Operator Splitting Covariance Steering for Safe Stochastic Nonlinear Control

TL;DR

This paper introduces an operator splitting covariance steering algorithm for safe stochastic nonlinear control, enabling more feasible solutions under complex constraints and demonstrated effectiveness in robotics applications and hardware tests.

Contribution

It proposes a novel operator splitting approach for covariance steering that improves feasibility and solution quality in nonlinear stochastic control problems.

Findings

The method outperforms standard SCP in simulation tests.

It handles stricter safety constraints effectively.

Successful hardware demonstrations confirm practical applicability.

Abstract

This paper presents a novel algorithm for solving distribution steering problems featuring nonlinear dynamics and chance constraints. Covariance steering (CS) is an emerging methodology in stochastic optimal control that poses constraints on the first two moments of the state distribution -- thereby being more tractable than full distributional control. Nevertheless, a significant limitation of current approaches for solving nonlinear CS problems, such as sequential convex programming (SCP), is that they often generate infeasible or poor results due to the large number of constraints. In this paper, we address these challenges, by proposing an operator splitting CS approach that temporarily decouples the full problem into subproblems that can be solved in parallel. This relaxation does not require intermediate iterates to satisfy all constraints simultaneously prior to convergence, which enhances exploration and improves feasibility in such non-convex settings. Simulation results across a variety of robotics applications verify the ability of the proposed method to find better solutions even under stricter safety constraints than standard SCP. Finally, the applicability of our framework on real systems is also confirmed through hardware demonstrations