TY - GEN
T1 - Differential dynamic programming with nonlinear constraints
AU - Xie, Zhaoming
AU - Liu, C. Karen
AU - Hauser, Kris
N1 - Publisher Copyright:
© 2017 IEEE.
PY - 2017/7/21
Y1 - 2017/7/21
N2 - Differential dynamic programming (DDP) is a widely used trajectory optimization technique that addresses nonlinear optimal control problems, and can readily handle nonlinear cost functions. However, it does not handle either state or control constraints. This paper presents a novel formulation of DDP that is able to accommodate arbitrary nonlinear inequality constraints on both state and control. The main insight in standard DDP is that a quadratic approximation of the value function can be derived using a recursive backward pass, however the recursive formulae are only valid for unconstrained problems. The main technical contribution of the presented method is a derivation of the recursive quadratic approximation formula in the presence of nonlinear constraints, after a set of active constraints has been identified at each point in time. This formula is used in a new Constrained-DDP (CDDP) algorithm that iteratively determines these active set and is guaranteed to converge toward a local minimum. CDDP is demonstrated on several underactuated optimal control problems up to 12D with obstacle avoidance and control constraints and is shown to outperform other methods for accommodating constraints.
AB - Differential dynamic programming (DDP) is a widely used trajectory optimization technique that addresses nonlinear optimal control problems, and can readily handle nonlinear cost functions. However, it does not handle either state or control constraints. This paper presents a novel formulation of DDP that is able to accommodate arbitrary nonlinear inequality constraints on both state and control. The main insight in standard DDP is that a quadratic approximation of the value function can be derived using a recursive backward pass, however the recursive formulae are only valid for unconstrained problems. The main technical contribution of the presented method is a derivation of the recursive quadratic approximation formula in the presence of nonlinear constraints, after a set of active constraints has been identified at each point in time. This formula is used in a new Constrained-DDP (CDDP) algorithm that iteratively determines these active set and is guaranteed to converge toward a local minimum. CDDP is demonstrated on several underactuated optimal control problems up to 12D with obstacle avoidance and control constraints and is shown to outperform other methods for accommodating constraints.
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U2 - 10.1109/ICRA.2017.7989086
DO - 10.1109/ICRA.2017.7989086
M3 - Conference contribution
AN - SCOPUS:85028014003
T3 - Proceedings - IEEE International Conference on Robotics and Automation
SP - 695
EP - 702
BT - ICRA 2017 - IEEE International Conference on Robotics and Automation
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2017 IEEE International Conference on Robotics and Automation, ICRA 2017
Y2 - 29 May 2017 through 3 June 2017
ER -