.math.usm.edu/lambers/mat460/fall09/lecture29.pdf},
year = {2009}
}
@article{Park2012,
author = {Park, Hae Won and Sreenath, Koushil and Ramezani, Alireza and Grizzle, J. W.},
doi = {10.1109/ICRA.2012.6225056},
file = {:home/matt/Documents/Mendeley Desktop/Park et al. - 2012 - Switching control design for accommodating large step-down disturbances in bipedal robot walking.pdf:pdf},
isbn = {9781467314039},
issn = {10504729},
journal = {Proceedings - IEEE International Conference on Robotics and Automation},
pages = {45--50},
title = {{Switching control design for accommodating large step-down disturbances in bipedal robot walking}},
year = {2012}
}
@article{Klein2012,
author = {Klein, Georges and Berrut, Jean-Paul},
doi = {10.1007/s10543-011-0357-x},
file = {:home/matt/Documents/Mendeley Desktop/art{\%}3A10.1007{\%}2Fs10543-011-0357-x.pdf:pdf},
issn = {0006-3835},
journal = {BIT Numerical Mathematics},
keywords = {2000,41a05,41a20,65d05,65d32,barycentric form,mathematics subject classification,quadrature,rational interpolation},
number = {2},
pages = {407--424},
title = {{Linear barycentric rational quadrature}},
volume = {52},
year = {2012}
}
@article{Betts1992,
abstract = {The most effective numerical techniques for the solution of trajectory optimization and optimal control problems combine a nonlinear iteration procedure with some type of parametric approximation to the trajectory dynamics. Early methods attempted to parameterize the dynamics using a small number of variables because the iterative search procedures could not successfully solve larger problems. With the development of more robust nonlinear programming algorithms, it is now feasible and desirable to consider formulations of the trajectory optimization problem incorporating a large number of variables and constraints. The purpose of this paper is to address the manner in which a trajectory is parameterized and the design of the nonlinear programming algorithm to effectively deal with this formulation.},
author = {Betts, John T. and Huffman, William P.},
doi = {10.2514/3.20819},
file = {:home/matt/Documents/Mendeley Desktop/3{\%}2E20819.pdf:pdf},
isbn = {0731-5090},
issn = {0731-5090},
journal = {Journal of Guidance, Control, and Dynamics},
number = {1},
pages = {198--206},
title = {{Application of sparse nonlinear programming to trajectory optimization}},
volume = {15},
year = {1992}
}
@article{Kumar2014,
abstract = {We study the problem of designing dynamically feasible trajectories and controllers that drive a quadrotor to a desired state in state space. We focus on the development of a family of trajectories deﬁned as a sequence of segments, each with a controller parameterized by a goal state or region in state space. Each controller is developed from the dynamic model of the robot and then iteratively reﬁned through successive experimental trials in an automated fashion to account for errors in the dynamic model and noise in the actuators and sensors. We show that this approach permits the development of trajectories and controllers enabling such aggressive maneuvers as ﬂying through narrow, vertical gaps and perching on inverted surfaces with high precision and repeatability.},
author = {Mellinger, Daniel and Michael, Nathan and Kumar, Vijay},
doi = {10.1007/978-3-642-28572-1_25},
file = {:home/matt/Documents/Mendeley Desktop/The International Journal of Robotics Research-2012-Mellinger-664-74.pdf:pdf},
isbn = {9783642285714},
issn = {1610742X},
journal = {Springer Tracts in Advanced Robotics},
keywords = {control,quadrotors,trajectory generation},
pages = {361--373},
title = {{Trajectory generation and control for precise aggressive maneuvers with quadrotors}},
volume = {79},
year = {2014}
}
@article{Hehn2015,
abstract = {—This paper presents a trajectory generation algorithm that efficiently computes high-performance flight trajectories that are capable of moving a quadrocopter from a large class of ini-tial states to a given target point that will be reached at rest. The approach consists of planning separate trajectories in each of the three translational degrees of freedom, and ensuring feasibility by deriving decoupled constraints for each degree of freedom through approximations that preserve feasibility. The presented algorithm can compute a feasible trajectory within tens of microseconds on a laptop computer; remaining computation time can be used to itera-tively improve the trajectory. By replanning the trajectory at a high rate, the trajectory generator can be used as an implicit feedback law similar to model predictive control. The solutions generated by the algorithm are analyzed by comparing them with time-optimal motions, and experimental results validate the approach.},
author = {Hehn, Markus and {D 'andrea}, Raffaello},
doi = {10.1109/TRO.2015.2432611},
file = {:home/matt/Documents/Mendeley Desktop/07128399.pdf:pdf},
issn = {1552-3098},
journal = {Ieee Transactions on Robotics},
keywords = {Index Terms—Motion control,optimal control,quadrocopter,trajectory generation,unmanned aerial vehicles},
number = {4},
pages = {877--892},
title = {{Real-Time Trajectory Generation for Quadrocopters}},
volume = {31},
year = {2015}
}
@article{Golub1968,
abstract = {Several algorithms are given and compared for computing Gauss quadrature rules. It is shown that given the three term recurrence relation for the orthogonal polynomials generated by the weight function, the quadrature rule may be generated by computing the eigenvalues and first component of the orthornor- malized eigenvectors of a symmetric tridiagonal matrix. An algorithm is also pre- sented for computing the three term recurrence relation from the moments of the weight function.},
author = {Golub, Gene H. and Welsch, John H.},
doi = {10.1090/S0025-5718-69-99647-1},
file = {:home/matt/Documents/Mendeley Desktop//Golub, Welsch - 1968 - Calculation of Gauss quadrature rules.pdf:pdf},
isbn = {00255718},
issn = {0025-5718},
journal = {Mathematics of Computation},
number = {106},
pages = {221--221},
title = {{Calculation of Gauss quadrature rules}},
volume = {23},
year = {1968}
}
@article{Saramago2000,
author = {Saramago, {\^{A}} F P and Ste, Valder},
file = {:home/matt/Documents/Mendeley Desktop/Saramago, Ste - 2000 - Optimal trajectory planning of robot manipulators in the presence of moving obstacles.pdf:pdf},
title = {{Optimal trajectory planning of robot manipulators in the presence of moving obstacles}},
volume = {35},
year = {2000}
}
@article{Vandenberghet1996,
abstract = {In semidefinite programming, one minimizes a linear function subject to the constraint that an affine combination of synunetric matrices is positive semidefinite. Such a constraint is nonlinear and nonsmooth, but convex, so semidefinite programs are convex optimization problems. Semidefinite programming unifies several standard problems (e.g., linear and quadratic programming) and finds many applications in engineering and combinatorial optimization. Although semidefinite programs are much more general than linear programs, they are not much harder to solve. Most interior-point methods for linear programming have been generalized to semidefinite programs. As in linear programming, these methods have polynomial worst-case complexity and perform very well in practice. This paper gives a survey of the theory and applications of semidefinite programs and an introduction to primaldual interior-point methods for their solution.},
author = {Vandenberghet, Lieven and Boyd, Stephen},
file = {:home/matt/Documents/Mendeley Desktop//Vandenberghet, Boyd - 1996 - Semidefinite programming.pdf:pdf},
journal = {SIAM Review},
keywords = {15a18,49m45,65k05,90c25,90c27,90c90,93b51,ams subject classifications,combinatorial optimization,convex optimization,eigenvalue optimization,interior-point methods,semidefinite programming,system and control theory},
number = {1},
pages = {49--95},
title = {{Semidefinite programming*}},
volume = {38},
year = {1996}
}
@article{Yang2009,
annote = {five link biped},
author = {Yang, T. and Westervelt, E. R. and Serrani, a. and Schmiedeler, J. P.},
doi = {10.1007/s10514-009-9126-y},
file = {:home/matt/Documents/Mendeley Desktop/Yang et al. - 2009 - A framework for the control of stable aperiodic walking in underactuated planar bipeds.pdf:pdf},
issn = {0929-5593},
journal = {Autonomous Robots},
keywords = {bipedal robotics,nonlinear control theory,stable aperiodic walking},
month = {jul},
number = {3},
pages = {277--290},
title = {{A framework for the control of stable aperiodic walking in underactuated planar bipeds}},
url = {http://link.springer.com/10.1007/s10514-009-9126-y},
volume = {27},
year = {2009}
}
@article{Ross2003,
abstract = {We consider nonlinear optimal control problems with mixed statecontrol constraints. A discretization of the Bolza problem by a Legendre pseudospectral method is considered. It is shown that the operations of discretization and dualization are not commutative. A set of Closure Conditions are introduced to commute these operations. An immediate consequence of this is a Covector Mapping Theorem (CMT) that provides an order-preserving transformation of the Lagrange multipliers associated with the discretized problem to the discrete covectors associated with the optimal control problem. A natural consequence of the CMT is that for pure state-constrained problems, the dual variables can be easily related to the D-form of the Lagrangian of the Hamiltonian. We demonstrate the practical advantage of our results by numerically solving a state-constrained optimal control problem without deriving the necessary conditions. The costates obtained by an application of our CMT show excellent agreement with the exact analytical solution.},
author = {Ross, I Michael and Fahroo, Fariba},
doi = {10.1007/978-3-540-45056-6_21},
file = {:home/matt/Documents/Mendeley Desktop/Ross, Fahroo - 2003 - Legendre pseudospectral approximations of optimal control problems.pdf:pdf},
isbn = {9783540404743},
journal = {New Trends in Nonlinear Dynamics and Control and their Applications},
number = {January},
pages = {327--342},
title = {{Legendre pseudospectral approximations of optimal control problems}},
url = {http://www.springerlink.com/index/mmcgta9q1xmamvwq.pdf},
volume = {295},
year = {2003}
}
@book{Driscoll2014,
annote = {Chebfun},
author = {Driscoll, Tobin A and Hale, Nicholas and Trefethen, Lloyd N.},
edition = {1},
publisher = {Pafnuty Publications, Oxford},
title = {{Chebfun Guide}},
year = {2014}
}
@article{Byl2009,
abstract = {Legged robots that operate in the real world are inherently subject to stochasticity in their dynamics and uncertainty about the terrain. Owing to limited energy budgets and limited control authority, these "disturbances" cannot always be canceled out with high-gain feedback. Minimally actuated walking machines subject to stochastic disturbances no longer satisfy strict conditions for limit-cycle stability, however, they can still demonstrate impressively long-living periods of continuous walking. Here, we employ tools from stochastic processes to examine the "stochastic stability" of idealized rimless-wheel and compass-gait walking on randomly generated uneven terrain. Furthermore, we employ tools from numerical stochastic optimal control to design a controller for an actuated compass gait model which maximizes a measure of stochastic stability-the mean first-passage time-and compare its performance with a deterministic counterpart. Our results demonstrate that walking is well characterized as a metastable process, and that the stochastic dynamics of walking should be accounted for during control design in order to improve the stability of our machines.},
author = {Byl, K. and Tedrake, R.},
doi = {10.1177/0278364909340446},
file = {:home/matt/Documents/Mendeley Desktop/Byl, Tedrake - 2009 - Metastable Walking Machines.pdf:pdf},
isbn = {0278-3649},
issn = {0278-3649},
journal = {The International Journal of Robotics Research},
keywords = {compass gait,ity metrics,legged locomotion,mean first-passage time 1,metastability,namic walking,passive dy-,rimless wheel,rough terrain,stabil-},
number = {8},
pages = {1040--1064},
title = {{Metastable Walking Machines}},
volume = {28},
year = {2009}
}
@misc{SOS_Betts_2013,
author = {Betts, John T.},
publisher = {Applied Mathematical Analysis, LLC},
title = {{SOS: Sparse Optimization Suite - User's Guide}},
url = {https://www.astos.de/products/sos},
year = {2013}
}
@article{Chevallereau2003,
abstract = {Describes the design, construction and control of an experimental bipedal robot platform for the study of walking.},
author = {Chevallereau, By Christine and Abba, Gabriel and Aoustin, Yannick and Plestan, Franck and Westervelt, E R and Canudas-de-wit, Carlos and Grizzle, J W},
doi = {10.1109/MCS.2003.1234651},
file = {:home/matt/Documents/Mendeley Desktop/Chevallereau et al. - 2003 - RABBIT：A Testbed for Advanced Control Theory.pdf:pdf},
issn = {02721708},
journal = {IEEE Control Systems Mag.},
keywords = {RABBIT,advanced control theory testbed,bipedal robot platform,legged locomotion,walking},
pages = {57--79},
title = {{RABBIT：A Testbed for Advanced Control Theory}},
volume = {23},
year = {2003}
}
@inproceedings{Srinivasan2010,
author = {Srinivasan, Manoj},
booktitle = {Dynamic Walking Conference},
file = {:home/matt/Documents/Mendeley Desktop/Srinivasan - 2010 - Trajectory Optimization , a brief introduction.pdf:pdf},
publisher = {Ohio State University},
title = {{Trajectory Optimization , a brief introduction}},
url = {http://www.movement.osu.edu/software/DW2010/OptimTrajim{\_}ManojSrinivasan2010.pdf},
year = {2010}
}
@book{Betts2010,
address = {Philadelphia, PA},
author = {Betts, John T.},
editor = {Mathematics, Society for Industrial and Applied},
publisher = {Siam},
title = {{Practical Methods for Optimal Control and Estimation Using Nonlinear Programming}},
year = {2010}
}
@article{Patterson2013,
author = {Patterson, Michael A and Rao, Anil V},
doi = {10.1145/0000000.0000000},
file = {:home/matt/Documents/Mendeley Desktop//Patterson, Rao - 2013 - GPOPS − II A MATLAB Software for Solving Multiple-Phase Optimal Control Problems Using hp – Adaptive Gaussi.pdf:pdf},
number = {3},
pages = {1--41},
title = {{GPOPS − II : A MATLAB Software for Solving Multiple-Phase Optimal Control Problems Using hp – Adaptive Gaussian Quadrature Collocation Methods and Spa and rse Nonlinear Programming}},
volume = {39},
year = {2013}
}
@article{Gill2005a,
author = {Gill, Philip E and Murray, Walter and Saunders, Michael A and Gilit, E and Saunderst, Michael A},
file = {:home/matt/Documents/Mendeley Desktop/20453604.pdf:pdf},
journal = {SIAM Review},
number = {1},
pages = {99--131},
title = {{SNOPT : An SQP Algorithm for Large-Scale Constrained Optimization *}},
volume = {47},
year = {2005}
}
@techreport{Tedrake2009,
author = {Tedrake, Russ},
booktitle = {Course Notes for MIT 6.832},
file = {:home/matt/Documents/Mendeley Desktop/Tedrake{\_}notes.pdf:pdf},
title = {{Underactuated Robotics: Learning, Planning, and Control for Efficient and Agile Machines}},
url = {https://homes.cs.washington.edu/{~}todorov/courses/amath579/Tedrake{\_}notes.pdf},
year = {2009}
}
@article{Chettibi2004a,
abstract = {We discuss the problem of minimum cost trajectory planning for robotic manipulators. It consists of linking two points in the operational space while minimizing a cost function, taking into account dynamic equations of motion as well as bounds on joint positions, velocities, jerks and torques. This generic optimal control problem is transformed, via a clamped cubic spline model of joint temporal evolutions, into a non-linear constrained optimization problem which is treated then by the Sequential Quadratic Programming (SQP) method. Applications involving grasping mobile object or obstacle avoidance are shown to illustrate the efficiency of the proposed planner. ?? 2004 Elsevier SAS. All rights reserved.},
author = {Chettibi, T. and Lehtihet, H. E. and Haddad, M. and Hanchi, S.},
doi = {10.1016/j.euromechsol.2004.02.006},
file = {:home/matt/Documents/Mendeley Desktop/Chettibi et al. - 2004 - Minimum cost trajectory planning for industrial robots.pdf:pdf},
issn = {09977538},
journal = {European Journal of Mechanics, A/Solids},
keywords = {Grasping mobile objects,Motion planning,Non-linear optimization,Obstacles avoidance,Robotic manipulators},
number = {4},
pages = {703--715},
title = {{Minimum cost trajectory planning for industrial robots}},
volume = {23},
year = {2004}
}
@article{Pham2013,
abstract = {Finding the Time-Optimal Parameterization of a given Path (TOPP) subject to kinodynamic constraints is an essential component in many robotic theories and applications. The objective of this article is to provide a general, fast and robust implementation of this component. For this, we give a complete solution to the issue of dynamic singularities, which are the main cause of failure in existing implementations. We then present an open-source implementation of the algorithm in C++/Python and demonstrate its robustness and speed in various robotics settings.},
archivePrefix = {arXiv},
arxivId = {1312.6533},
author = {Pham, Quang-Cuong},
doi = {10.1109/TRO.2014.2351113},
eprint = {1312.6533},
file = {:home/matt/Documents/Mendeley Desktop/1312.6533v2.pdf:pdf},
number = {3},
title = {{A General, Fast, and Robust Implementation of the Time-Optimal Path Parameterization Algorithm}},
url = {http://arxiv.org/abs/1312.6533 http://dx.doi.org/10.1109/TRO.2014.2351113},
year = {2013}
}
@misc{Kelly2015b,
author = {Kelly, Matthew P.},
title = {{OptimTraj - Trajectory Optimization Library for Matlab}},
url = {https://github.com/MatthewPeterKelly/OptimTraj},
year = {2015}
}
@book{Trefethen2012,
author = {Trefethen, Lloyd N},
file = {:home/matt/Documents/Mendeley Desktop/Trefethen - 2012 - and Approximation Practice.pdf:pdf},
publisher = {SIAM},
title = {{Approximation Theory and Approximation Practice}},
year = {2013}
}
@article{Mueller2015,
author = {Mueller, Mark W. and Hehn, Markus and D'Andrea, Raffaello},
doi = {10.1016/B978-190399666-9/50013-0},
file = {:home/matt/Documents/Mendeley Desktop/mueTRO15.pdf:pdf},
isbn = {9781903996669},
title = {{A computationally efficient motion primitive for quadrocopter trajectory generation}},
year = {2015}
}
@article{Casti1980,
abstract = {The classicalinear-quadratic-Gaussian (LQG) problem from optimal control theory is surveyed with respecto recent developments inthe following areas: singular control, state/control constraints, the LQG inverse problem, and algebraic/geometric structure. Itis shown that a number of important results obtained during the past few years have substantially illuminated the global structure of the class of all LQG problems, as well as materially enhancing the capability of dealing with important practical aspects of LQG problem solutions. A number of outstanding research problems are also introduce},
author = {Casti, J.},
file = {:home/matt/Documents/Mendeley Desktop/2029806.pdf:pdf},
isbn = {0036144595294},
journal = {1SIAM Review},
number = {4},
title = {{SIAM Review,}},
volume = {22},
year = {980}
}
@misc{Sussmann1997,
author = {Sussmann, Hector J. and Willems, Jan C.},
file = {:home/matt/Documents/Mendeley Desktop/Sussmann, Willems - 1997 - 300{\_}Years{\_}of{\_}Optimal{\_}Control.pdf.pdf:pdf},
keywords = {brachistochrone},
mendeley-tags = {brachistochrone},
title = {{300{\_}Years{\_}of{\_}Optimal{\_}Control.pdf}},
year = {1997}
}
@article{Baltensperger1999,
abstract = {We discuss here the errors incurred using the standard formula for calculating the pseudospectral differentiation matrices for C̆ebys̆ev-Gauss-Lobatto points. We propose explanations for these errors and suggest more precise methods for calculating the ... },
author = {Baltensperger, R. and Berrut, J.-P.},
doi = {10.1016/S0898-1221(98)00240-5},
file = {:home/matt/Documents/Mendeley Desktop/Baltensperger, Berrut - 1999 - The errors in calculating the pseudospectral differentiation matrices for C̆ebys̆ev-Gauss-Lobatto point.pdf:pdf},
issn = {08981221},
journal = {Computers {\&} Mathematics with Applications},
number = {1},
pages = {41--48},
title = {{The errors in calculating the pseudospectral differentiation matrices for C̆ebys̆ev-Gauss-Lobatto points}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0898122198002405},
volume = {37},
year = {1999}
}
@article{Darby2011,
author = {Darby, Christopher L. and Garg, Divya and Rao, Anil V.},
doi = {10.2514/1.A32040},
file = {:home/matt/Documents/Mendeley Desktop/Darby, Garg, Rao - 2011 - Costate Estimation using Multiple-Interval Pseudospectral Methods.pdf:pdf},
issn = {0022-4650},
journal = {Journal of Spacecraft and Rockets},
month = {sep},
number = {5},
pages = {856--866},
title = {{Costate Estimation using Multiple-Interval Pseudospectral Methods}},
url = {http://arc.aiaa.org/doi/abs/10.2514/1.A32040},
volume = {48},
year = {2011}
}
@article{Srinivasan2006,
abstract = {Although people's legs are capable of a broad range of muscle-use and gait patterns, they generally prefer just two. They walk, swinging their body over a relatively straight leg with each step, or run, bouncing up off a bent leg between aerial phases. Walking feels easiest when going slowly, and running feels easiest when going faster. More unusual gaits seem more tiring. Perhaps this is because walking and running use the least energy. Addressing this classic conjecture with experiments requires comparing walking and running with many other strange and unpractised gaits. As an alternative, a basic understanding of gait choice might be obtained by calculating energy cost by using mechanics-based models. Here we use a minimal model that can describe walking and running as well as an infinite variety of other gaits. We use computer optimization to find which gaits are indeed energetically optimal for this model. At low speeds the optimization discovers the classic inverted-pendulum walk, at high speeds it discovers a bouncing run, even without springs, and at intermediate speeds it finds a new pendular-running gait that includes walking and running as extreme cases.},
author = {Srinivasan, Manoj and Ruina, Andy},
doi = {10.1038/nature04113},
file = {:home/matt/Documents/Mendeley Desktop/Srinivasan, Ruina - 2006 - Computer optimization of a minimal biped model discovers walking and running.pdf:pdf},
issn = {1476-4687},
journal = {Nature},
keywords = {Computer Simulation,Energy Metabolism,Gait,Gait: physiology,Humans,Models, Biological,Running,Running: physiology,Walking,Walking: physiology},
month = {jan},
number = {7072},
pages = {72--5},
pmid = {16155564},
title = {{Computer optimization of a minimal biped model discovers walking and running.}},
url = {http://www.ncbi.nlm.nih.gov/pubmed/16155564},
volume = {439},
year = {2006}
}
@article{Ames2014,
author = {Ames, Aaron D. and Galloway, Kevin and Sreenath, Koushil and Grizzle, Jessy W.},
doi = {10.1109/TAC.2014.2299335},
file = {:home/matt/Documents/Mendeley Desktop/Ames et al. - 2014 - Rapidly Exponentially Stabilizing Control Lyapunov Functions and Hybrid Zero Dynamics.pdf:pdf},
issn = {0018-9286},
journal = {IEEE Transactions on Automatic Control},
month = {apr},
number = {4},
pages = {876--891},
title = {{Rapidly Exponentially Stabilizing Control Lyapunov Functions and Hybrid Zero Dynamics}},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6709752},
volume = {59},
year = {2014}
}
@article{Hansen2001,
abstract = {This paper puts forward two useful methods for self-adaptation of the mutation distribution - the concepts of derandomization and cumulation. Principle shortcomings of the concept of mutative strategy parameter control and two levels of derandomization are reviewed. Basic demands on the self-adaptation of arbitrary (normal) mutation distributions are developed. Applying arbitrary, normal mutation distributions is equivalent to applying a general, linear problem encoding. The underlying objective of mutative strategy parameter control is roughly to favor previously selected mutation steps in the future. If this objective is pursued rigorously, a completely derandomized self-adaptation scheme results, which adapts arbitrary normal mutation distributions. This scheme, called covariance matrix adaptation (CMA), meets the previously stated demands. It can still be considerably improved by cumulation - utilizing an evolution path rather than single search steps. Simulations on various test functions reveal local and global search properties of the evolution strategy with and without covariance matrix adaptation. Their performances are comparable only on perfectly scaled functions. On badly scaled, non-separable functions usually a speed up factor of several orders of magnitude is observed. On moderately mis-scaled functions a speed up factor of three to ten can be expected.},
annote = {CMAES},
author = {Hansen, N and Ostermeier, a},
doi = {10.1162/106365601750190398},
file = {:home/matt/Documents/Mendeley Desktop/Hansen, Ostermeier - 2001 - Completely derandomized self-adaptation in evolution strategies.pdf:pdf},
issn = {1063-6560},
journal = {Evolutionary computation},
keywords = {Algorithms,Biological Evolution,Computer Simulation,Models, Genetic,Models, Statistical,Mutation,Stochastic Processes},
month = {jan},
number = {2},
pages = {159--95},
pmid = {11382355},
title = {{Completely derandomized self-adaptation in evolution strategies.}},
url = {http://www.ncbi.nlm.nih.gov/pubmed/11382355},
volume = {9},
year = {2001}
}
@article{Dai2014,
abstract = {To plan dynamic, whole-body motions for robots, one conventionally faces the choice between a complex, full- body dynamic model containing every link and actuator of the robot, or a highly simplified model of the robot as a point mass. In this paper we explore a powerful middle ground between these extremes. We exploit the fact that while the full dynamics of humanoid robots are complicated, their centroidal dynamics (the evolution of the angular momentum and the center of mass (COM) position) are much simpler. By treating the dynamics of the robot in centroidal form and directly optimizing the joint trajectories for the actuated degrees of freedom, we arrive at a method that enjoys simpler dynamics, while still having the expressiveness required to handle kinematic constraints such as collision avoidance or reaching to a target. We further require that the robot's COM and angular momentum as computed from the joint trajectories match those given by the centroidal dynamics. This ensures that the dynamics considered by our optimization are equivalent to the full dynamics of the robot, provided that the robot's actuators can supply sufficient torque. We demonstrate that this algorithm is capable of generating highly-dynamic motion plans with examples of a humanoid robot negotiating obstacle course elements and gait optimization for a quadrupedal robot. Additionally, we show that we can plan without pre-specifying the contact sequence by exploiting the complementarity conditions between contact forces and contact distance.},
author = {Dai, Hongkai and Valenzuela, Andres and Tedrake, Russ},
doi = {10.1109/HUMANOIDS.2014.7041375},
file = {:home/matt/Documents/Mendeley Desktop/Dai, Valenzuela, Tedrake - 2014 - Whole-body Motion Planning with Simple Dynamics and Full Kinematics.pdf:pdf},
isbn = {9781479971732},
journal = {International Conference on Humanoid Robots},
number = {JANUARY 2014},
pages = {295--302},
title = {{Whole-body Motion Planning with Simple Dynamics and Full Kinematics}},
year = {2014}
}
@article{Garg2009,
abstract = {An overview is presented of three different pseudospectral methods based on collocation at Legendre-Gauss (LG), Legendre-Gauss-Radau (LGR), and Legendre-Gauss-Lobatto (LGL) points. For each of the schemes presented here, (1) the state at the final time can be expressed in terms of a quadrature rule associated with the collocatio n points, (2) the state at the initial time is approximated by interpolation, and (3) the control and the state are approximated at the collocation points. The LG-based and LGR-based schemes presented here employ polynomials to approximate the state that are the same degree as the number of collocation points. In the corresponding LGL scheme, the state approximation is a polynomial that is one degree lower than the number of collocation points. Each of these scheme can be expressed in either a differential or an integral formulation. The LG a nd LGR differentiation and inte- gration matrices are invertible, and the differential and i ntegral versions are equivalent. The LGL differentiation matrix is singular and the equivalence between the differential and in- tegral version is lost. For each scheme, the transformation between the KKT multipliers of the discrete nonlinear programming problem and costates of the continuous optimal control problem is developed. The LGL collocation is the only scheme for which the differentiation matrices for the state and the costate dynamics are the same. Two examples are used to assess the accuracy and features of each collocation scheme.},
author = {Garg, D and Patterson, Ma and Hager, Ww},
file = {:home/matt/Documents/Mendeley Desktop//Garg, Patterson, Hager - 2009 - An Overview of Three Pseudospectral Methods for the Numerical Solution of Optimal Control Problems.pdf:pdf},
journal = {Advances in the {\ldots}},
pages = {1--17},
title = {{An Overview of Three Pseudospectral Methods for the Numerical Solution of Optimal Control Problems}},
url = {http://vdol.mae.ufl.edu/ConferencePublications/unifiedFrameworkAAS.pdf},
year = {2009}
}
@article{Posa2015,
author = {Posa, Michael and Kuindersma, Scott and Tedrake, Russ},
file = {:home/matt/Documents/Mendeley Desktop/Posa15.pdf:pdf},
number = {724454},
title = {{Optimization and stabilization of trajectories for constrained dynamical systems}},
year = {2016}
}
@inproceedings{Long2006,
abstract = {A trajectory generation algorithm using direct collocation with nonlinear programming is successfully demonstrated in simulation. Direct collocation, which approximates the states and controls with piecewise polynomials, has been widely used in space and manned aircraft applications, but has only seen limited use in UAV applications. The algorithm is successfully applied to the generation of a UAV trajectory that provides maximum viewing time for a camera mounted on the UAV. The target can be stationary or moving. Multiple UAVs are considered. In this case, the objective is to provide maximum sensor coverage time using a combination of the UAVs. No specific initial guesses are required to ensure the algorithm is successful.},
author = {Geiger, Brian R and Horn, Joseph F and Delullo, Anthony M and Long, Lyle N},
booktitle = {AIAA J. Guidance},
file = {:home/matt/Documents/Mendeley Desktop/aiaa2006{\_}6199.pdf:pdf},
pages = {1--13},
title = {{Optimal Path Planning of UAVs Using Direct Collocation with Nonlinear Programming}},
year = {2006}
}
@article{Ansari2014,
author = {Ansari, Alex and Murphey, Todd},
file = {:home/matt/Documents/Mendeley Desktop//Ansari, Murphey - 2014 - Sequential Action Control Closed-Form Optimal Control for Nonlinear Systems.pdf:pdf},
journal = {IEEE Transactions on Robotics},
title = {{Sequential Action Control : Closed-Form Optimal Control for Nonlinear Systems}},
year = {2014}
}
@article{Majumdar2013,
author = {Majumdar, Anirudha and Ahmadi, Amir Ali and Tedrake, Russ},
doi = {10.1109/ICRA.2013.6631149},
file = {:home/matt/Documents/Mendeley Desktop/Majumdar, Ahmadi, Tedrake - 2013 - Control design along trajectories with sums of squares programming.pdf:pdf},
isbn = {978-1-4673-5643-5},
journal = {2013 IEEE International Conference on Robotics and Automation},
month = {may},
pages = {4054--4061},
publisher = {Ieee},
title = {{Control design along trajectories with sums of squares programming}},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6631149},
year = {2013}
}
@article{Bellman1956,
author = {Bellman, R},
file = {:home/matt/Documents/Mendeley Desktop/pnas00713-0067.pdf:pdf},
issn = {0027-8424},
journal = {Proceedings of the National Academy of Sciences of the United States of America},
number = {10},
pages = {767--769},
pmid = {16589948},
title = {{Dynamic Programming and Lagrange Multipliers.}},
volume = {42},
year = {1956}
}
@article{Murray1984,
author = {Murray, D. M. and Yakowitz, S. J.},
doi = {10.1007/BF00934463},
file = {:home/matt/Documents/Mendeley Desktop/murray{\_}yakowitz1984.pdf:pdf},
issn = {00223239},
journal = {Journal of Optimization Theory and Applications},
keywords = {Nonlinear programming,nonlinear dynamics,optimal control,optimal control algorithms,quadratic convergence},
number = {3},
pages = {395--414},
title = {{Differential dynamic programming and Newton's method for discrete optimal control problems}},
volume = {43},
year = {1984}
}
@article{Bhounsule2014,
author = {Bhounsule, P. a. and Cortell, J. and Grewal, a. and Hendriksen, B. and Karssen, J. G. D. and Paul, C. and Ruina, a.},
doi = {10.1177/0278364914527485},
file = {:home/matt/Documents/Mendeley Desktop/Bhounsule et al. - 2014 - Low-bandwidth reflex-based control for lower power walking 65 km on a single battery charge.pdf:pdf},
isbn = {0278364914527},
issn = {0278-3649},
journal = {The International Journal of Robotics Research},
keywords = {control design,efficiency,energy,legged robot,locomotion,stability},
month = {jun},
number = {10},
pages = {1305--1321},
title = {{Low-bandwidth reflex-based control for lower power walking: 65 km on a single battery charge}},
url = {http://ijr.sagepub.com/cgi/doi/10.1177/0278364914527485},
volume = {33},
year = {2014}
}
@book{Boor1978,
author = {de Boor, Carl and de Boor, Carl},
editor = {Sciences, Applied Mathematical},
publisher = {Springer},
title = {{A Practical Guide to Splines}},
year = {1978}
}
@article{Programming2006,
author = {Programming, Large-scale Nonlinear and Gill, Philip E and Murray, Walter and Saunders, Michael A},
file = {:home/matt/Documents/Mendeley Desktop/Programming et al. - 2006 - User ' s Guide for SNOPT Version 7 Software for.pdf:pdf},
keywords = {c software,fortran software,large-scale nonlinear programming,limited-storage quasi-newton updates,nonlinear constraints,optimization,sqp methods},
pages = {1--116},
title = {{User ' s Guide for SNOPT Version 7 : Software for}},
year = {2006}
}
@article{Garcia1989,
abstract = {We refer to Model Predictive Control (MPC) as that family of controllers in which there is a direct use of an explicit and separately identifiable model. Control design methods based on the MPC concept have found wide acceptance in industrial applications and have been studied by academia. The reason for such popularity is the ability of MPC designs to yield high performance control systems capable of operating without expert intervention for long periods of time. In this paper the issues of importance that any control system should address are stated. MPC techniques are then reviewed in the light of these issues in order to point out their advantages in design and implementation. A number of design techniques emanating from MPC, namely Dynamic Matrix Control, Model Algorithmic Control, Inferential Control and Internal Model Control, are put in perspective with respect to each other and the relation to more traditional methods like Linear Quadratic Control is examined. The flexible constraint handling capabilities of MPC are shown to be a significant advantage in the context of the overall operating objectives of the process industries and the 1-, 2-, and ∞-norm formulations of the performance objective are discussed. The application of MPC to non-linear systems is examined and it is shown that its main attractions carry over. Finally, it is explained that though MPC is not inherently more or less robust than classical feedback, it can be adjusted more easily for robustness.},
author = {Garc{\'{i}}a, Carlos E. and Prett, David M. and Morari, Manfred},
doi = {10.1016/0005-1098(89)90002-2},
file = {:home/matt/Documents/Mendeley Desktop/1-s2.0-0005109889900022-main.pdf:pdf},
isbn = {0005-1098},
issn = {00051098},
journal = {Automatica},
keywords = {--computer control,a direct use of,al,an,as,constrained control,in which there is,mpc,predictive control,process control,quadratic programming,that family of controllers,tmd--we refer to model},
number = {3},
pages = {335--348},
title = {{Model predictive control: Theory and practice—A survey}},
volume = {25},
year = {1989}
}
@article{Posa2013a,
author = {Posa, Michael and Tedrake, Russ},
file = {:home/matt/Documents/Mendeley Desktop/Posa, Tedrake - 2013 - Direct Trajectory Optimization of Rigid Body Dynamical Systems Through Contact.pdf:pdf},
journal = {Algorithmic Foundations of Robotics X},
pages = {527--542},
title = {{Direct Trajectory Optimization of Rigid Body Dynamical Systems Through Contact}},
year = {2013}
}
@article{Mordatch2012,
author = {Mordatch, Igor and Todorov, Emanuel and Popovi{\'{c}}, Zoran},
doi = {10.1145/2185520.2335394},
file = {:home/matt/Documents/Mendeley Desktop/Mordatch, Todorov, Popovi{\'{c}} - 2012 - Discovery of complex behaviors through contact-invariant optimization.pdf:pdf},
issn = {07300301},
journal = {ACM Transactions on Graphics},
keywords = {control,physics-based animation},
month = {jul},
number = {4},
pages = {1--8},
title = {{Discovery of complex behaviors through contact-invariant optimization}},
url = {http://dl.acm.org/citation.cfm?doid=2185520.2335394},
volume = {31},
year = {2012}
}
@article{Rao2009,
author = {Rao, Av},
doi = {10.1515/jnum-2014-0003},
file = {:home/matt/Documents/Mendeley Desktop//Rao - 2009 - A survey of numerical methods for optimal control.pdf:pdf},
isbn = {978-0-87703-557-2},
issn = {1569-3953},
journal = {Advances in the Astronautical Sciences},
pages = {497--528},
title = {{A survey of numerical methods for optimal control}},
url = {http://vdol.mae.ufl.edu/ConferencePublications/trajectorySurveyAAS.pdf},
volume = {135},
year = {2009}
}
@article{Ngo2012,
abstract = {This paper considers the problem of optimizing the ratio {\$}\backslashmathrm{\{}Tr{\}}[V{\^{}}{\{}T{\}}AV]/\backslashmathrm{\{}Tr{\}}[V{\^{}}{\{}T{\}}BV]{\$} over all unitary matrices {\$}V{\$} with {\$}p{\$} columns, where {\$}A,B{\$} are two positive definite matrices. This problem is common in supervised learning techniques. However, because its numerical solution is typically expensive it is often replaced by the simpler optimization problem which consists of optimizing {\$}\backslashmathrm{\{}Tr{\}}[V{\^{}}{\{}T{\}}AV]{\$} under the constraint that {\$}V{\^{}}{\{}T{\}}BV=I{\$}, the identity matrix. The goal of this paper is to examine this trace ratio optimization problem in detail, to consider different algorithms for solving it, and to illustrate the use of these algorithms for dimensionality reduction.},
author = {Ngo, T. T. and Bellalij, M. and Saad, Y.},
doi = {10.1137/120864799},
file = {:home/matt/Documents/Mendeley Desktop//Ngo, Bellalij, Saad - 2012 - The Trace Ratio Optimization Problem.pdf:pdf},
issn = {0036-1445},
journal = {SIAM Review},
keywords = {1,10,1137,120864799,15a18,68t10,a number of techniques,ams subject classifications,classification,doi,face recognition,high-dimen-,in machine learning and,introduction,linear dimensionality reduction,trace optimization},
number = {3},
pages = {545--569},
title = {{The Trace Ratio Optimization Problem}},
volume = {54},
year = {2012}
}
@article{Hale2013,
abstract = {An efficient algorithm for the accurate computation of Gauss–Legendre and Gauss–Jacobi quadrature nodes and weights is presented. The algorithm is based on Newton's root-finding method with initial guesses and function evaluations computed via asymptotic formulae. The n-point quadrature rule is computed in O(n) operations to an accuracy of essentially double precision for any n ≥ 100.},
archivePrefix = {arXiv},
arxivId = {1410.5286},
author = {Hale, Nicholas and Townsend, Alex},
doi = {10.1137/120889873},
eprint = {1410.5286},
file = {:home/matt/Documents/Mendeley Desktop//Hale, Townsend - 2013 - Fast and Accurate Computation of Gauss--Legendre and Gauss--Jacobi Quadrature Nodes and Weights.pdf:pdf},
issn = {1064-8275},
journal = {SIAM Journal on Scientific Computing},
keywords = {General},
number = {2},
pages = {A652--A674},
title = {{Fast and Accurate Computation of Gauss--Legendre and Gauss--Jacobi Quadrature Nodes and Weights}},
url = {http://eprints.maths.ox.ac.uk/1629/$\backslash$nhttp://epubs.siam.org/doi/abs/10.1137/120889873},
volume = {35},
year = {2013}
}
@article{Richter2013,
abstract = {We explore the challenges of planning trajectories for quadrotors through cluttered indoor environments. We extend the existing work on polynomial trajec- tory generation by presenting a method of jointly optimizing polynomial path seg- ments in an unconstrained quadratic program that is numerically stable for high- order polynomials and large numbers of segments, and is easily formulated for ef- ficient sparse computation.We also present a technique for automatically selecting the amount of time allocated to each segment, and hence the quadrotor speeds along the path, as a function of a single parameter determining aggressiveness, subject to actuator constraints. The use of polynomial trajectories, coupled with the differen- tially flat representation of the quadrotor, eliminates the need for computationally intensive sampling and simulation in the high dimensional state space of the vehi- cle during motion planning. Our approach generates high-quality trajectories much faster than purely sampling-based optimal kinodynamic planning methods, but sac- rifices the guarantee of asymptotic convergence to the global optimum that those methods provide. We demonstrate the performance of our algorithm by efficiently generating trajectories through challenging indoor spaces and successfully travers- ing them at speeds up to 8 m/s. A demonstration of our algorithm and flight perfor- mance is available at: http://groups.csail.mit.edu/rrg/quad{\_}polynomial{\_} trajectory{\_}planning.},
author = {Richter, Charles and Bry, Adam and Roy, Nicholas},
file = {:home/matt/Documents/Mendeley Desktop/Richter, Bry, Roy - 2013 - Polynomial Trajectory Planning for Aggressive Quadrotor Flight in Dense Indoor Environments.pdf:pdf},
journal = {Isrr},
number = {Isrr},
pages = {1--16},
title = {{Polynomial Trajectory Planning for Aggressive Quadrotor Flight in Dense Indoor Environments}},
url = {http://groups.csail.mit.edu/rrg/papers/ISRR13{\_}Richter.pdf},
year = {2013}
}
@article{Razzaghi1994,
author = {Razzaghi, Mohsen and Elnagar, Gamal N.},
file = {:home/matt/Documents/Mendeley Desktop/Razzaghi, Elnagar - 1994 - A pseudospectral collocation method for the brachistochrone problem.pdf:pdf},
journal = {Mathematics and Computers in Simulation},
title = {{A pseudospectral collocation method for the brachistochrone problem}},
year = {1994}
}
@article{Wilkey1995,
author = {Wilkey, N M},
file = {:home/matt/Documents/Mendeley Desktop/1-s2.0-009457659500096I-main.pdf:pdf},
journal = {Acta Astronautica},
number = {3},
pages = {149--162},
title = {{OPTIMAL CONTROL OF A SATELLITE-ROBOT SYSTEM USING DIRECT COLLOCATION WITH NON-LINEAR PROGRAMMING}},
volume = {36},
year = {1995}
}
@techreport{Abbeel2012,
author = {Abbeel, Pieter},
file = {:home/matt/Documents/Mendeley Desktop/Abbeel - 2012 - Optimal Control for Linear Dynamical Systems and Quadratic Cost.pdf:pdf},
keywords = {LQR},
mendeley-tags = {LQR},
title = {{Optimal Control for Linear Dynamical Systems and Quadratic Cost}},
year = {2012}
}
@article{Herman1996a,
abstract = {The method of collocation and nonlinear programming has been used recently to solve a number of optimal control problems. In this method polynomials are commonly used to represent the state variable time histories over subintervals of the total time of interest. These polynomials correspond to a family of modified-Gaussian quadrature rules known as the Gauss-Lobatto rules. Presently, relatively low-order rules from the Gauss-Lobatto family, such as the trapezoid and Simpson`s rule, are used to construct collocation solution schemes. In this work higher-order Gauss-Lobatto quadrature rules are formulated using collocation point selection based on a particular family of Jacobi polynomials. The advantage of using a quadrature rule of higher order is that the approximation using the higher degree polynomial may be more accurate, due to finite precision arithmetic, than a formulation based on a lower degree polynomial. In addition, the number of subintervals and, therefore, the number of nonlinear programming parameters needed to solve a problem accurately may be significantly reduced from that required if the conventional trapezoidal or Simpson`s quadrature schemes are used. An optimal trajectory maximizing final energy for a low-thrust spacecraft is used to demonstrate the benefits of using the higher-order schemes. (28 References).},
author = {Herman, A L and Conway, B A},
doi = {10.2514/3.21662},
file = {:home/matt/Documents/Mendeley Desktop//Herman, Conway - 1996 - Direct optimization using collocation based on high-order Gauss-Lobatto quadrature rules(2).pdf:pdf;:home/matt/Documents/Mendeley Desktop/3{\%}2E21662.pdf:pdf},
isbn = {0731-5090},
issn = {0731-5090},
journal = {{\{}AIAA{\}} Journal of Guidance, Control, and Dynamics},
number = {3},
pages = {522--529},
title = {{Direct optimization using collocation based on high-order Gauss-Lobatto quadrature rules}},
volume = {19},
year = {1996}
}
@inproceedings{Rezazadeh2015,
address = {Seattle, WA},
author = {Rezazadeh, Siavash and Hurst, Jonathan W},
booktitle = {IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004},
file = {:home/matt/Documents/Mendeley Desktop/Rezazadeh et al. - 2015 - Toward Step-by-Step Synthesis of Stable Gaits for Underactuated Compliant Legged Robots.pdf:pdf},
isbn = {9781479969234},
pages = {4532--4538},
title = {{Toward Step-by-Step Synthesis of Stable Gaits for Underactuated Compliant Legged Robots}},
year = {2015}
}
@article{Betts1998,
author = {Betts, John T},
file = {:home/matt/Documents/Mendeley Desktop/surveyppr.pdf:pdf},
journal = {Journal of Guidance, Control, and Dynamics},
pages = {1--56},
title = {{A Survey of Numerical Methods for Trajectory Optimization}},
year = {1998}
}
@article{Canuto1988,
author = {Canuto, C. and Hussaini, M.Y. and Quarteroni, A. and Zang, T.A.},
file = {:home/matt/Documents/Mendeley Desktop//Canuto et al. - 1988 - Spectral Methods in Fluid Dynamcs.pdf:pdf},
title = {{Spectral Methods in Fluid Dynamcs}},
year = {1988}
}
@article{Levine2014,
abstract = {Direct policy search methods offer the promise of automatically learning controllers for complex, high-dimensional tasks. However, prior applications of policy search often required specialized, low-dimensional policy classes, limiting their generality. In this work, we introduce a policy search algorithm that can directly learn high-dimensional, general-purpose policies, represented by neural networks. We formulate the policy search problem as an optimization over trajectory distributions, alternating between optimizing the policy to match the trajectories, and optimizing the trajectories to match the policy and minimize expected cost. Our method can learn policies for complex tasks such as bipedal push recovery and walking on uneven terrain, while outperforming prior methods.},
author = {Levine, Sergey and Edu, S},
file = {:home/matt/Documents/Mendeley Desktop/levine14.pdf:pdf},
journal = {Eecs.Berkeley.Edu},
title = {{Learning Complex Neural Network Policies with Trajectory Optimization}},
url = {http://www.eecs.berkeley.edu/{~}svlevine/papers/cgps.pdf},
volume = {32},
year = {2014}
}
@book{Press1992,
author = {Press, William H. and Teukolsky, Saul A and Vetterling, William T. and Flannery, Brian P.},
edition = {Second Edi},
publisher = {Cambridge University Press},
title = {{Numerical Recipes in C}}
}
@article{Hehn2012,
author = {Hehn, M and Andrea, R},
file = {:home/matt/Documents/Mendeley Desktop/hehn{\_}dandrea{\_}interception.pdf:pdf},
journal = {Iros},
pages = {4979--4984},
title = {{Real Time Trajectory Generation for Interception Maneuvers with Quadrocopters.}},
year = {2012}
}
@article{Hager2010,
author = {Hager, William W and Rao, Anil V},
file = {:home/matt/Documents/Mendeley Desktop//Hager, Rao - 2010 - Gauss Pseudospectral Method for Solving Infinite-Horizon Optimal Control Problems.pdf:pdf},
number = {August},
pages = {1--9},
title = {{Gauss Pseudospectral Method for Solving Infinite-Horizon Optimal Control Problems}},
year = {2010}
}
@book{Luenberger2008,
author = {Luenberger, David G. and Ye, Yinyu},
edition = {Third Edit},
publisher = {Springer},
title = {{Linear and Nonlinear Programming}},
year = {2008}
}
@article{Gasparetto2007,
abstract = {A new method for smooth trajectory planning of robot manipulators is described in this paper. In order to ensure that the resulting trajectory is smooth enough, an objective function containing a term proportional to the integral of the squared jerk (defined as the derivative of the acceleration) along the trajectory is considered. Moreover, a second term, proportional to the total execution time, is added to the expression of the objective function. In this way it is not necessary to define the total execution time before running the algorithm. Fifth-order B-splines are then used to compose the overall trajectory. With respect to other trajectory optimization techniques, the proposed method enables one to set kinematic constraints on the robot motion, expressed as upper bounds on the absolute values of velocity, acceleration and jerk. The algorithm has been tested in simulation yielding good results, which have also been compared with those provided by another important trajectory planning technique. ?? 2006 Elsevier Ltd. All rights reserved.},
author = {Gasparetto, A. and Zanotto, V.},
doi = {10.1016/j.mechmachtheory.2006.04.002},
file = {:home/matt/Documents/Mendeley Desktop/Gasparetto, Zanotto - 2007 - A new method for smooth trajectory planning of robot manipulators.pdf:pdf},
issn = {0094114X},
journal = {Mechanism and Machine Theory},
keywords = {B-splines,Jerk,Optimization,Robot manipulators,Smoothness,Trajectory planning},
number = {4},
pages = {455--471},
title = {{A new method for smooth trajectory planning of robot manipulators}},
volume = {42},
year = {2007}
}
@article{Bhounsule2014a,
author = {Bhounsule, P. a. and Cortell, J. and Grewal, A. and Hendriksen, B. and Karssen, J. G. D. and Paul, C. and Ruina, A.},
file = {:home/matt/Documents/Mendeley Desktop/Bhounsule et al. - 2014 - MULTIMEDIA EXTENSION {\#} 1 International Journal of Robotics Research Low-bandwidth reflex-based control for low.pdf:pdf},
journal = {International Journal of Robotics Research},
title = {{MULTIMEDIA EXTENSION {\#} 1 International Journal of Robotics Research Low-bandwidth reflex-based control for lower power walking : 65 km on a single battery charge}},
year = {2014}
}
@article{Garg2010,
abstract = {A unified framework is presented for the numerical solution of optimal control problems using collocation at LegendreGauss (LG), LegendreGaussRadau (LGR), and LegendreGaussLobatto (LGL) points. It is shown that the LG and LGR differentiation matrices are rectangular and full rank whereas the LGL differentiation matrix is square and singular. Consequently, the LG and LGR schemes can be expressed equivalently in either differential or integral form, while the LGL differential and integral forms are not equivalent. Transformations are developed that relate the Lagrange multipliers of the discrete nonlinear programming problem to the costates of the continuous optimal control problem. The LG and LGR discrete costate systems are full rank while the LGL discrete costate system is rank-deficient. The LGL costate approximation is found to have an error that oscillates about the true solution and this error is shown by example to be due to the null space in the LGL discrete costate system. An example is considered to assess the accuracy and features of each collocation scheme. ?? 2010 Elsevier Ltd. All rights reserved.},
author = {Garg, Divya and Patterson, Michael and Hager, William W. and Rao, Anil V. and Benson, David a. and Huntington, Geoffrey T.},
doi = {10.1016/j.automatica.2010.06.048},
file = {:home/matt/Documents/Mendeley Desktop//Garg et al. - 2010 - A unified framework for the numerical solution of optimal control problems using pseudospectral methods.pdf:pdf},
issn = {00051098},
journal = {Automatica},
keywords = {Nonlinear programming,Optimal control,Pseudospectral methods},
number = {11},
pages = {1843--1851},
publisher = {Elsevier Ltd},
title = {{A unified framework for the numerical solution of optimal control problems using pseudospectral methods}},
url = {http://dx.doi.org/10.1016/j.automatica.2010.06.048},
volume = {46},
year = {2010}
}
@article{Ritz2011,
abstract = {A numerical method for computing quadrocopter maneuvers between two states is presented. Computed maneuvers satisfy Pontryagin's minimum principle with respect to time-optimality. First, in order to obtain the structure of time-optimal maneuvers, we apply the minimum principle to a first-principles, two-dimensional quadrotor model. Then we present a numerical algorithm that enables the computation of maneuvers for arbitrary initial and final states. The developed method is used to compute a set of maneuvers, which are discussed and demonstrated experimentally in the ETH Zurich Flying Machine Arena testbed.},
author = {Ritz, Robin and Hehn, Markus and Lupashin, Sergei and D{\&}apos;Andrea, Raffaello},
doi = {10.1109/IROS.2011.6048382},
file = {:home/matt/Documents/Mendeley Desktop/ritz{\_}hehn{\_}lupashin{\_}dandrea{\_}benchmarking.pdf:pdf},
isbn = {9781612844541},
issn = {2153-0858},
journal = {IEEE International Conference on Intelligent Robots and Systems},
pages = {5179--5186},
title = {{Quadrocopter performance benchmarking using optimal control}},
year = {2011}
}
@article{Atkeson2008,
abstract = {We combine three threads of research on approximate dynamic programming: sparse random sampling of states, value function and policy approximation using local models, and using local trajectory optimizers to globally optimize a policy and associated value function. Our focus is on finding steady-state policies for deterministic time-invariant discrete time control problems with continuous states and actions often found in robotics. In this paper, we describe our approach and provide initial results on several simulated robotics problems.},
author = {Atkeson, Christopher G and Stephens, Benjamin J},
doi = {10.1109/TSMCB.2008.926610},
file = {:home/matt/Documents/Mendeley Desktop/Atkeson, Stephens - 2008 - Random sampling of states in dynamic programming.pdf:pdf},
issn = {1941-0492},
journal = {IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics : a publication of the IEEE Systems, Man, and Cybernetics Society},
keywords = {Computer Simulation,Feedback,Models, Statistical,Nonlinear Dynamics,Programming, Linear,Robotics,Robotics: methods,Systems Theory},
month = {aug},
number = {4},
pages = {924--9},
pmid = {18632379},
title = {{Random sampling of states in dynamic programming.}},
url = {http://www.ncbi.nlm.nih.gov/pubmed/18632379},
volume = {38},
year = {2008}
}
@article{Davies1997,
abstract = {Dynamic Programming, Q-learning and other discrete Markov Decision$\backslash$nProcess solvers can be applied to continuous d-dimensional state-spaces by$\backslash$nquantizing the state space into an array of boxes. This is often problematic$\backslash$nabove two dimensions: a coarse quantization can lead to poor policies, and$\backslash$nfine quantization is too expensive. Possible solutions are variable-resolution$\backslash$ndiscretization, or function approximation by neural nets. A third option,$\backslash$nwhich has been little studied in the reinforcement...},
author = {Davies, S.},
doi = {10.1.1.53.3361},
file = {:home/matt/Documents/Mendeley Desktop/Davies - 1997 - Multidimensional triangulation and interpolation for reinforcement learning.pdf:pdf},
isbn = {0262100657},
issn = {10495258},
journal = {Advances in neural information processing systems},
pages = {1005--1011},
title = {{Multidimensional triangulation and interpolation for reinforcement learning}},
url = {http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.53.3361{\&}rep=rep1{\&}type=pdf},
year = {1997}
}
@inproceedings{Saglam2015,
abstract = {For an underactuated biped on a constant-slope terrain, the hybrid zero dynamics (HZD) controller framework provides exponentially stable walking motions. In this paper, we quantify the stability of such a control system on rough terrain by estimating the expected number of steps before failure. In addition, we show how to switch between multiple HZD controllers (optionally using terrain look-ahead) to increase the stability dramatically, e.g., 10 thousand steps compared to 10. To do this robustly, we make use of the new meshing method proposed in this paper.},
address = {Seattle, WA},
author = {Saglam, Cenk Oguz and Byl, Katie},
booktitle = {International Conference on Robotics and Automation},
file = {:home/matt/Documents/Mendeley Desktop//Saglam, Byl - 2015 - Meshing Hybrid Zero Dynamics for Rough Terrain Walking(2).pdf:pdf},
isbn = {9781479969227},
number = {1},
pages = {5718--5725},
title = {{Meshing Hybrid Zero Dynamics for Rough Terrain Walking}},
year = {2015}
}
@article{Qin2003,
abstract = {This paper provides an overview of commercially available model predictive control (MPC) technology, both linear and nonlinear, based primarily on data provided by MPC vendors. A brief history of industrial MPC technology is presented first, followed by results of our vendor survey of MPC control and identification technology. A general MPC control algorithm is presented, and approaches taken by each vendor for the different aspects of the calculation are described. Identification technology is reviewed to determine similarities and differences between the various approaches. MPC applications performed by each vendor are summarized by application area. The final section presents a vision of the next generation of MPC technology, with an emphasis on potential business and research opportunities.},
author = {Qin, S.Joe and Badgwell, Thomas a.},
doi = {10.1016/S0967-0661(02)00186-7},
file = {:home/matt/Documents/Mendeley Desktop/1-s2.0-S0967066102001867-main.pdf:pdf},
isbn = {09670661},
issn = {09670661},
journal = {Control Engineering Practice},
number = {7},
pages = {733--764},
pmid = {19361737},
title = {{A survey of industrial model predictive control technology}},
volume = {11},
year = {2003}
}
@article{Gardner2006,
author = {Gardner, Everette S.},
doi = {10.1016/j.ijforecast.2006.03.005},
file = {:home/matt/Documents/Mendeley Desktop/Gardner - 2006 - Exponential smoothing The state of the art—Part II.pdf:pdf},
issn = {01692070},
journal = {International Journal of Forecasting},
keywords = {arima,comparative methods,discount weighted,evaluation,exponential smoothing,identification,intermittent demand,inventory control,invertibility,kernel,model selection,prediction intervals,regression,stability,state-space models,time series},
number = {4},
pages = {637--666},
title = {{Exponential smoothing: The state of the art—Part II}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0169207006000392},
volume = {22},
year = {2006}
}
@inproceedings{Todorov2014,
author = {Todorov, Emanuel},
booktitle = {International Conference on Robotics and Automation},
file = {:home/matt/Documents/Mendeley Desktop/Todorov - Unknown - Convex and analytically-invertible dynamics with contacts and constraints Theory and implementation in MuJoCo.pdf:pdf},
title = {{Convex and analytically-invertible dynamics with contacts and constraints : Theory and implementation in MuJoCo}},
year = {2014}
}
@inproceedings{Diehl2009,
address = {Heidelberg, Germany},
author = {Diehl, Moritz and Bock, Hans Georg and Diedam, Holger and Wieber, Pierre-brice and Fast, Pierre-brice Wieber and Multiple, Direct},
booktitle = {Fast Direct Multiple Shooting Algorithms for Optimal Robot Control},
file = {:home/matt/Documents/Mendeley Desktop/Diehl et al. - 2004 - Fast Direct Multiple Shooting Algorithms for Optimal Robot.pdf:pdf},
title = {{Fast Direct Multiple Shooting Algorithms for Optimal Robot}},
year = {2004}
}
@article{Paoletti2014,
author = {Paoletti, P and Mahadevan, L},
file = {:home/matt/Documents/Mendeley Desktop/Paoletti, Mahadevan - 2014 - Intermittent locomotion as an optimal control strategy Intermittent locomotion as an optimal control strate.pdf:pdf},
keywords = {applied mathematics,mechanics},
number = {January},
title = {{Intermittent locomotion as an optimal control strategy Intermittent locomotion as an optimal control strategy}},
year = {2014}
}
@article{Petersen2008,
author = {Petersen, KB and Pedersen, MS},
doi = {10.1111/j.1365-294X.2006.03161.x},
file = {:home/matt/Documents/Mendeley Desktop/matrixOperations.pdf:pdf},
isbn = {0962-1083 (Print)$\backslash$r0962-1083 (Linking)},
issn = {09621083},
journal = {Technical University of Denmark},
keywords = {derivative of,derivative of inverse matrix,determinant,differentiate a matrix,matrix algebra,matrix identities,matrix relations},
pages = {1--25},
pmid = {17284204},
title = {{The matrix cookbook}},
url = {http://www.cim.mcgill.ca/{~}dudek/417/Papers/matrixOperations.pdf},
year = {2008}
}
@article{Shen1995,
author = {Shen, Jie},
file = {:home/matt/Documents/Mendeley Desktop/Shen - 1995 - Efficient Spectral-Galerkin Method II. Direct Solvers of second- and fourth-order equations using chebyshev polynomials.pdf:pdf},
journal = {SIAM J. Sci. Comput.},
keywords = {biharmonic equation,chebyshev polynomial,direct,helmholtz equation,spectral-galerkin method},
number = {1},
pages = {74--87},
title = {{Efficient Spectral-Galerkin Method II. Direct Solvers of second- and fourth-order equations using chebyshev polynomials.}},
volume = {16},
year = {1995}
}
@article{Gasparetto2008,
abstract = {A technique for optimal trajectory planning of robot manipulators is presented in this paper. In order to get the optimal trajectory, an objective function composed of two terms is minimized: a first term proportional to the total execution time and another one proportional to the integral of the squared jerk (defined as the derivative of the acceleration) along the trajectory. This latter term ensures that the resulting trajectory is smooth enough. The proposed technique enables one to take into account kinematic constraints on the robot motion, expressed as upper bounds on the absolute values of velocity, acceleration and jerk. Moreover, it does not require the total execution time of the trajectory to be set a priori. The algorithm has been tested in simulation yielding good results, also in comparison with those provided by another important trajectory planning technique. ?? 2007 Elsevier Ltd. All rights reserved.},
author = {Gasparetto, Alessandro and Zanotto, Vanni},
doi = {10.1016/j.rcim.2007.04.001},
file = {:home/matt/Documents/Mendeley Desktop/1-s2.0-S0736584507000543-main.pdf:pdf},
isbn = {07365845},
issn = {07365845},
journal = {Robotics and Computer-Integrated Manufacturing},
keywords = {Execution time,Jerk,Optimization,Robotics,Splines,Trajectory planning},
number = {3},
pages = {415--426},
title = {{A technique for time-jerk optimal planning of robot trajectories}},
volume = {24},
year = {2008}
}
@article{Stewart2000,
abstract = {In this paper a new time-stepping method for simulating systems of
rigid bodies is given. Unlike methods which take an instantaneous point
of view, our method is based on impulse-momentum equations, and so does
not need to explicitly resolve impulsive forces. On the other hand, our
method is distinct from previous impulsive methods in that it does not
require explicit collision checking and it can handle simultaneous
impacts. Numerical results are given for one planar and one three
dimensional example, which demonstrate the practicality of the method,
and its convergence as the step size becomes small},
author = {Stewart, D and Trinkle, J C},
doi = {10.1109/ROBOT.2000.844054},
file = {:home/matt/Documents/Mendeley Desktop/STicra00.pdf:pdf},
isbn = {0-7803-5886-4},
issn = {1050-4729},
journal = {Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065)},
title = {{An implicit time-stepping scheme for rigid body dynamics with Coulomb friction}},
volume = {1},
year = {2000}
}
@article{Enright1990,
abstract = {A recently developed method for solving optimal trajectory problems uses a piecewise-polynomial representation of the state and control variables, enforces the equations of motion via a collocation procedure, and thus approximates the original calculus-of-variations problem with a nonlinear-programming problem, which is solved numerically. This paper identifies this method as a direct transcription method and proceeds to investigate the relationship between the original optimal-control problem and the nonlinear-programming problem. The discretized adjoint equation of the collocation method is found to have deficient accuracy, and an alternate scheme which discretizes the equations of motion using an explicit Runge-Kutta parallel-shooting approach is developed. Both methods are applied to finite-thrust spacecraft trajectory problems, including a low-thrust escape spiral, a three-burn rendezvous, and a low-thrust transfer to the moon.},
author = {Enright, Paul J. and Conway, Bruce a.},
doi = {10.2514/3.20934},
file = {:home/matt/Documents/Mendeley Desktop/Enright, Conway - 1990 - Discrete approximations to optimal trajectories using direct transcription and nonlinear programming.pdf:pdf},
isbn = {0731-5090},
issn = {0731-5090},
number = {4},
title = {{Discrete approximations to optimal trajectories using direct transcription and nonlinear programming}},
volume = {15},
year = {1990}
}
@article{Saramago1998,
abstract = {This paper considers a solution to the problem of moving a robot manipulator with minimum cost along a specified geometric path. The optimal traveling time and the minimum mechanical energy of the actuators are considered together to build a multi-objective function and the results depend on the associated weighting factors. The optimization problem is subject to physical constraints. The mathematical model takes into account the manipulator nonlinear coupled equations of motion. Numerical results for manipulator arms with three and six degrees of freedom are presented.},
author = {Saramago, S. F. P. and {Steffen Jr.}, V.},
doi = {http://dx.doi.org/10.1016/S0094-114X(97)00110-9},
file = {:home/matt/Documents/Mendeley Desktop/Saramago, Steffen Jr. - 1998 - Optimization of the Trajectory Plannung of Robot Manipulators Taking Into Account the Dynamics of the Sys.pdf:pdf},
issn = {0094-114X},
journal = {Mechanism and Machine Theory},
number = {7},
pages = {883--894},
title = {{Optimization of the Trajectory Plannung of Robot Manipulators Taking Into Account the Dynamics of the System}},
url = {http://www.sciencedirect.com/science/article/pii/S0094114X97001109},
volume = {33},
year = {1998}
}
@article{VonStryk1993,
author = {von Stryk, Oskar},
doi = {10.1002/1099-1514(200009/10)21:5<233::AID-OCA667>3.0.CO;2-B},
file = {:home/matt/Documents/Mendeley Desktop/von Stryk - 1993 - Numerical solution of optimal control problems by direct collocation.pdf:pdf},
issn = {01432087},
journal = {Optimal Control},
number = {4},
pages = {129--143},
title = {{Numerical solution of optimal control problems by direct collocation}},
url = {http://link.springer.com/chapter/10.1007/978-3-0348-7539-4{\_}10},
volume = {111},
year = {1993}
}
@article{Veeraklaew2001,
author = {Veeraklaew, Tawiwat and Agrawal, Sunil K.},
doi = {10.2514/2.4733},
file = {:home/matt/Documents/Mendeley Desktop/2{\%}2E4733.pdf:pdf},
issn = {0731-5090},
journal = {Journal of Guidance, Control, and Dynamics},
number = {2},
pages = {228--236},
title = {{New Computational Framework for Trajectory Optimization of Higher-Order Dynamic Systems}},
volume = {24},
year = {2001}
}
@book{Ziegel1987,
author = {Ziegel, Eric and Press, William and Flannery, Brian and Teukolsky, Saul and Vetterling, William},
booktitle = {Technometrics},
doi = {10.2307/1269484},
file = {:home/matt/Documents/Mendeley Desktop/Ziegel et al. - 1987 - Numerical Recipes The Art of Scientific Computing.pdf:pdf},
isbn = {0521431085},
issn = {00401706},
month = {nov},
number = {4},
pages = {501},
title = {{Numerical Recipes: The Art of Scientific Computing}},
url = {http://www.jstor.org/stable/1269484?origin=crossref},
volume = {29},
year = {1987}
}
@inproceedings{Schall2011,
author = {Kalakrishnan, Mrinal},
booktitle = {International Conference on Robotics and Automation2},
file = {:home/matt/Documents/Mendeley Desktop/00463527d432e3d2f8000000.pdf:pdf},
title = {{STOMP : Stochastic Trajectory Optimization for Motion Planning}},
year = {2011}
}
@book{Jacobson1970,
author = {Jacobson, David H. and Mayne, David Q.},
isbn = {0444000704},
publisher = {Elsevier},
title = {{Differential Dynamic Programming}},
year = {1970}
}
@article{Alipanah2007,
author = {Alipanah, a. and Razzaghi, M. and Dehghan, M.},
doi = {10.1016/j.chaos.2006.04.071},
file = {:home/matt/Documents/Mendeley Desktop/Alipanah, Razzaghi, Dehghan - 2007 - Nonclassical pseudospectral method for the solution of brachistochrone problem.pdf:pdf},
issn = {09600779},
journal = {Chaos, Solitons {\&} Fractals},
number = {5},
pages = {1622--1628},
title = {{Nonclassical pseudospectral method for the solution of brachistochrone problem}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0960077906004395},
volume = {34},
year = {2007}
}
@article{Vlassenbroeck1988,
author = {Vlassenbroeck, Jacques and Dooren, R Van},
file = {:home/matt/Documents/Mendeley Desktop/Vlassenbroeck, Dooren - 1988 - A Chebyshev technique for solving nonlinear optimal control problems.pdf:pdf},
journal = {Automatic Control, IEEE {\ldots}},
number = {4},
title = {{A Chebyshev technique for solving nonlinear optimal control problems}},
url = {http://ieeexplore.ieee.org/xpls/abs{\_}all.jsp?arnumber=192187},
volume = {33},
year = {1988}
}
@article{Stryk1992,
author = {von Stryk, O and Bulirsch, R. and Bulirsh, R.},
file = {:home/matt/Documents/Mendeley Desktop/Stryk92-optimization.pdf:pdf},
journal = {Annals of Operations Researach},
keywords = {constrained optimal control,direct collocation,estimates of adjoint variables,hybrid approach,multiple shooting,nonlinear dynamic systems,nonlinear optimization},
number = {1},
pages = {357--373},
title = {{Direct and indirect methods for trajectory optimization}},
volume = {37},
year = {1992}
}
@article{Tucker1970,
abstract = {{\%}1. The minimum cost of transport (the minimum ratio of metabolic rate to the product of speed and body weight) for various walking, running and flying animals is functionally related to the type of transport and to body weight. The same functional relations hold for poikilotherms and homeotherms, and for five or more decades of body weight. 2. The cost of transport for a flying animal is less than that for a walker or a runner of the same size. The two costs differ by a factor of 27 for animals weighing 0"01 kg. 3. Large birds and mammals have costs of transport that are about the same as those for automobiles and small propeller airplanes.},
author = {Tucker, V a},
doi = {10.1016/0010-406X(70)91006-6},
file = {:home/matt/Documents/Mendeley Desktop/Tucker - 1970 - Energetic cost of locomotion in animals.pdf:pdf},
isbn = {0010-406X},
issn = {0010406X},
journal = {Comparative biochemistry and physiology},
number = {4},
pages = {841--846},
pmid = {4952698},
title = {{Energetic cost of locomotion in animals.}},
volume = {34},
year = {1970}
}
@article{Mueller2013,
abstract = {This paper presents a method for generating quadrocopter trajectories in real time, from some initial state to a final state defined by position, velocity and acceleration in a specified amount of time. The end state captures the attitude to within a rotation about the thrust axis. Trajectory generation is done by formulating the trajectory of the quadrocopter in its jerk, in discrete time, and then solving a convex optimisation problem on each decoupled axis. Convex bounds are derived to include feasibility constraints with respect to the quadrocopter's total allowable thrust and angular rates.},
author = {Mueller, M.W. and D'Andrea, R.},
file = {:home/matt/Documents/Mendeley Desktop/mueECC13.pdf:pdf},
isbn = {9783952417348},
journal = {Proceedings of the European Control Conference (ECC), 2013},
pages = {1383--1389},
title = {{A model predictive controller for quadrocopter state interception}},
url = {http://ieeexplore.ieee.org/xpls/abs{\_}all.jsp?arnumber=6669415},
year = {2013}
}
@article{Elnagar1998,
author = {Elnagar, G N and Kazemi, M a},
file = {:home/matt/Documents/Mendeley Desktop/Elnagar, Kazemi - 1998 - Pseudospectral Chebyshev optimal control of constrained nonlinear dynamical systems.pdf:pdf},
journal = {Computational Optimization and Applications},
keywords = {chebyshev polynomials,optimal control,smoothing filters,spectral numerical methods},
pages = {195--217},
title = {{Pseudospectral Chebyshev optimal control of constrained nonlinear dynamical systems}},
url = {http://www.springerlink.com/index/h0378m3v1g4j5mq1.pdf$\backslash$npapers2://publication/uuid/A6E5D398-9E9C-4846-9604-C497CCDDFBE4},
volume = {217},
year = {1998}
}
@article{Biegler2009,
abstract = {Integration of real-time optimization and control with higher level decision-making (scheduling and planning) is an essential goal for profitable operation in a highly competitive environment. While integrated large-scale optimization models have been formulated for this task, their size and complexity remains a challenge to many available optimization solvers. On the other hand, recent development of powerful, large-scale solvers leads to a reconsideration of these formulations, in particular, through development of efficient large-scale barrier methods for nonlinear programming (NLP). As a result, it is now realistic to solve NLPs on the order of a million variables, for instance, with the IPOPT algorithm. Moreover, the recent NLP sensitivity extension to IPOPT quickly computes approximate solutions of perturbed NLPs. This allows on-line computations to be drastically reduced, even when large nonlinear optimization models are considered. These developments are demonstrated on dynamic real-time optimization strategies that can be used to merge and replace the tasks of (steady-state) real-time optimization and (linear) model predictive control. We consider a recent case study of a low density polyethylene (LDPE) process to illustrate these concepts. ?? 2008 Elsevier Ltd. All rights reserved.},
author = {Biegler, L. T. and Zavala, V. M.},
doi = {10.1016/j.compchemeng.2008.08.006},
file = {:home/matt/Documents/Mendeley Desktop//Biegler, Zavala - 2009 - Large-scale nonlinear programming using IPOPT An integrating framework for enterprise-wide dynamic optimization.pdf:pdf},
isbn = {0098-1354},
issn = {00981354},
journal = {Computers and Chemical Engineering},
keywords = {IPOPT,Model predictive control,Moving horizon estimation,Nonlinear programming,Real-time optimization,Sensitivity},
mendeley-tags = {IPOPT},
pages = {575--582},
title = {{Large-scale nonlinear programming using IPOPT: An integrating framework for enterprise-wide dynamic optimization}},
volume = {33},
year = {2009}
}
@incollection{Ng2012,
abstract = {We now begin our study of reinforcement learning and adaptive control. In supervised learning, we saw algorithms that tried to make their outputs mimic the labels y given in the training set. In that setting, the labels gave an unambiguous " right answer " for each of the inputs x. In contrast, for many sequential decision making and control problems, it is very difficult to provide this type of explicit supervision to a learning algorithm. For example, if we have just built a four-legged robot and are trying to program it to walk, then initially we have no idea what the " correct " actions to take are to make it walk, and so do not know how to provide explicit supervision for a learning algorithm to try to mimic. In the reinforcement learning framework, we will instead provide our al-gorithms only a reward function, which indicates to the learning agent when it is doing well, and when it is doing poorly. In the four-legged walking ex-ample, the reward function might give the robot positive rewards for moving forwards, and negative rewards for either moving backwards or falling over. It will then be the learning algorithm's job to figure out how to choose actions over time so as to obtain large rewards. Reinforcement learning has been successful in applications as diverse as autonomous helicopter flight, robot legged locomotion, cell-phone network routing, marketing strategy selection, factory control, and efficient web-page indexing. Our study of reinforcement learning will begin with a definition of the Markov decision processes (MDP), which provides the formalism in which RL problems are usually posed. 1 2 1 Markov decision processes A Markov decision process is a tuple (S, A, {\{}P sa {\}}, $\gamma$, R), where: • S is a set of states. (For example, in autonomous helicopter flight, S might be the set of all possible positions and orientations of the heli-copter.) • A is a set of actions. (For example, the set of all possible directions in which you can push the helicopter's control sticks.) • P sa are the state transition probabilities. For each state s ∈ S and action a ∈ A, P sa is a distribution over the state space. We'll say more about this later, but briefly, P sa gives the distribution over what states we will transition to if we take action a in state s. • $\gamma$ ∈ [0, 1) is called the discount factor.},
author = {Ng, Andrew},
booktitle = {Machine Learning},
chapter = {XIII - Rei},
file = {:home/matt/Documents/Mendeley Desktop/cs229-notes12.pdf:pdf},
organization = {Stanford University},
pages = {1--15},
title = {{Stanford CS 229 Lecture Notes}},
url = {http://cs229.stanford.edu/notes/cs229-notes12.pdf},
year = {2012}
}
@article{Hunter2016,
author = {Hunter, David and Nikolov, Geno},
file = {:home/matt/Documents/Mendeley Desktop/2584838.pdf:pdf},
journal = {American Mathematical Society},
number = {229},
pages = {269--282},
title = {{On the Error Term of Symmetric Gauss-Lobatto Quadrature Formulae for Analytic Functions}},
url = {http://www.jstor.org/stable/2584838},
volume = {69},
year = {2016}
}
@article{Lawden1991,
author = {Lawden, Derek F.},
doi = {10.2514/3.20703},
file = {:home/matt/Documents/Mendeley Desktop/Lawden - 1991 - Rocket trajectory optimization - 1950-1963.pdf:pdf},
issn = {0731-5090},
journal = {Journal of Guidance, Control, and Dynamics},
number = {4},
pages = {705--711},
title = {{Rocket trajectory optimization - 1950-1963}},
volume = {14},
year = {1991}
}
@article{Williams2009,
author = {Williams, Paul},
doi = {10.2514/1.42731},
file = {:home/matt/Documents/Mendeley Desktop/1{\%}2E42731.pdf:pdf},
issn = {0731-5090},
journal = {Journal of Guidance, Control, and Dynamics},
number = {4},
pages = {1392--1395},
title = {{Hermite-Legendre-Gauss-Lobatto Direct Transcription in Trajectory Optimization}},
url = {http://arc.aiaa.org/doi/abs/10.2514/1.42731},
volume = {32},
year = {2009}
}
@misc{MatlabOptimizationToolbox2014,
author = {Mathworks},
keywords = {FMINCON fmincon},
mendeley-tags = {FMINCON fmincon},
title = {{Matlab Optimization Toolbox}},
url = {http://www.mathworks.com/products/optimization/},
year = {2014}
}
@book{Fornberg1996,
author = {Fornberg, Bengt},
isbn = {0-521-49582-2 (hc)},
publisher = {Cambridge University Press},
title = {{A practical guide to pseudospectral methods}},
year = {1996}
}
@article{Darby2011a,
abstract = {An hp-adaptive pseudospectral method is presented for numerically solving optimal control problems.The method presented in this paper iteratively determines the number of segments, the width of eachsegment, and the polynomial degree required in each segment in order to obtain a solution to a user-specified accuracy. Starting with a global pseudospectral approximation for the state, on each iterationthe method determines locations for the segment breaks and the polynomial degree in each segment foruse on the next iteration. The number of segments and the degree of the polynomial on each segmentcontinue to be updated until a user-specified tolerance is met. The terminology ‘hp' is used becausethe segment widths (denoted h) and the polynomial degree (denoted p) in each segment are determinedsimultaneously. It is found that the method developed in this paper leads to higher accuracy solutions withless computational effort and memory than is required in a global pseudospectral method. Consequently,the method makes it possible to solve complex optimal control problems using pseudospectral methodsin cases where a global pseudospectral method would be computationally intractable. Finally, the utilityof the method is demonstrated on a variety of problems of varying complexity. Copyright 䉷 2010 JohnWiley {\&} Sons, Ltd.},
author = {Darby, Christopher L. and Hagar, WIlliam W. and Rao, Anil V.},
doi = {10.1002/oca.957},
file = {:home/matt/Documents/Mendeley Desktop/Darby{\_}et{\_}al-2011-Optimal{\_}Control{\_}Applications{\_}and{\_}Methods.pdf:pdf},
journal = {Optimal Control Applications and Methods},
keywords = {collocation methods,nonlinear optimization,pseudospectral methods},
pages = {476--502},
title = {{An hp-adaptive pseudospectral method for solving optimal control problems}},
volume = {32},
year = {2011}
}
@article{Hansen2006,
abstract = {This paper investigates sigma-self-adaptation for real valued evolutionary algorithms on linear fitness functions. We identify the step-size logarithm log sigma as a key quantity to understand strategy behavior. Knowing the bias of mutation, recombination, and selection on log sigma is sufficient to explain sigma-dynamics and strategy behavior in many cases, even from previously reported results on non-linear and/or noisy fitness functions. On a linear fitness function, if intermediate multi-recombination is applied on the object parameters, the i-th best and the i-th worst individual have the same sigma-distribution. Consequently, the correlation between fitness and step-size sigma is zero. Assuming additionally that sigma-changes due to mutation and recombination are unbiased, then sigma-self-adaptation enlarges sigma if and only if mu {\textless} lambda/2, given (mu, lambda)-truncation selection. Experiments show the relevance of the given assumptions.},
author = {Hansen, Nikolaus},
doi = {10.1162/evco.2006.14.3.255},
file = {:home/matt/Documents/Mendeley Desktop/Hansen - 2006 - An analysis of mutative sigma-self-adaptation on linear fitness functions.pdf:pdf},
issn = {1063-6560},
journal = {Evolutionary computation},
keywords = {Adaptation,Algorithms,Biological,Biological Evolution,CMA-ES,CMAES,Genetic,Genetic Variation,Genetics,Linear Models,Models,Mutation,Population,Recombination,Selection},
mendeley-tags = {CMA-ES,CMAES},
month = {jan},
number = {3},
pages = {255--75},
pmid = {16903793},
title = {{An analysis of mutative sigma-self-adaptation on linear fitness functions.}},
url = {http://www.ncbi.nlm.nih.gov/pubmed/16903793},
volume = {14},
year = {2006}
}
@article{Augugliaro2012,
abstract = {This paper presents an algorithm that generates collision-free trajectories in three dimensions for multiple vehicles within seconds. The problem is cast as a non-convex optimization problem, which is iteratively solved using sequential convex programming that approximates non-convex constraints by using convex ones. The method generates trajectories that account for simple dynamics constraints and is thus independent of the vehicle's type. An extensive a posteriori vehicle-specific feasibility check is included in the algorithm. The algorithm is applied to a quadrocopter fleet. Experimental results are shown.},
author = {Augugliaro, Federico and Schoellig, Angela P. and D'Andrea, Raffaello},
doi = {10.1109/IROS.2012.6385823},
file = {:home/matt/Documents/Mendeley Desktop/AugugliaroIROS2012.pdf:pdf},
isbn = {9781467317375},
issn = {21530858},
journal = {IEEE International Conference on Intelligent Robots and Systems},
pages = {1917--1922},
title = {{Generation of collision-free trajectories for a quadrocopter fleet: A sequential convex programming approach}},
year = {2012}
}
@article{Parter1999,
author = {Parter, Seymour V},
file = {:home/matt/Documents/Mendeley Desktop//Parter - 1999 - On the Legendre-Gauss-Lobatto Points and Weights.pdf:pdf},
journal = {Journal of Scientific Computing},
number = {4},
pages = {347--355},
title = {{On the Legendre-Gauss-Lobatto Points and Weights}},
volume = {14},
year = {1999}
}
@article{VonStryk1999,
abstract = {This report forms the user's guide forVersion 2.1 of , a set of Fortran subroutines designed to solve optimal control problems of systems described by (first order) ordinary differential equations subject to general inequality or equality constraints on the control and/or state variables. Discontinuities in the right hand side of the differential equations can be treated as well as multi-phase problems. The user must provide subroutines that define the objective and the constraint functions. Subroutines for derivatives of the problem functions are not required. is a direct collocation method : By a discretization of state and control variables the infinite dimensional optimal control problem is transcribed into a sequence of (finite dimensional) nonlinearly constrained optimization problems (NLPs). Optimal Control Theory and adjoint differential equations are not required in order to apply the algorithm. The NLPs are solved either by the dense Sequential Quadratic Programming (SQP) method NPSOL (Gill, Murray, Saunders, and Wright ) or by the sparse SQP method SNOPT (Gill, Murray, and Saunders , Version 5.3-4 or higher). also computes reliable estimates of the adjoint variables, the multiplier func- tions of state constraints and the switching structure. Therefore the method can conveniently be combined with an indirect method such as multiple shooting . Supplementary programs are provided for supporting a visualization of the numerical results.},
annote = {DIRCOL},
author = {von Stryk, O and von Stryk, O and von Stryk, O and von Stryk, O and von Stryk, O},
file = {:home/matt/Documents/Mendeley Desktop/von Stryk et al. - 1999 - User's guide for DIRCOL A direct collocation method for the numerical solution of optimal control problems.pdf:pdf},
journal = {Lehrstuhl f{\"{u}}r H{\"{o}}here Mathematik und Numerische},
number = {November},
title = {{User's guide for DIRCOL: A direct collocation method for the numerical solution of optimal control problems}},
url = {http://scholar.google.com/scholar?hl=en{\&}btnG=Search{\&}q=intitle:User?s+Guide+for+A+Direct+Collocation+Method+for+the+Numerical+Solution+of+Optimal+Control+Problems{\#}1},
year = {1999}
}
@article{Uno1989,
abstract = {In this paper, we study trajectory planning and control in voluntary, human arm movements. When a hand is moved to a target, the central nervous system must select one specific trajectory among an infinite number of possible trajectories that lead to the target position. First, we discuss what criterion is adopted for trajectory determination. Several resear- chers measured the hand trajectories of skilled move- ments and found common invariant features. For example, when moving the hand between a pair of targets, subjects tended to generate roughly straight hand paths with bell-shaped speed profiles. On the basis of these observations and dynamic optimization theory, we propose a mathematical model which accounts for formation of hand trajectories. This model is formulated by defining an objective function, a measure of performance for any possible movement: square of the rate of change of torque integrated over the entire movement.},
author = {Uno, Y. and Kawato, M. and Suzuki, R.},
doi = {10.1007/BF00204593},
file = {:home/matt/Documents/Mendeley Desktop/Uno, Kawato, Suzuki - 1989 - Formation and control of optimal trajectory in human multijoint arm movement.pdf:pdf},
isbn = {0340-1200},
issn = {0340-1200},
journal = {Biological Cybernetics},
number = {2},
pages = {89--101},
pmid = {2742921},
title = {{Formation and control of optimal trajectory in human multijoint arm movement}},
volume = {61},
year = {1989}
}
@article{Muller2013,
abstract = {An algorithm is proposed allowing for the rapid generation and evaluation of quadrocopter state interception trajectories. These trajectories are from arbitrary initial states to final states defined by the vehicle position, velocity and acceleration with a specified end of time. Sufficient criteria are then derived allowing trajectories to be tested for feasibility with respect to thrust and body rates. It is also shown that the range of a linear combination of the vehicle state can be solved for in closed form, useful e.g. for testing that the position remains within a box. The algorithm is applied by revisiting the problem of finding a trajectory to hit a ball towards a target with a racket attached to a quadrocopter. The trajectory generator is used in a model predictive control like strategy, where thousands of trajectories are generated and evaluated at every controller update step, with the first input of the optimal trajectory being sent to the vehicle. It is shown that the method can generate and evaluate on the order of one million trajectories per second on a standard laptop computer.},
author = {M{\"{u}}ller, Mark W and Hehn, Markus and D{\&}{\#}039;Andrea, Raffaello},
file = {:home/matt/Documents/Mendeley Desktop/mueIROS13.pdf:pdf},
isbn = {978-1-4673-6357-0},
pages = {3480--3486},
title = {{A computationally efficient algorithm for state-to-state quadrocopter trajectory generation and feasibility verification:  BT  - 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)}},
year = {2013}
}
@article{Franc2014,
annote = {Integral vs Differential Form: Section 3.1},
author = {Francolin, Camila C and Benson, David A and Hager, William W and Rao, Anil V},
file = {:home/matt/Documents/Mendeley Desktop/Francolin et al. - 2014 - Costate Estimation in Optimal Control Using Integral Gaussian Quadrature Orthogonal Collocation Methods.pdf:pdf},
journal = {Optimal Control Applications and Methods},
title = {{Costate Estimation in Optimal Control Using Integral Gaussian Quadrature Orthogonal Collocation Methods}},
year = {2014}
}
@article{Laurie2001,
abstract = {Gaussian formulas for a linear functional L (such as a weighted integral) are best computed from the recursion coefficients relating the monic polynomials orthogonal with respect to L. In Gauss-type formulas, one or more extraneous conditions (such as pre-assigning certain nodes) replace some of the equations expressing exactness when applied to high-order polynomials. These extraneous conditions may be applied by modifying the same number of recursion coefficients. We survey the methods of computing formulas from recursion coefficients, methods of obtaining recursion coefficients and modifying them for Gauss-type formulas, and questions of existence and numerical accuracy associated with those computations. ?? 2001 Elsevier Science B.V.},
author = {Laurie, Dirk P.},
doi = {10.1016/S0377-0427(00)00506-9},
file = {:home/matt/Documents/Mendeley Desktop//Laurie - 2001 - Computation of Gauss-type quadrature formulas.pdf:pdf},
issn = {03770427},
journal = {Journal of Computational and Applied Mathematics},
keywords = {Gaussian quadrature,Kronrod,Lobatto,Numerical integration,Radau},
number = {1-2},
pages = {201--217},
title = {{Computation of Gauss-type quadrature formulas}},
volume = {127},
year = {2001}
}
@article{Berrut2004a,
abstract = {Barycentric interpolation is a variant of Lagrange polynomial interpolation that is fast and stable. It deserves to be known as the standard method of polynomial interpolation. Dedicated to the memory of Peter Henrici (1923-1987)},
author = {Berrut, Jean-Paul and Trefethen, Lloyd N.},
doi = {10.1137/S0036144502417715},
file = {:home/matt/Documents/Mendeley Desktop/barycentric.pdf:pdf},
issn = {0036-1445},
journal = {SIAM Review},
keywords = {Numerical analysis},
number = {3},
pages = {501--517},
title = {{Barycentric Lagrange Interpolation}},
url = {http://eprints.maths.ox.ac.uk/1212/$\backslash$nhttp://epubs.siam.org/doi/abs/10.1137/S0036144502417715},
volume = {46},
year = {2004}
}
@article{Ma2012,
abstract = {This brief presents a model-based predictive control (MPC) approach to building cooling systems with thermal energy storage. We focus on buildings equipped with a water tank used for actively storing cold water produced by a series of chillers. First, simplified models of chillers, cooling towers, thermal storage tanks, and buildings are developed and validated for the purpose of model-based control design. Then an MPC for the chilling system operation is proposed to optimally store the thermal energy in the tank by using predictive knowledge of building loads and weather conditions. This brief addresses real-time implementation and feasibility issues of the MPC scheme by using a simplified hybrid model of the system, a periodic robust invariant set as terminal constraints, and a moving window blocking strategy. The controller is experimentally validated at the University of California, Merced. The experiments show a reduction in the central plant electricity cost and an improvement of its efficiency.},
author = {Ma, Y and Borrelli, F and Hencey, B and Coffey, B and Bengea, S and Haves, P},
doi = {10.1109/TCST.2011.2124461},
file = {:home/matt/Documents/Mendeley Desktop/05739562.pdf:pdf},
isbn = {1063-6536},
issn = {1063-6536},
journal = {IEEE Transactions on Control Systems Technology},
number = {3},
pages = {796--803},
title = {{Model Predictive Control for the Operation of Building Cooling Systems}},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5739562},
volume = {20},
year = {2012}
}
