Differential dynamic programming with nonlinear constraints

Published

Conference Paper

© 2017 IEEE. 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.

Full Text

Duke Authors

Cited Authors

  • Xie, Z; Liu, CK; Hauser, K

Published Date

  • July 21, 2017

Published In

Start / End Page

  • 695 - 702

International Standard Serial Number (ISSN)

  • 1050-4729

International Standard Book Number 13 (ISBN-13)

  • 9781509046331

Digital Object Identifier (DOI)

  • 10.1109/ICRA.2017.7989086

Citation Source

  • Scopus