Data-Driven Motion Planning for Uncertain Nonlinear Systems

2025-07-31

AI Summary

This paper addresses safe motion planning for uncertain nonlinear systems without requiring an explicit system dynamics model. The proposed fully data-driven framework constructs a sequence of overlapping ellipsoidal invariant sets via random sampling; learns local state-feedback gains for each set from data; and synthesizes a piecewise affine controller using convex-hull approximations and simplex interpolation to guarantee invariance. An intermediate-node insertion strategy ensures safe transitions between path segments. The key contribution is the first integration of data-driven LMI solving, ellipsoidal invariant set learning, and interpolation-based piecewise control within a model-free motion planning paradigm. Simulation results demonstrate that the method efficiently generates trajectories that are safe, dynamically feasible, robust to uncertainties, and amenable to real-time implementation.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Security and Privacy: Data transparency and provenance

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.

Problem

• Data-driven motion planning for uncertain nonlinear systems
• Constructing invariant polytopes without system dynamics models
• Ensuring safe transitions via interpolated state-feedback controllers

Innovation

• Data-driven motion planning for nonlinear systems
• Invariant polytopes via convex admissible regions
• Simplex-based real-time gain interpolation