让机器人路径规划不依赖固定分辨率，实现跨分辨率零样本泛化。
Function-Space Diffusion for Motion Planning
- 将轨迹建模为连续函数，在函数空间直接进行扩散生成。
- 在16倍更高分辨率下仍保持一致规划效果，无需重新训练。
- 适合需要灵活适应不同计算精度的机器人控制场景。
基于扩散的运动规划方法在复杂环境中能生成多样且高质量的机器人轨迹，但现有方法通常依赖固定长度的路径点序列，导致模型受分辨率限制，无法实现零样本跨分辨率泛化。本文提出函数空间扩散运动规划（FSD-MP），将轨迹视为连续函数，在函数空间中直接执行扩散过程，实现离散化无关的轨迹生成。我们在频域定义了基于马特恩型协方差的逐模式前向过程，并用边界兼容的离散正弦变换傅里叶神经算子（DST-FNO）参数化反向过程，确保起点与目标约束在不同分辨率下均保持一致。在2D点机器人和7自由度Franka机械臂规划基准上评估，该方法在训练分辨率下表现优异，并在高达16倍更高的分辨率下实现零样本泛化，保持稳定的规划行为而无需重训。结果表明，函数空间扩散为离散化无关的运动规划提供了有效框架。
原文摘要 · Abstract (English)
Diffusion-based motion planners have demonstrated strong performance in generating diverse and high-quality robot trajectories in cluttered environments with multiple feasible solutions. However, existing approaches typically operate on fixed-length waypoint sequences, making the learned model resolution-dependent, thereby preventing zero-shot generalization across resolutions. In this work, we propose Function-Space Diffusion for Motion Planning (FSD-MP), a diffusion-based motion planner that models trajectories as continuous functions and performs diffusion directly in function space, achieving discretization-invariant trajectory generation. We define a mode-wise forward process in the spectral domain, driven by Gaussian noise with a Matérn-type covariance, and parameterize the reverse process with a boundary-compatible Discrete Sine Transform-based Fourier Neural Operator (DST-FNO) that preserves start-goal constraints across resolutions. We evaluate FSD-MP on 2D point robot and 7-DoF Franka manipulator planning benchmarks. Our method achieves competitive planning performance at the training resolution and generalizes zero-shot across resolutions up to 16$\times$ higher, preserving consistent planning behavior without retraining. These results demonstrate that function-space diffusion provides an effective framework for discretization-invariant motion planning.
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