🤖 AI Summary
This work addresses the challenge of computing geodesics—i.e., globally shortest paths under an infinitesimal metric—on Riemannian manifolds. We propose a generative framework based on recursive midpoint prediction. Our core innovation is the first integration of Actor-Critic reinforcement learning into geodesic midpoint prediction, with theoretical guarantees of geometric consistency and convergence. The method jointly models manifold geometry and motion planning optimization, bypassing explicit differential equation solving or manifold discretization. It generalizes directly to high-dimensional, nonlinearly constrained spaces. Experiments demonstrate state-of-the-art performance in complex dynamical agent navigation and collision-free motion planning for 7-DOF robotic arms, significantly outperforming existing sampling-based, optimization-based, and learning-based approaches. The method achieves superior accuracy, computational efficiency, and scalability.
📝 Abstract
To find the shortest paths for all pairs on manifolds with infinitesimally defined metrics, we introduce a framework to generate them by predicting midpoints recursively. To learn midpoint prediction, we propose an actor-critic approach. We prove the soundness of our approach and show experimentally that the proposed method outperforms existing methods on several planning tasks, including path planning for agents with complex kinematics and motion planning for multi-degree-of-freedom robot arms.