Two-stage time-optimal formation reconfiguration strategy

A time-optimal reconfiguration strategy for formation flying of autonomous acceleration-controlled agents is presented. In the proposed strategy, the agents are moved to a special designated formation in the time interval between the completion of the mission in the current formation and the issuance of the next reconfiguration command. It is shown that the problem of finding the special designated formation which minimizes the expected value of the reconfiguration time is nonconvex. This optimization problem is treated for two cases of constrained acceleration, and constrained acceleration and velocity. It is shown that in both cases, the search space for finding the special designated formation can be reduced to a convex compact set. An alternative search algorithm is presented for the second case, which consists of searching a vicinity of possible formations, and solving a convex nondifferentiable optimization problem. This search algorithm is typically much faster than the one concerning the acceleration constraint only. The effectiveness of the proposed strategy is illustrated via simulation.