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

This paper 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 dynamics 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, this paper provides a characterization of DDP vs. iLQR following push disturbances. One challenge is that DDP often requires regularization to ensure the algorithm improves its control law from iteration to iteration, and an expensive matrix reconditioning is often necessary. We explore a novel methodology to carry out this matrix reconditioning, which considers the local geometry of the cost landscape. The resulting controller is shown to achieve lower costs and withstand larger disturbances as compared to traditional regularization schemes.