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

Motion planning for robotic manipulators is a fundamental problem in robotics. Classical optimization-based methods typically rely on the gradients of signed distance fields (SDF) 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 SDF, CDFs are differentiable almost everywhere and thus pro- vide 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 avoid- ance. While effective, these methods are computationally expen- sive 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 the CDF representation 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 con- trol 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.