Potential Based Diffusion Motion Planning

TL;DR

The paper introduces a diffusion-based potential motion planner that learns trajectory-level energy landscapes to enable efficient, gradient-based optimization for high-dimensional planning. By training an energy-based diffusion model E_θ with a denoising objective, the approach yields a globally-influenced energy landscape that reduces local minima issues and enables composition of multiple constraints through simple energy summation. It demonstrates probabilistic completeness under positive-density sampling and shows strong, scalable performance across base and composite environments, including static/dynamic obstacles and real-world pedestrian datasets. The results indicate significant improvements in success rate, planning time, and collision checks compared to both classical and learning-based planners, with robust generalization via compositionality. Practical impact includes faster, more flexible planning in robotics settings with evolving constraints and multi-agent environments.

Abstract

Effective motion planning in high dimensional spaces is a long-standing open problem in robotics. One class of traditional motion planning algorithms corresponds to potential-based motion planning. An advantage of potential based motion planning is composability -- different motion constraints can be easily combined by adding corresponding potentials. However, constructing motion paths from potentials requires solving a global optimization across configuration space potential landscape, which is often prone to local minima. We propose a new approach towards learning potential based motion planning, where we train a neural network to capture and learn an easily optimizable potentials over motion planning trajectories. We illustrate the effectiveness of such approach, significantly outperforming both classical and recent learned motion planning approaches and avoiding issues with local minima. We further illustrate its inherent composability, enabling us to generalize to a multitude of different motion constraints.

Figures (20)

• Figure 1: Illustrative Example of Composing Diffusion Energy Potentials. Our approach learns different potential functions over motion planning trajectories $q_{1:N}$ (orange dashed lines). Different potentials can be combined and optimized to construct new motion plans that avoid obstacles encoded in both potential functions.
• Figure 2: Trajectory Denoising Process. The trajectory is randomly initialized from Gaussian in timestep $S = 100$. Noise is iteratively removed via the gradient of the energy function as given in equation \ref{['eqn:diffusion_opt']}. A feasible trajectory can be obtained at timestep $S = 0$.
• Figure 3: Visualization of the Motion Refining Scheme. A proposal plan is first generated by denoising an initial Gaussian noise. If collision is detected, a small noise is added to the proposal and the new plan is generated by denoising the partially noisy trajectory.
• Figure 4: Environment Demonstration. Maze2D: a point robot moving in 2D workspace with the highlighted blocks as obstacles. KUKA: robotic arm with 7 DoF operating on a tabletop. The grey cuboids are obstacles. Dual KUKA 14D: Two side by side KUKA arms operate simultaneously.
• Figure 5: Quantitative Comparisons in Motion Planning Environments. Three metrics of three environments from 2D to 14D are reported. From left to right: a) number of collision checks, b) success rate, c) planning time.