We present a novel 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 an initial application for evaluating our method, we apply it 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, without relying on an initial guess, and that our method succeeds in finding trajectories where a state-of-the-art baseline for contact-rich planning usually fails. We demonstrate the quality of these plans on a real robotic system.

翻译：本文提出了一种新颖的机器人系统全局运动规划方法，适用于通过接触与环境交互的场景。该方法利用凸优化工具直接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接触序列，而凸集则用于建模固定接触模式下的准静态动力学。针对每种接触模式，我们采用半定规划来松弛由物体位姿、接触位置和接触力同时优化导致的非凸动力学问题。由此得到整体规划问题的紧凸松弛形式，该形式可高效求解并快速舍入以获得可行的接触密集型轨迹。作为评估本方法的初步应用，我们将其应用于平面推动任务。大量实验表明：我们的凸优化方法生成的规划方案始终保持在全局最优解的小百分比范围内，且无需依赖初始猜测；在接触密集型规划任务中，当现有先进基线方法通常失效时，本方法仍能成功找到轨迹。我们在真实机器人系统上验证了这些规划方案的质量。