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

2026-03-07

AI Summary

This work proposes a robust trajectory optimization and control method for nonlinear, non-Gaussian stochastic systems without distributional assumptions, ensuring satisfaction of chance constraints. By integrating conformal inference with neural contraction metrics, the approach constructs finite-sample coverage confidence sets for closed-loop dynamics and introduces a joint nonconformity score to unify the characterization of contraction efficacy and stochastic disturbance effects. Chance constraints are then conservatively tightened into tractable deterministic forms. This method represents the first integration of statistical contraction analysis with conformal inference, delivering non-conservative yet computable closed-loop safety guarantees without requiring prior knowledge of system distributions or structural assumptions. Simulations and hardware experiments demonstrate its effectiveness in generating dynamically feasible and safe trajectories in safety-critical scenarios.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Constraint Optimization
• Intelligent Robots: State Estimation

Application Category

• Security and Privacy: Large-scale security measurements
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

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.

Problem

• chance-constrained optimization
• non-Gaussian stochastic systems
• trajectory optimization
• distribution-free control
• closed-loop guarantees

Innovation

• conformal inference
• chance-constrained optimization
• contraction theory
• distribution-free control
• non-Gaussian stochastic systems