用神经微分方程实现任意起点终点的安全运动规划
Goal-Conditioned Neural ODEs with Guaranteed Safety and Stability for Learning-Based All-Pairs Motion Planning
- 通过双李普希茨微分同胚构建目标条件神经微分方程
- 保证全局指数稳定与安全集前向不变性，收敛速度有界
- 适用于机器人路径规划，尤其适合需安全保障的场景
本文提出一种基于学习的全对运动规划方法，允许初始状态和目标状态为安全集中的任意点。通过双李普希茨微分同胚构建平滑的目标条件神经常微分方程（neural ODEs）。理论分析表明，该模型在任意目标位置下均能提供全局指数稳定性与安全性（安全集前向不变性）保证。同时，建立了收敛速率、跟踪误差和向量场模长的显式上界。所提方法可通过双李普希茨神经网络实现可训练的学习框架，并能融合示范数据。在二维走廊导航任务中验证了其有效性。
原文摘要 · Abstract (English)
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.
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