We present a method for global motion planning of robotic systems that interact with the environment through contacts. Our method directly handles the hybrid nature of such tasks using tools from convex optimization. We formulate the motion-planning problem as a shortest-path problem in a graph of convex sets, where a path in the graph corresponds to a contact sequence and a convex set models the quasi-static dynamics within a fixed contact mode. For each contact mode, we use semidefinite programming to relax the nonconvex dynamics that results from the simultaneous optimization of the object's pose, contact locations, and contact forces. The result is a tight convex relaxation of the overall planning problem, that can be efficiently solved and quickly rounded to find a feasible contact-rich trajectory. As a first application of this technique, we focus on the task of planar pushing. Exhaustive experiments show that our convex-optimization method generates plans that are consistently within a small percentage of the global optimum. We demonstrate the quality of these plans on a real robotic system.

翻译：本文提出了一种用于机器人系统通过接触与环境交互的全局运动规划方法。我们的方法直接利用凸优化工具处理此类任务的混合特性。我们将运动规划问题表述为凸集图上的最短路径问题，其中图中的路径对应一个接触序列，而凸集则对固定接触模式内的准静态动力学进行建模。对于每种接触模式，我们使用半定规划来松弛由物体位姿、接触位置和接触力同步优化所导致的非凸动力学。最终得到整个规划问题的紧凸松弛，该松弛可高效求解并快速取整以找到可行的接触丰富轨迹。作为该技术的首次应用，我们聚焦于平面推动任务。大量实验表明，我们的凸优化方法生成的规划结果始终与全局最优解保持在很小的偏差范围内。我们在真实机器人系统上验证了这些规划的质量。