Interior Point Differential Dynamic Programming, Redux

Abstract: We present IPDDP2, a structure-exploiting algorithm for solving discrete-time, finite-horizon optimal control problems (OCPs) with nonlinear constraints. Inequality constraints are handled using a primal-dual interior point formulation and step acceptance for equality constraints follows a line-search filter approach. The iterates of the algorithm are derived under the Differential Dynamic Programming (DDP) framework. A proof of local quadratic convergence of the IPDDP2 iterates is provided. Our numerical experiments evaluate IPDDP2 on over 500 OCPs derived from five different classes of robotic motion planning problems, three of which are contact-implicit trajectory optimisation problems. IPDDP2 demonstrates improvements in robustness against existing constrained DDP algorithms for contact-implicit planning, while being significantly faster than general-purpose solver IPOPT. We provide a full implementation of IPDDP2 in the Julia programming language.