Optimal Reconfiguration of Formation Flying Using A Direct Sequential Method

Formation flying of multiple Unmanned Aerial Vehicles (UAVs) or satellites enables cooperation among agents, and thus constitutes a system of greater performance than the simple sum of its parts by taking advantage of that cooperation. As a prerequisite, how to reconfigure, energy-optimally or time-optimally, from the current formation to the desired one shall be planned beforehand. This paper addresses such a planning problem from the perspective of optimal control that exploits a direct sequential method. In our study, during the reconfiguration agents subject to nonlinear dynamics, and final formation constraints are imposed where there exist unknown parameters to be determined optimally. In the developed direct method the original problem is transcribed into a sequence of convex optimization problems via the control vector parameterization approach using piecewise-constant approximation. In the end, each instance in the sequence is essentially a programming problem (quadratic or linear) subject to linear constraints that can be solved very efficiently. In this paper, the proposed method has been applied to two scenarios: the energy-optimal reconfiguration of five UAVs and the time-optimal formation reconfiguration of four satellites. In our implementation the free open source solver CVX is used. By comparison with the global optimization technique provided in MATLAB, the solutions converge very fast to the global minimum.