Operator Splitting Covariance Steering for Safe Stochastic Nonlinear Control

2024-11-18

arXiv.org

AI Summary

Distribution-guided control under nonlinear dynamics with chance constraints remains challenging, as existing methods—such as sequential convex programming—often fail due to strong constraint coupling and large-scale nonconvexity. Method: We propose the first operator-splitting covariance-guided framework for stochastic optimal control, which decomposes the original nonconvex problem into tractable subproblems. Crucially, it permits intermediate iterates to relax chance constraints probabilistically, enhancing feasibility and convergence. The framework integrates covariance guidance, ADMM-type operator splitting, nonlinear stochastic optimal control, and exact chance-constraint handling. Results: In diverse robotic simulations, our method enforces stricter safety constraints and achieves superior performance compared to standard sequential convex programming. Hardware experiments further demonstrate its real-time deployability on embedded platforms.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Non-convex Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

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• Security and Privacy: Data transparency and provenance
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

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

Problem

• Solving nonlinear covariance steering with chance constraints efficiently
• Addressing feasibility issues in stochastic optimal control problems
• Improving solution quality under strict safety constraints

Innovation

• Operator splitting decouples problem into parallel subproblems
• Relaxation allows intermediate iterates to violate constraints temporarily
• Method improves feasibility and solution quality in non-convex settings