Trajectory planning for multi-UAVs using penalty sequential convex pro-gramming

Trajectory planning of multiple unmanned aerial vehicles (UAVs) is an optimal control problem which subjects to nonlinear motion and nonconvex path constraints. Based on the sequential convex programming approach, such nonconvex optimal control is approximated to be a series of convex optimization subproblems, which can be solved by the state-of-the-art convex optimization algorithm. A good balance between solution quality and computational tractability can then be achieved. Nonconvex optimal control model for multi-UAV trajectory planning is formulated first, and is then approximated to be a convex optimization by discretization and convexification methods. To convexify the nonconvex model, equations of motion of UAVs are linearized, and constraints of threat avoidance and inter-UAVs collision avoidance are convexified. Meanwhile, an inter-sample threat avoidance method is provided to guarantee UAVs' safety at intervals between discrete trajectory points. Based on convex optimization formulation, the detailed procedure of using sequential convex programming based on penalty function to solve multi-UAV trajectory planning is provided. Numerical simulations are conducted to show the effectiveness of the proposed method. The results show that the method can acquire the solution with better optimality and efficiency than the pseudospectral method, especially for larger scale UAV formation.