Two-stage time-optimal formation reconfiguration strategy under acceleration and velocity constraints

In this paper, a two-stage time-optimal reconfiguration strategy for formation flying of autonomous agents under acceleration and velocity constraints is presented. In the proposed strategy, the agents are moved to a special designated formation in the time interval between the accomplishment of the last reconfiguration task and the issuance of the next reconfiguration command, referred to as the idle time. The special designated formation is obtained in such a way that the expected value of the reconfiguration time under the existing constraints is minimized. The problem of finding the special designated formation turns out to be non-convex. The previously reported results for the case of acceleration constraint only are shown to remain valid under the additional velocity constraint. An alternative search algorithm for finding the special designated formation is presented which consists of searching a vicinity of possible formations, which can even be skipped under certain conditions, and solving a convex non-differentiable optimization problem. This search algorithm is typically much faster than the one associated with the acceleration constraint only. A normbounded subgradient is obtained for the corresponding convex non-differentiable objective function, and the problem is numerically solved using the subgradient method. The effectiveness of the proposed strategy is illustrated via simulation.