Collectively Rotating Formation and Containment Deployment of Multiagent Systems: A Polar Coordinate-Based Finite Time Approach

This paper investigates the problem of achieving rotating formation and containment simultaneously via finite time control schemes for multiagent systems. It is nontrivial to maintain rotating formation where the desired formation structure is time-varying and only neighboring information is available. The underlying problem becomes even more complicated if containment is imposed yet finite time convergence is required at the same time. To tackle this problem, a polar coordinate-based approach is exploited in this paper. Finite time control protocols are established for leader agents and follower agents, respectively, such that three goals are achieved in finite time concurrently: 1) all the agents maintain a stable rotating motion around a common circular center with a common (possibly time-varying) angular velocity; 2) the leader agents form and maintain a prespecified rotating formation structure; and 3) the follower agents converge to the shifting convex hull shaped by the dynamically moving (circling) leaders. It is the polar coordinate expression that simplifies the formulation of the rotating formation-containment problem and facilitates the finite time control design process. The effectiveness of the proposed control scheme is illustrated via both formative mathematical analysis and numerical simulation.