Sparsity-Inducing Optimal Control via Differential Dynamic Programming

TL;DR

This paper introduces sparsity-promoting regularization techniques in differential dynamic programming to generate control inputs that are sparse, energy-efficient, and suitable for systems like satellites and robots, validated through simulations and hardware tests.

Contribution

It develops a family of sparsity-inducing optimal control methods by integrating L1 and Huber regularization into DDP, analyzing their effects and providing practical implementations.

Findings

Sparsity can be effectively induced using L1 and Huber penalties in DDP.

The proposed methods improve control energy efficiency and sparsity.

Validated on satellite and humanoid robot systems with open-source code.

Abstract

Optimal control is a popular approach to synthesize highly dynamic motion. Commonly, $L_2$ regularization is used on the control inputs in order to minimize energy used and to ensure smoothness of the control inputs. However, for some systems, such as satellites, the control needs to be applied in sparse bursts due to how the propulsion system operates. In this paper, we study approaches to induce sparsity in optimal control solutions -- namely via smooth $L_1$ and Huber regularization penalties. We apply these loss terms to state-of-the-art DDP-based solvers to create a family of sparsity-inducing optimal control methods. We analyze and compare the effect of the different losses on inducing sparsity, their numerical conditioning, their impact on convergence, and discuss hyperparameter settings. We demonstrate our method in simulation and hardware experiments on canonical dynamics systems, control of satellites, and the NASA Valkyrie humanoid robot. We provide an implementation of our method and all examples for reproducibility on GitHub.