GPD: Guided Polynomial Diffusion for Motion Planning

2025-01-30

AI Summary

Diffusion models for robot motion planning suffer from slow inference (due to multi-step denoising), inefficient gradient guidance, and difficulty balancing trajectory diversity with collision avoidance. To address these bottlenecks, this work introduces a novel diffusion paradigm operating in the trajectory parameter space—specifically, the Bernstein polynomial coefficient space—to enable compact, differentiable trajectory representation. We further propose a single-model trajectory stitching algorithm grounded in diffusion-based diversity, which jointly incorporates cost-function gradient guidance and explicit collision constraints to generate collision-free trajectories while preserving diversity. Extensive evaluation demonstrates substantial improvements over state-of-the-art diffusion-based planners: on robotic arm tasks, our method achieves a 2.1× speedup in inference time and a 12.7% increase in success rate. Ablation studies confirm the effectiveness of each component.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Computer Vision: Diffusion Models for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• Diffusion-based Motion Planners
• Learning Efficiency
• Path Optimization

Innovation

• Bernstein coefficients
• trajectory parameter space
• enhanced learning efficiency