Goal-Conditioned Neural ODEs with Guaranteed Safety and Stability for Learning-Based All-Pairs Motion Planning
This provides a safe and stable learning-based solution for motion planning tasks where initial and goal states are arbitrary, though it is incremental as it builds on existing neural ODE and bi-Lipschitz network methods.
The paper tackles the problem of all-pairs motion planning by constructing goal-conditioned neural ODEs with bi-Lipschitz diffeomorphisms, achieving guarantees of global exponential stability and safety with explicit bounds on convergence rate and tracking error.
This paper presents a learning-based approach for all-pairs motion planning, where the initial and goal states are allowed to be arbitrary points in a safe set. We construct smooth goal-conditioned neural ordinary differential equations (neural ODEs) via bi-Lipschitz diffeomorphisms. Theoretical results show that the proposed model can provide guarantees of global exponential stability and safety (safe set forward invariance) regardless of goal location. Moreover, explicit bounds on convergence rate, tracking error, and vector field magnitude are established. Our approach admits a tractable learning implementation using bi-Lipschitz neural networks and can incorporate demonstration data. We illustrate the effectiveness of the proposed method on a 2D corridor navigation task.