面向接触丰富操作的紧凸松弛方法
Towards Tight Convex Relaxations for Contact-Rich Manipulation
AI总结：
本文提出一种基于凸集图和半定规划的紧凸松弛方法，用于解决接触丰富操作的全局运动规划问题，在平面推动任务中无需初始猜测即可高效获得接近全局最优的可行轨迹。
摘要：
我们提出了一种新颖的方法，用于对通过接触与环境交互的机器人系统进行全局运动规划。我们的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形式化为凸集图中的最短路径问题，其中图中的路径对应于接触序列，凸集对固定接触模式内的准静态动力学进行建模。对于每个接触模式，我们使用半定规划来松弛由物体位姿、接触位置和接触力的同时优化所产生的非凸动力学。结果是对整体规划问题的一个紧凸松弛，可以被高效求解并快速舍入以获得可行的接触丰富轨迹。作为评估我们方法的初步应用，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始终在全局最优值的一个小百分比范围内，且不依赖初始猜测，并且我们的方法能够在最先进的接触丰富规划基线通常失败的情况下成功找到轨迹。我们在真实机器人系统上展示了这些规划的质量。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
