Unpowered approach and landing trajectory planning using second-order cone programming

Abstract Online trajectory planning is an effective way to improve the adaptability of a mission and the guidance reliability. This paper presents a trajectory planning algorithm developed by applying the convex optimization for the approach and landing phase of unpowered winged vehicles. Considering a four degree-of-freedom (DoF) dynamics system, as well as a number of control constraints, path constraints and terminal constraints, the trajectory planning problem is formulated as a nonconvex optimization problem. By using the exact convexification and successive convexification approaches, the nonconvex optimization problem is converted to a second-order cone programming problem, which can be efficiently solved by the interior point method. The exactness of the convex relaxation for the control variables is proved theoretically, and the numerical simulation results verify the effectiveness of the approach. The numerical simulation results also indicate that the proposed algorithm has high efficiency, and the trajectory generated using the proposed algorithm is remarkably similar to that obtained using the propagation algorithm developed for the Space Shuttle.