Conformal Constraint Tightening for Chance-Constrained Motion Planning with Unknown Dynamics

2026-07-24

AI Summary

Existing motion planning approaches struggle to guarantee task success probabilities on real systems when the underlying dynamics are unknown or inaccurately modeled. This work proposes a planner-agnostic constraint tightening framework that, for the first time, integrates conformal prediction into chance-constrained motion planning. By establishing distribution-free probabilistic bounds on the deviation between trajectories generated by a nominal model and those of the true system, the method dynamically tightens planning constraints without requiring an accurate dynamics model. Consequently, trajectories planned using only the nominal model provably ensure task completion on the real system with a user-specified probability. Theoretical analysis and empirical evaluations demonstrate that the proposed approach significantly improves real-world task success rates across diverse task distributions, outperforming baseline methods that rely solely on nominal models.

Abstract

Motion planning algorithms compute control sequences that drive autonomous robots to goal regions while avoiding unsafe states. Existing methods, from sampling-based planning to deep reinforcement learning, typically provide task-completion guarantees only with respect to a nominal model or simulator, which may be invalidated when the true dynamics are unknown or difficult to model accurately. This letter addresses this limitation for systems with unknown dynamics and an available approximate nominal model, contributing a planner-agnostic constraint-tightening procedure that equips existing planners with a probabilistic task-completion guarantee on the true system. We leverage conformal prediction to provide a probabilistic bound on the nominal-to-true trajectory deviation over a distribution of planning problems. We tighten the planning constraints using that bound, and show that solving the tightened problem under the nominal model is a sufficient condition for solving the original problem on the true system with a prescribed probability. We validate the theoretical guarantees empirically and demonstrate substantially improved task completion relative to nominal-model planning.

Problem

• chance-constrained
• motion planning
• unknown dynamics
• conformal prediction
• constraint tightening

Innovation

• conformal prediction
• chance-constrained planning
• constraint tightening
• unknown dynamics
• probabilistic guarantees