Safe robot motion generation is critical for practical applications from manufacturing to homes. In this work, we proposed a stochastic optimization-based motion generation method to generate collision-free and time-optimal motion for the articulated robot represented by composite signed distance field (SDF) networks. First, we propose composite SDF networks to learn the SDF for articulated robots. The learned composite SDF networks combined with the kinematics of the robot allow for quick and accurate estimates of the minimum distance between the robot and obstacles in a batch fashion. Then, a stochastic optimization-based trajectory planning algorithm generates a spatial-optimized and collision-free trajectory offline with the learned composite SDF networks. This stochastic trajectory planner is formulated as a Bayesian Inference problem with a time-normalized Gaussian process prior and exponential likelihood function. The Gaussian process prior can enforce initial and goal position constraints in Configuration Space. Besides, it can encode the correlation of waypoints in time series. The likelihood function aims at encoding task-related cost terms, such as collision avoidance, trajectory length penalty, boundary avoidance, etc. The kernel updating strategies combined with model-predictive path integral (MPPI) is proposed to solve the maximum a posteriori inference problems. Lastly, we integrate the learned composite SDF networks into the trajectory planning algorithm and apply it to a Franka Emika Panda robot. The simulation and experiment results validate the effectiveness of the proposed method.

翻译：安全机器人运动生成从制造业到家庭应用均至关重要。本文提出一种基于随机优化的运动生成方法，为通过组合符号距离场网络表示的关节型机器人生成无碰撞且时间最优的运动。首先，我们提出组合符号距离场网络以学习关节型机器人的符号距离场。学习得到的组合符号距离场网络与机器人运动学相结合，能够快速准确批量估计机器人与障碍物之间的最小距离。然后，基于随机优化的轨迹规划算法利用学习后的组合符号距离场网络离线生成空间优化且无碰撞的轨迹。该随机轨迹规划器被公式化为一个贝叶斯推断问题，采用时间归一化高斯过程先验和指数似然函数。高斯过程先验能够强制实现配置空间中的初始位置与目标位置约束，并能编码时间序列中路径点的相关性。似然函数旨在编码与任务相关的代价项，如避碰、轨迹长度惩罚、边界规避等。结合模型预测路径积分，提出核更新策略以解决最大后验推断问题。最后，我们将学习后的组合符号距离场网络集成到轨迹规划算法中，并在Franka Emika Panda机器人上应用该方法。仿真与实验结果验证了所提方法的有效性。