EQM-MPD EQUIVARIANT ON-MANIFOLD MOTION PLANNING DIFFUSION

Fast, reliable and versatile motion planning algorithms are essential for robots with many degrees of freedom in complex, dynamic environments. Diffusion models have been proposed as a faster alternative to classical planners by providing informative priors on distributions of trajectories. However, they are currently trained to overfit to environments with fixed object configurations and need to be re-trained when these conditions change. This limits applicability in tasks like robotic manipulation where environments change dynamically and initial configurations vary. We show that diffusion-guidance is not sufficient to adapt the model to large changes that can happen during execution or even from different initialization. Moreover, current approaches ignore the underlying topology of the state space thus requiring heavy guidance that dominates planning time and reduces efficiency dramatically. To address these, we propose a novel diffusion motion planner, EqM-MPD that operates directly on the robot's state space manifold and produces an equivariant prior distribution on trajectories. Our approach eliminates the need for retraining under rigid transformations. Moreover, our diffusion on state space manifold converges faster during guidance. We show that our approach achieves efficient, robust and generalizable planning that is especially useful for manipulation advancing beyond prior limitations.