Stabilization of collective formations with speed and controller gain heterogeneity and saturation

This paper studies collective formations of multi-agent systems, modeled with unicycle dynamics, while admitting heterogeneity in both controller gains and speeds of the agents along with saturation on the controller outputs. This addresses a practical scenario where the speeds are usually nonidentical and the controller gains may vary due to imperfect implementation. The paper analyzes the effect of both heterogeneous controller gains and speeds simultaneously on the collective formations obtained by optimizing the average linear momentum of the group of agents. A detailed analysis of the two-agent system is given in the paper and some results on the locus of the collective centroid with varying controller gains are obtained. Effect of saturation is also studied for two cases when the controller gains are bounded and when the control efforts are bounded. Simulation examples are given to illustrate the theoretical findings.