Establishment of UAV formation flight using control Vector parameterization and sequential convex programming

Formation flight of multiple Unmanned Aerial Vehicles (UAVs) could provide an effective, efficient yet low cost alternative to existing technologies. This paper addresses the energy-optimal establishment of UAV formation flight that shall satisfy final configuration constraints. First, the problem of formation establishment is formulated as an energy-optimal control problem which is constrained by the nonlinear dynamics. Then, the optimal control problem is solved using a direct method. In this direct method the original problem is transcribed into a sequence of convex optimization problems via the control vector parameterization approach. After that, the sequential convex programming (SCP) technology is employed to derive the optimal solution. Essentially, each instance of SCP is a quadratic programming problem subject to linear constraints that can be solved very efficiently. In the end, the proposed method is applied to the establishment of V formation for three UAVs, where the free open source solver CVX is exploited. By comparison with the global optimization technique provided in MATLAB, the solution converges very fast to the global minimum.