Data-Driven Motion Planning for Uncertain Nonlinear Systems

TL;DR

This paper introduces a data-driven motion planning method for nonlinear systems that constructs invariant polytopes around sampled waypoints, ensuring safe and feasible paths without relying on explicit system models.

Contribution

The paper presents a novel data-driven framework that constructs invariant polytopes and computes control gains directly from data, bypassing the need for explicit system dynamics models.

Findings

Successfully plans safe paths for nonlinear systems in simulations.

Demonstrates invariant polytopes ensure system safety during motion.

Real-time control gains interpolation maintains system within safe regions.

Abstract

This paper proposes a data-driven motion-planning framework for nonlinear systems that constructs a sequence of overlapping invariant polytopes. Around each randomly sampled waypoint, the algorithm identifies a convex admissible region and solves data-driven linear-matrix-inequality problems to learn several ellipsoidal invariant sets together with their local state-feedback gains. The convex hull of these ellipsoids, still invariant under a piece-wise-affine controller obtained by interpolating the gains, is then approximated by a polytope. Safe transitions between nodes are ensured by verifying the intersection of consecutive convex-hull polytopes and introducing an intermediate node for a smooth transition. Control gains are interpolated in real time via simplex-based interpolation, keeping the state inside the invariant polytopes throughout the motion. Unlike traditional approaches that rely on system dynamics models, our method requires only data to compute safe regions and design state-feedback controllers. The approach is validated through simulations, demonstrating the effectiveness of the proposed method in achieving safe, dynamically feasible paths for complex nonlinear systems.