Robust distributed algorithm for building closed-chain formations by homogeneous robotic teams, with establishing informational connectivity

A homogeneous team of an unknown size consists of indiscernible mobile robots that carry no communication facilities and cannot play distinct roles and so should be driven a common control rule. The state of any robot is partly described by the value of its output variable, which is scalar and cyclic, like, e.g., an angular measure; the length of the cycle is unknown in general. Robots with complex second-order dynamics and uncertainties are treated, their speeds and control signals are confined within a priori bounds. Every robot has access only to its own speed and to the relative outputs of any peer that is within a finite “visibility range” if nothing “obscures” the view to the peer. A distributed continuous-time computationally cheap protocol is offered that achieves a situation where the outputs of the robots are evenly distributed over the cycle and evolve according to a given common speed profile. This protocol does not use the neighbor’s relative speeds, ensures theoretically exact convergence to the targeted deployment, succeeds in the absence of the initial informational connectivity of the team, is robust against losses and insertions of team members, and excludes collisions among the robots. These findings are illustrated via application to a platoon of wheeled robots performing a sentry mission on a rough terrain with unknown and unpredictably changing road conditions. The proposed algorithm is justified by a mathematically rigorous convergence result; its performance is confirmed by computer simulation tests.