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

arXiv: https://arxiv.org/abs/2603.07092 · HTML: https://mlsanity.com/paper/2603.07092/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 47 references that are in the map.
- First posted on arXiv 7 Mar 2026.

## Builds on (most cited first, 29 of 29)

- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Learning-based Model Predictive Control for Safe Exploration](https://mlsanity.com/paper/1803.08287/) (2018)
- [Safe Planning in Dynamic Environments using Conformal Prediction](https://mlsanity.com/paper/2210.10254/) (2022)
- [Cautious Model Predictive Control using Gaussian Process Regression](https://mlsanity.com/paper/1705.10702/) (2017)
- [Adaptive Conformal Prediction for Motion Planning among Dynamic Agents](https://mlsanity.com/paper/2212.00278/) (2022)
- [Learning Certified Control using Contraction Metric](https://mlsanity.com/paper/2011.12569/) (2020)
- [Contraction Theory for Nonlinear Stability Analysis and Learning-based Control: A Tutorial Overview](https://mlsanity.com/paper/2110.00675/) (2021)
- [Control Contraction Metrics: Convex and Intrinsic Criteria for Nonlinear Feedback Design](https://mlsanity.com/paper/1503.03144/) (2015)
- [Formal Verification and Control with Conformal Prediction](https://mlsanity.com/paper/2409.00536/) (2024)
- [The Scenario Approach for Stochastic Model Predictive Control with Bounds on Closed-Loop Constraint Violations](https://mlsanity.com/paper/1307.5640/) (2013)
- [Neural Contraction Metrics for Robust Estimation and Control: A Convex Optimization Approach](https://mlsanity.com/paper/2006.04361/) (2020)
- [Distributionally Robust Chance Constrained Data-enabled Predictive Control](https://mlsanity.com/paper/2006.01702/) (2020)
- [Safe Perception-Based Control under Stochastic Sensor Uncertainty using Conformal Prediction](https://mlsanity.com/paper/2304.00194/) (2023)
- [Safe Feedback Motion Planning: A Contraction Theory and L1-Adaptive Control Based Approach](https://mlsanity.com/paper/2004.01142/) (2020)
- [Statistical Safety and Robustness Guarantees for Feedback Motion Planning of Unknown Underactuated Stochastic Systems](https://mlsanity.com/paper/2212.06874/) (2022)
- [Dynamic Tube MPC for Nonlinear Systems](https://mlsanity.com/paper/1907.06553/) (2019)
- [Optimal Covariance Control for Stochastic Systems Under Chance Constraints](https://mlsanity.com/paper/1804.02829/) (2018)
- [Safety-Critical Control with Uncertainty Quantification using Adaptive Conformal Prediction](https://mlsanity.com/paper/2407.03569/) (2024)
- [Conformal Predictive Programming for Chance Constrained Optimization](https://mlsanity.com/paper/2402.07407/) (2024)
- [Conformal Prediction for Distribution-free Optimal Control of Linear Stochastic Systems](https://mlsanity.com/paper/2411.19132/) (2024)
- [Trajectory Optimization of Chance-Constrained Nonlinear Stochastic Systems for Motion Planning Under Uncertainty](https://mlsanity.com/paper/2106.02801/) (2021)
- [Recursively Feasible Stochastic Model Predictive Control using Indirect Feedback](https://mlsanity.com/paper/1812.06860/) (2018)
- [Predictive control for nonlinear stochastic systems: Closed-loop guarantees with unbounded noise](https://mlsanity.com/paper/2407.13257/) (2024)
- [Statistical Guarantees in Data-Driven Nonlinear Control: Conformal Robustness for Stability and Safety](https://mlsanity.com/paper/2506.06228/) (2025)
- [Discrete-time Contraction-based Control of Nonlinear Systems with Parametric Uncertainties using Neural Networks](https://mlsanity.com/paper/2105.05432/) (2021)
- [Distributionally Robust Model Predictive Control with Total Variation Distance](https://mlsanity.com/paper/2203.12062/) (2022)
- [Uncertainty-aware Safe Exploratory Planning using Gaussian Process and Neural Control Contraction Metric](https://mlsanity.com/paper/2105.06567/) (2021)
- [Conformal Contraction for Robust Nonlinear Control with Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2507.13613/) (2025)

## Abstract (arXiv)

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.