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.

翻译：设计通过接触实现操作的轨迹具有挑战性，因为它需要同时推理物体与机器人的轨迹以及复杂的接触序列。本文提出了一种新颖的框架，用于高效地同时设计接触丰富操作中机器人、物体及接触的轨迹。我们提出了一种分层优化框架：混合整数线性规划（MILP）在近似动力学约束下选择机器人与物体之间的最优接触，随后非线性规划（NLP）在考虑完整非线性约束的条件下优化机器人（们）及物体的轨迹。我们提出了一种使用二进制编码技术的双线性约束凸松弛方法，使得MILP能够以更优的计算复杂度提供更紧致的解。所提出的框架在多种操作任务上进行了评估，结果表明其能够在提供计算优势的同时推理复杂的多接触交互。我们还通过使用双手机器人系统的硬件实验验证了我们的框架。