Designing trajectories for manipulation through contact is challenging as it requires reasoning of object \& robot trajectories as well as complex contact sequences simultaneously. In this paper, we present a novel framework for simultaneously designing trajectories of robots, objects, and contacts efficiently for contact-rich manipulation. We propose a hierarchical optimization framework where Mixed-Integer Linear Program (MILP) selects optimal contacts between robot \& object using approximate dynamical constraints, and then a NonLinear Program (NLP) optimizes trajectory of the robot(s) and object considering full nonlinear constraints. We present a convex relaxation of bilinear constraints using binary encoding technique such that MILP can provide tighter solutions with better computational complexity. The proposed framework is evaluated on various manipulation tasks where it can reason about complex multi-contact interactions while providing computational advantages. We also demonstrate our framework in hardware experiments using a bimanual robot system. The video summarizing this paper and hardware experiments is found https://youtu.be/s2S1Eg5RsRE?si=chPkftz_a3NAHxLq

本研究针对在进行接触丰富操控时设计轨迹面临的挑战，提出了一种新颖的分层优化框架，能够高效地同时设计机器人、物体和接触的轨迹。通过结合混合整数线性规划（MILP）和非线性规划（NLP），该框架在计算复杂度方面提供了优势，并在多种操作任务中证明了其在复杂多接触交互中的有效性。

基于紧凸松弛的多模态操作的分层接触丰富轨迹优化