Topology-Informed Quasi-Static Motion Planning for Continuum Robots With Contacts

Continuum robots (CR) can achieve excellent dexterity and flexibility, making them suitable for navigating through cluttered environments and safely interacting with obstacles. Due to the underactuated nature of CRs, the contact mode between the robot and environment affects the static robot configuration. We show that the configuration space topology induced by environmental obstacles can be characterized by a quotient structure with a quotient space consisting of zero-actuation configurations. We propose to use the quotient space as a road map for motion planning to reduce computational load for exploration. Specifically, we propose an algorithm that identifies the quotient space as a graph of configuration modes by constructing a graph of convex sets in the free workspace, conducting tree search and convex optimizations to find candidate configurations, and then using elastic energy minimization to find the modes. We then use a motion planner which finds a path in the quotient space graph and constructs a continuous path in the configuration space. We demonstrate our method in several complex 3D environments and show that our method outperforms baselines in terms of computation time and success rate.