Second-Order Differential Dynamic Programming for Whole-Body MPC of Legged Robots

JOHN NDEGWA NGANGA, He Li, Patrick Wensing

Keywords: Optimal control, Hybrid systems, Robotics, Optimization, Model predictive control

TL;DR: We showcase the first use-case of full second-order Differential Dynamic Programming algorithm for a whole-body model for model predictive control on legged robot hardware.

Abstract: This work presents the first use-case of full second-order Differential Dynamic Programming (DDP) with a whole-body model for model predictive control on legged robot hardware. Recent advances in the literature show that DDP can be simplified by exploiting the dynamics structure in the algorithm, allowing the use of reverse-mode derivative accumulation to efficiently compute sensitives. These advances allow DDP to be run at similar compute times as the iterative LQR (iLQR) algorithm, its first-order counterpart. Beyond a hardware implementation of these past theoretical developments for a robot making regular contact with the environment, this paper provides a characterization of full DDP vs. iLQR following push disturbances with a quadruped robot. The resulting DDP controller is shown to achieve lower costs and withstand bigger disturbances as compared to iLQR.

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