GPD: Guided Polynomial Diffusion for Motion Planning

TL;DR

This paper introduces GPD, a guided polynomial diffusion method for motion planning that enhances inference speed and guidance effectiveness by operating in the Bernstein coefficient space and employs a stitching algorithm for collision-free trajectories.

Contribution

It proposes a novel diffusion in parametric trajectory space using Bernstein coefficients and a stitching algorithm, improving speed and guidance in diffusion-based motion planning.

Findings

Outperforms current SOTA diffusion-based motion planners for manipulators.

Enables collision-free trajectory generation with a single cost-guided model.

Provides an ablation study on key components of the approach.

Abstract

Diffusion-based motion planners are becoming popular due to their well-established performance improvements, stemming from sample diversity and the ease of incorporating new constraints directly during inference. However, a primary limitation of the diffusion process is the requirement for a substantial number of denoising steps, especially when the denoising process is coupled with gradient-based guidance. In this paper, we introduce, diffusion in the parametric space of trajectories, where the parameters are represented as Bernstein coefficients. We show that this representation greatly improves the effectiveness of the cost function guidance and the inference speed. We also introduce a novel stitching algorithm that leverages the diversity in diffusion-generated trajectories to produce collision-free trajectories with just a single cost function-guided model. We demonstrate that our approaches outperform current SOTA diffusion-based motion planners for manipulators and provide an ablation study on key components.