实时避障机械臂运动规划，用并行计算提升响应速度

Real-time and collision-free motion planning remains challenging for robotic manipulation in unknown environments due to continuous perception updates and the need for frequent online replanning. To address these challenges, we propose a parallel mapping and motion planning framework that tightly integrates Euclidean Distance Transform (EDT)-based environment representation with a sampling-based model predictive control (SMPC) planner. On the mapping side, a dense distance-field-based representation is constructed using a GPU-based EDT and augmented with a robot-masked update mechanism to prevent false self-collision detections during online perception. On the planning side, motion generation is formulated as a stochastic optimization problem with a unified objective function and efficiently solved by evaluating large batches of candidate rollouts in parallel within a SMPC framework, in which a geometrically consistent pose tracking metric defined on SE(3) is incorporated to ensure fast and accurate convergence to the target pose. The entire mapping and planning pipeline is implemented on the GPU to support high-frequency replanning. The effectiveness of the proposed framework is validated through extensive simulations and real-world experiments on a 7-DoF robotic manipulator. More details are available at: https://zxw610.github.io/ParaMaP.