Stable and collision-free manipulation of an elastic rod using multiple grippers

Despite the widespread adoption of robots in manufacturing, many tasks that involve handling and assembly of deformable objects are still completed manually. Automating these tasks requires reasoning about deformations, instabilities, and self-contact experienced by the deformable objects. As a canonical example of such a task, I will discuss the problem of deforming a slender elastic rod into a desired configuration using two or more robotic grippers that grasp the rod at multiple points. In the case when the grippers are required to grasp the rod at fixed arc lengths, I will show that the set of all equilibrium configurations of the rod that are stable is path-connected. If the grippers are allowed to slide along the rod, I will show that the set of all equilibrium configurations that are both stable and non-self-intersecting is path-connected. The proofs of these two results are constructive and provide analytical solutions that can be exploited when designing algorithms for automated handling of slender structures.