Formation control using replicator–mutator dynamics for multiple mobile autonomous agents

We present a leader–follower formation control algorithm based on replicator–mutator dynamics and complex Laplacian. The networked multi-agent system is composed of several multiple mobile autonomous agents keeping its formation. Replicator–mutator dynamics are used to reach consensus of the formation, to assure a faster convergence time for a leader–follower formation, and to avoid potential collisions between followers. First, we calculate the normalized Laplacian matrix of the associated communication graph and develop a consensus algorithm based on replicator–mutator dynamics. Then, we determine the complex Laplacian matrix for a particular planar formation. Finally, we obtain the position of the followers and we draw a geometric formation in a defined trajectory. The algorithm may modify the consensus agreement by modifying the mutation strength and the value of strategies frequency in geometric formations and avoiding potential collisions between followers. The proposed control algorithm maintains the formation geometric in any path in the complex plane and can be used with an unlimited number of vehicles without modifying the algorithm. Simulations are presented to illustrate the effectiveness of our formation control algorithm.