A distributed robust convergence algorithm for multi-robot systems in the presence of faulty robots

In this paper, we propose a distributed control policy to achieve rendezvous by a set of robots even when some robots in the system do not follow the prescribed policy. These nonconforming robots correspond to faults in the multi-robot systems, and our control policy is thus a fault-tolerant policy. We consider the case in which each robot is an autonomous decision maker that is anonymous (i.e., robots are indistinguishable to one another), memoryless (i.e., each robot makes decisions based upon only its current information), and dimensionless (i.e., collision checking is not considered). Each robot has a limited sensing range, and is able to directly estimate the state of only those robots within that sensing range, which induces a network topology for the multi-robot systems. We assume that it is not possible for the fault-free robots to identify the faulty robots (e.g., due to the anonymous property of the robots). Our main result is a practical algorithm that achieves approximate rendezvous in the face of faulty robots under a few assumptions on the network topology. In simulation results, we show that our algorithm performs better in the face of faulty robots than other contemporary convergence algorithms, e.g., the circumcenter law, and local coordinate averaging.