Reconfiguring Chain-Type Modular Robots Based on the Carpenter's Rule Theorem

Reconfiguring chain-type modular robots has been considered a difficult problem scaling poorly with increasing numbers of modules. We address the reconfiguration problem for robots in 2D by presenting centralized and decentralized algorithms based on the Carpenter’s Rule Theorem [5]. The theorem guarantees the existence of instantaneous collision-free unfolding motions which monotonically increase the distance between all joint pairs until an open chain is straightened or a closed chain is convexified. The motions can be found by solving a convex program. Compared to the centralized version, the decentralized algorithm utilizes local proximity sensing and limited communications between subsets of nearby modules. Because the decentralized version reduces the number of joint pairs considered in each convex optimization, it is a practical solution when run in parallel for large numbers of modules.