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.

翻译：机械臂运动规划是机器人学中的一个基本问题。经典的基于优化的方法通常依赖于符号距离场的梯度来施加避碰约束。然而，这些方法容易陷入局部极小值，并在符号距离场梯度消失时失效。近年来，配置空间距离场被引入，它直接在机器人的配置空间中建模距离。与工作空间符号距离场不同，配置空间距离场几乎处处可微，因此能提供可靠的梯度信息。另一方面，无梯度方法（如模型预测路径积分控制）利用长时域滚动生成轨迹来实现避碰。尽管有效，但由于需要大量轨迹样本、重复碰撞检测以及设计含异质物理单位的代价函数的困难，这些方法计算成本高昂。本文提出一个将配置空间距离场与模型预测路径积分相结合的框架，以实现机器人在其配置空间中的直接导航。利用配置空间距离场的梯度，我们将模型预测路径积分代价统一到关节空间，并将时域缩减至一步，从而大幅降低计算量，同时在实践中保持避碰能力。实验证明，我们的方法在二维环境中达到近100%的成功率，并在包含复杂障碍物的挑战性7自由度Franka机械臂仿真中持续保持高成功率。此外，该方法实现了超过750 Hz的控制频率，显著优于基于优化的方法和标准模型预测路径积分基线。这些结果凸显了所提出的CDF-MPPI框架在高维运动规划中的有效性和高效性。