用伯恩斯坦系数表示轨迹，加速扩散模型运动规划并提升避障能力。
GPD: Guided Polynomial Diffusion for Motion Planning
- 在轨迹参数空间中使用伯恩斯坦系数进行扩散采样
- 仅需一次成本引导即可生成无碰撞路径，推理速度显著提升
- 适合机器人运动规划场景，尤其对实时性要求高的任务
基于扩散的运动规划方法因采样多样性及推理时可直接融入新约束而日益流行。然而，扩散过程通常需要大量去噪步骤，尤其当与梯度引导结合时更为明显。本文提出在轨迹参数空间中进行扩散，其中轨迹参数以伯恩斯坦系数表示。该表示显著提升了成本函数引导的有效性与推断速度。同时引入一种新颖的拼接算法，利用扩散生成轨迹的多样性，仅通过一次成本引导模型即可生成无碰撞路径。实验表明，该方法在机械臂运动规划上优于当前最先进扩散模型，并进行了关键组件的消融研究。
原文摘要 · Abstract (English)
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.
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