Optimal deployment of heterogeneous mobile agents on a circle

In this paper optimal deployment of a network of mobile agents with different maximum traveling speed is considered, where the agents are constrained to move on a circle. The goal is to drive the multi-agent network to final configurations such that the shortest arrival time from the mobile agents to any point on the circle is minimized. A necessary and sufficient condition for optimal network configuration is firstly given. Then, distributed control laws are developed to drive the mobile agents to the optimal configuration. Finally, the results are extended to the case of mobile agents with identical maximum speed. A simulation example is also provided to illustrate the effectiveness of the proposed algorithm.