One-Step Model Predictive Path Integral for Manipulator Motion Planning Using Configuration Space Distance Fields

摘要

Motion planning for robotic manipulators is a fundamental problem in robotics. Classical optimization-based methods typically rely on the gradients of signed distance fields (SDFs) to impose collision-avoidance constraints. However, these methods are susceptible to local minima and may fail when the SDF gradients vanish. Recently, Configuration Space Distance Fields (CDFs) have been introduced, which directly model distances in the robot's configuration space. Unlike workspace SDFs, CDFs are differentiable almost everywhere and thus provide reliable gradient information. On the other hand, gradient-free approaches such as Model Predictive Path Integral (MPPI) control leverage long-horizon rollouts to achieve collision avoidance. While effective, these methods are computationally expensive due to the large number of trajectory samples, repeated collision checks, and the difficulty of designing cost functions with heterogeneous physical units. In this paper, we propose a framework that integrates CDFs with MPPI to enable direct navigation in the robot's configuration space. Leveraging CDF gradients, we unify the MPPI cost in joint-space and reduce the horizon to one step, substantially cutting computation while preserving collision avoidance in practice. We demonstrate that our approach achieves nearly 100% success rates in 2D environments and consistently high success rates in challenging 7-DOF Franka manipulator simulations with complex obstacles. Furthermore, our method attains control frequencies exceeding 750 Hz, substantially outperforming both optimization-based and standard MPPI baselines. These results highlight the effectiveness and efficiency of the proposed CDF-MPPI framework for high-dimensional motion planning.