Sparsity-Inducing Optimal Control via Differential Dynamic Programming
This addresses the need for sparse control in specific systems such as satellites and robots, but is incremental as it builds on existing DDP solvers with new regularization techniques.
The paper tackles the problem of inducing sparsity in optimal control solutions for systems like satellites that require burst-like control inputs, by applying smooth L1 and Huber regularization penalties to DDP-based solvers, resulting in a family of methods demonstrated in simulations and hardware experiments.
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.