A Game-Based Approach to Distributed Least-Distance Formation Tracking With a Moving Target

This paper is concerned with game-based distributed least-distance formation tracking with a moving target. More specifically, the agents aim to form a desired shape while enclosing a moving target with a least overall distance. Different from most of the existing results on formation tracking, the key challenge for least-distance formation tracking under consideration is that the distances between the agents and the target are not required to be predefined but are autonomously adjusted by solving a distance optimization problem. In particular, with the target being moving, the distance optimization problem is time-varying. To address this issue, a game-based formulation of distributed least-distance formation tracking is first presented, where first- and second-order integrator type agents are taken into account, respectively. Then, under the scenario in which all the agents know the position of the moving target, a new distributed Nash equilibrium seeking strategy that can be utilized to achieve distributed least-distance formation is constructed based on gradient search algorithms, regularization techniques and consensus protocols. Moreover, when it is further considered that only a subset of the agents can access the information of the moving target, a leader-following tracking protocol is introduced to estimate unknown information distributively. It is theoretically shown that the proposed strategies can globally steer the agents to form a desired shape while minimizing the overall distance to the moving target. Finally, the effectiveness of the established strategies is verified by respectively conducting simulation studies for a network of vehicles and quadrotors.