Sequential convex programming for nonlinear optimal control problems in UAV path planning

Usually, an UAV (Unmanned Aerial Vehicle) path planning problem can be modeled as a nonlinear optimal control problem with non-convex constraints in practical applications. However, it is quite difficult to obtain stable solutions quickly for this kind of non-convex optimization with certain convergence and optimality. In this paper, an algorithm is proposed to solve the problem through approximating the non-convex parts by a series of sequential convex programming problems. Under mild conditions, the sequence generated by the proposed algorithm is globally convergent to a KKT (Karush-Kuhn-Tucker) point of the original nonlinear problem, which is verified by a rigorous theoretical proof. Compared with other methods, the convergence and effectiveness of the proposed algorithm is demonstrated by trajectory planning applications.