Fetching the paper…
Reading the bibliography…
Differential dynamic programming (DDP) is a direct single shooting method for trajectory optimization.
R. E. Bellman, “ The Theory of Dynamic Programming ,” Bull. Amer. Math. Soc , 1954
1954
Earlier work this paper cites.
D. Mayne, “ A second-order gradient method for determining optimal trajectories of non-linear discrete-time systems ,” International Journal of Control , 1966
1966
Earlier work this paper cites.
R. Fletcher, “ A modified Marquardt subroutine for non-linear least squares ,” J. Math. Sci. , 1971
1971
Earlier work this paper cites.
K. Ohno, “ A new approach to differential dynamic programming for discrete time systems ,” IEEE Transactions on Automatic Control , vol. 23, no. 1, pp. 37–47, 1978
1978
Earlier work this paper cites.
D. Gabay, “ Minimizing a differentiable function over a differential manifold ,” J. Optim. Theory Appl. , vol. 37, 1982
1982
Earlier work this paper cites.
D. P. Bertsekas, “ Projected newton methods for optimization problems with simple constraints ,” SIAM Journal on Control and Optimization , 1982
1982
Earlier work this paper cites.
C. R. Hargraves and S. W. Paris, “ Direct trajectory optimization using nonlinear programming and collocation ,” J. Guidance , vol. 10, no. 4, 1987
1987
Earlier work this paper cites.
L. zhi Liao and C. A. Shoemaker, “ Advantages of Differential Dynamic Programming Over Newton’s Method for Discrete-Time Optimal Control Problems ,” Cornell University, Tech. Rep., 1992
1992
Earlier work this paper cites.
D. E. Kirk, Optimal Control Theory - An Introduction . Dover Publications, 1998
1998
Earlier work this paper cites.
R. H. Byrd, M. E. Hribar, and J. Nocedal, “ An Interior Point Algorithm for Large-Scale Nonlinear Programming ,” SIAM J. on Optimization , 1999
1999
Earlier work this paper cites.
W. Li and E. Todorov, “ Iterative Linear Quadratic Regulator Design for Nonlinear Biological Movement Systems ,” in ICINCO , 2004
2004
Earlier work this paper cites.
R. H. Byrd, N. I. M. Gould, J. Nocedal, and R. A. Waltz, “ An algorithm for nonlinear optimization using linear programming and equality constrained subproblems ,” Math. Program. , 2004
2004
Earlier work this paper cites.
P. E. Gill, W. Murray, and M. A. Saunders, “ SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization ,” SIAM Rev. , 2005
2005
Earlier work this paper cites.
R. H. Byrd, J. Nocedal, and R. A. Waltz, “ KNITRO: An integrated package for nonlinear optimization ,” in Large Scale Nonlinear Optimization, 35–59, 2006 , 2006
2006
Earlier work this paper cites.
A. Wächter and L. T. Biegler, “ On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming ,” Mathematical Programming , 2006
2006
Earlier work this paper cites.
P.-B. Wieber, “ Trajectory Free Linear Model Predictive Control for Stable Walking in the Presence of Strong Perturbations ,” in IEEE Int. Conf. Hum. Rob. (ICHR) , 2006
2006
Earlier work this paper cites.
J. Nocedal and S. J. Wright, Numerical Optimization , 2nd ed. New York, USA: Springer, 2006
2006
Earlier work this paper cites.
M. Diehl, H. G. Bock, H. Diedam, and P.-B. Wieber, “ Fast Direct Multiple Shooting Algorithms for Optimal Robot Control ,” in Proc. Fast Motions in Biomechanics Robot. Springer Berlin Heidelberg, 2006
2006
Earlier work this paper cites.
R. A. Waltz, J. L. Morales, J. Nocedal, and D. Orban, “ An Interior Algorithm for Nonlinear Optimization That Combines Line Search and Trust Region Steps ,” Math. Program. , 2006
2006
Cited alongside, same era.
R. Featherstone, Rigid Body Dynamics Algorithms . Berlin, Heidelberg: Springer-Verlag, 2007
2007
Cited alongside, same era.
G. Lantoine and R. Russell, “ A Hybrid Differential Dynamic Programming Algorithm for Robust Low-Thrust Optimization ,” in AIAA/AAS Astrodyn. Special. Conf. and Exhib. , 2008
2008
Cited alongside, same era.
U. Frese, “ A Framework for Sparse Non-Linear Least Squares Problems on Manifolds ,” Ph.D. dissertation, Universität Bremen, 2008
2008
Cited alongside, same era.
L. Hei, J. Nocedal, and R. A. Waltz, “ A Numerical Study of Active-Set and Interior-Point Methods for Bound Constrained Optimization ,” in Modeling, Simulation and Optimization of Complex Processes , 2008
Z. Xie, C. K. Liu, and K. Hauser, “ Differential dynamic programming with nonlinear constraints ,” in IEEE Int. Conf. Rob. Autom. (ICRA) , 2017
2017
Later among the works it cites.
J. Di Carlo, P. M. Wensing, B. Katz, G. Bledt, and S. Kim, “ Dynamic Locomotion in the MIT Cheetah 3 Through Convex Model-Predictive Control ,” in IEEE/RSJ Int. Conf. Intell. Rob. Sys. (IROS) , 2018
2018
Later among the works it cites.
A. W. Winkler, D. C. Bellicoso, M. Hutter, and J. Buchli, “ Gait and Trajectory Optimization for Legged Systems through Phase-based End-Effector Parameterization ,” IEEE Robot. Automat. Lett. (RA-L) , 2018
2018
Later among the works it cites.
W. Merkt, V. Ivan, and S. Vijayakumar, “ Leveraging Precomputation with Problem Encoding for Warm-Starting Trajectory Optimization in Complex Environments ,” in IEEE/RSJ Int. Conf. Intell. Rob. Sys. (IROS) , 2018
2018
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2008
Cited alongside, same era.
J. T. Betts, Practical Methods for Optimal Control and Estimation Using Nonlinear Programming , 2nd ed. USA: Cambridge University Press, 2009
2009
Cited alongside, same era.
J. Albersmeyer and M. Diehl, “ The Lifted Newton Method and Its Application in Optimization ,” SIAM J. on Optimization , 2010
2010
Cited alongside, same era.
Y. Tassa, “ Theory and Implementation of Biomimetic Motor Controllers ,” Ph.D. dissertation, Hebrew University of Jerusalem, 2011
2011
Cited alongside, same era.
Y. Tassa, T. Erez, and E. Todorov, “ Synthesis and stabilization of complex behaviors through online trajectory optimization ,” in IEEE/RSJ Int. Conf. Intell. Rob. Sys. (IROS) , 2012
2012
Cited alongside, same era.
B. Bell, “CppAD: A package for differentiation of C++ algorithms,” in ComputationalInfrastructure for Operations Research , 2012. [Online]. Available: http://www.coin-or.org/CppAD/
2012
Cited alongside, same era.
J. Baumgarte, “ Stabilization of constraints and integrals of motion in dynamical systems ,” Computer Methods in Applied Mechanics and Engineering , 1972
2013
Cited alongside, same era.
Y. Tassa, N. Mansard, and E. Todorov, “ Control-Limited Differential Dynamic Programming ,” in IEEE Int. Conf. Rob. Autom. (ICRA) , 2014
2014
Cited alongside, same era.
M. Giftthaler, M. Neunert, M. Stäuble, J. Buchli, and M. Diehl, “ A Family of Iterative Gauss-Newton Shooting Methods for Nonlinear Optimal Control ,” in IEEE/RSJ Int. Conf. Intell. Rob. Sys. (IROS) , 2018
2018
Later among the works it cites.
M. Neunert, M. Stauble, M. Giftthaler, C. D. Bellicoso, J. Carius, C. Gehring, M. Hutter, and J. Buchli, “ Whole-Body Nonlinear Model Predictive Control Through Contacts for Quadrupeds ,” IEEE Robot. Automat. Lett. (RA-L) , 2018
2018
Later among the works it cites.
J. Carpentier and N. Mansard, “ Analytical Derivatives of Rigid Body Dynamics Algorithms ,” in Robotics: Science and Systems (RSS) , 2018
2018
Later among the works it cites.
R. Budhiraja, J. Carpentier, C. Mastalli, and N. Mansard, “ Differential Dynamic Programming for Multi-Phase Rigid Contact Dynamics ,” in IEEE Int. Conf. Hum. Rob. (ICHR) , 2018
2018
Later among the works it cites.
T. A. Howell, B. Jackson, and Z. Manchester, “ ALTRO: A Fast Solver for Constrained Trajectory Optimization ,” in IEEE/RSJ Int. Conf. Intell. Rob. Sys. (IROS) , 2019
2019
Later among the works it cites.
C. Mastalli, R. Budhiraja, and N. Mansard, “Crocoddyl: a fast and flexible optimal control library for robot control under contact sequence,” https://github.com/loco-3d/crocoddyl , 2019
2019
Later among the works it cites.
C. Mastalli, I. Havoutis, M. Focchi, D. G. Caldwell, and C. Semini, “ Motion planning for quadrupedal locomotion: coupled planning, terrain mapping and whole-body control ,” IEEE Trans. Robot. (T-RO) , 2020
2020
Closest in time.
C. Mastalli, R. Budhiraja, W. Merkt, G. Saurel, B. Hammoud, M. Naveau, J. Carpentier, L. Righetti, S. Vijayakumar, and N. Mansard, “ Crocoddyl: An Efficient and Versatile Framework for Multi-Contact Optimal Control ,” in IEEE Int. Conf. Rob. Autom. (ICRA) , 2020
2020
Closest in time.
J. Marti-Saumell, J. Solà, C. Mastalli, and A. Santamaria-Navarro, “ Squash-Box Feasibility Driven Differential Dynamic Programming ,” in IEEE/RSJ Int. Conf. Intell. Rob. Sys. (IROS) , 2020
2020
Closest in time.
J. Leal, “CppADCodeGen,” https://github.com/joaoleal/CppADCodeGen/ , 2011–2020
2020
Closest in time.
T. S. Lembono, C. Mastalli, P. Fernbach, N. Mansard, and S. Calinon, “ Learning How to Walk: Warm-starting Optimal Control Solver with Memory of Motion ,” in IEEE Int. Conf. Rob. Autom. (ICRA) , 2020
2020
Closest in time.
J. Eßer, S. Kumar, H. Peters, V. Bargsten, J. d. G. Fernandez, C. Mastalli, O. Stasse, and F. Kirchner, “ Design, analysis and control of the series-parallel hybrid RH5 humanoid robot ,” in IEEE Int. Conf. Hum. Rob. (ICHR) , 2021
2021
Closest in time.
2022
Closest in time.