Data-Driven Motion Planning for Uncertain Nonlinear Systems

This article presents a data-driven motion-planning framework for nonlinear systems based on constructing a sequence of overlapping invariant polytopes. The planner randomly generates waypoints, and around each sampled waypoint, it learns a locally invariant polytopic safe set together with a corresponding local state-feedback gain. Each invariant polytope is obtained as the convex hull of a collection of invariant ellipsoids induced by a piecewise-affine controller. Safe and smooth transitions between waypoints are ensured by introducing an intermediate waypoint. 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 by comparing against a containment-based invariant-ellipsoid baseline and reporting planning time, sampling effort, and trajectory quality, demonstrating safe and dynamically feasible navigation in complex environments.