Formation Tracking Control of Multiagents in Constrained Space

In this paper, formation tracking control based on potential field is studied. The objective is to control a group of agents to track a desired trajectory while maintaining a given formation in nonomniscient constrained space. Aiming at this purpose, the average of all agents' positions is viewed as the virtual leader, and the task is translated into that controlling the virtual leader to track the center of the desired formation. The situation where agents may not have global environmental information will lead to that they may have to avoid collisions with unexpected spatial constraints. By introducing the concepts of line source and surface source, two main types of spatial constraints: 1) borders and 2) obstacles are defined mathematically and unified into a common expression in an artificial potential function. In this way, the tasks of formation tracking and obstacle avoidance in a bounded environment can be solved by the control law proposed in this paper. Furthermore, concerning the situation of multiple spatial constraints, a Dirac delta function is introduced. Meanwhile, a formation optimal algorithm is proposed to minimize the formation generation time cost. Following that, a controller is designed, and the conditions for asymptotic stability of multiagent systems are proved based on the Lyapunov function. The maximum duration that the conditions cannot be satisfied is elaborated to indicate whether the tracking task should be given up. Meanwhile, the impulsive influence from spatial constraints is analyzed. Finally, the simulation results are presented to illustrate the performance of proposed approaches.