Fall in! Sorting a Group of Robots with a Continuous Controller

This paper describes the first robotic system that solves a combinatorial computational problem by means of its own continuous dynamics. The goal of the system is to rearrange a set of robots on a line in a certain predefined order, thereby sorting them. Conventional pairwise between-robot rank comparisons suggested by traditional discrete state sorting algorithms are avoided by coupling robots in a Brockett double bracket flow system. A conventional multi-robot simulation with non-holonomic driving, noisy sensor data, collision avoidance and sensor occlusions suggests that this flow system can withstand perturbations introduced into the ideal dynamics by the physical limitations of real robots.