Statistical Contraction for Chance-Constrained Trajectory Optimization of Non-Gaussian Stochastic Systems

TL;DR

This paper introduces a distribution-free, statistically guaranteed method for robust trajectory optimization of nonlinear, non-Gaussian stochastic systems using conformal inference, enabling safe motion planning without distributional assumptions.

Contribution

It develops a novel conformal inference-based framework for chance-constrained control that provides finite-sample guarantees and applies to learning-based motion planners.

Findings

Successfully applied to motion planning in simulations.

Validated approach with hardware experiments.

Achieved safe, dynamically feasible trajectories.

Abstract

This paper presents novel method for distribution-free robust trajectory optimization and control of discrete-time, nonlinear, and non-Gaussian stochastic systems, with closed-loop guarantees on chance constraint satisfaction. Our framework employs conformal inference to generate coverage-based confidence sets for the closed-loop dynamics around arbitrary reference trajectories, by constructing a joint nonconformity score to quantify both the validity of contraction (i.e., incremental stability) conditions and the impact of external stochastic disturbance on the closed-loop dynamics, without any distributional assumptions. Via appropriate constraint tightening, chance constraints can be reformulated into tractable, statistically valid deterministic constraints on the reference trajectories. This enables a formal pathway to leverage and validate learning-based motion planners and controllers, such as those with neural contraction metrics, in safety-critical real-world applications. Notably, our statistical guarantees are non-diverging and can be computed with finite samples of the underlying uncertainty, without overly conservative structural priors. We demonstrate our approach in motion planning problems for designing safe, dynamically feasible trajectories in both numerical simulation and hardware experiments.