Statistical Contraction for Chance-Constrained Trajectory Optimization of Non-Gaussian Stochastic Systems
Rihan Aaron D’Silva and Hiroyasu Tsukamoto
AI summary
Problem
Chance-constrained trajectory optimization for nonlinear systems typically requires restrictive distributional assumptions or intractable computations, leaving a gap in providing closed-loop probabilistic guarantees for non-Gaussian stochastic dynamics.
Approach
The method uses weighted conformal prediction to construct finite-sample confidence sets around learned contraction metrics and tracking policies, then applies constraint tightening to reformulate probabilistic requirements into deterministic optimization conditions.
Key results
- Constructs distribution-free confidence sets for closed-loop dynamics using weighted conformal prediction
- Defines a joint nonconformity score to quantify contraction validity and disturbance impact
- Reforms chance constraints into tractable deterministic constraints via constraint tightening
- Validates closed-loop constraint satisfaction on Dubins car simulations and Crazyflie drone hardware
Why it matters
Enables rigorous, data-driven safety certification for learning-based motion planners in safety-critical robotic applications without relying on parametric noise models.
Abstract
We present a distribution-free approach to robust trajectory optimization and control of discrete-time, nonlinear, and non-Gaussian stochastic systems, with closed-loop guaran- tees on chance constraint satisfaction. Our framework employs conformal inference to generate coverage-based confidence sets for the closed-loop dynamics around arbitrary reference trajectories under uncertainty. It thereby constructs 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 tight- ening, chance constraints can be reformulated into tractable, statistically valid deterministic constraints on the reference trajectories. This enables a formal pathway to certify the performance of 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 simulations and hardware experiments.