graph of mutual reachable sets

The 'graph of mutual reachable sets' is a novel data structure introduced to address the challenge of achieving optimal plans in contact-rich manipulation (CRM). Unlike traditional model-based planners that prioritize feasibility, this approach focuses on optimality. It works by first constructing this graph offline, where each node represents a 'mutual reachable set' – a collection of all possible object orientations attainable from a given initial object orientation and grasp. In the subsequent online phase, a planner navigates this precomputed graph to sequence local motions into a globally optimized trajectory. This methodology is crucial for robotics and automation, particularly in tasks requiring complex interactions between a manipulator and its environment, as it enables more efficient and natural manipulation by fully exploiting the advantages of CRM, making globally optimized contact-rich manipulation practical for real-world applications.