Reliable and efficient trajectory planning for fixed-wing UAVs via nonlinearity transfer and convexification

This paper investigates the trajectory planning problem for fixed-wing UAVs with various constraints. Solving the problem by nonlinear programming or successive convex programming often involves a high computation burden or risk of non-convergence. To enhance reliability and efficiency, we decompose the problem into two subproblems for optimizing the path and the speed, respectively. Multiple nonlinearity transfer and moderate conservative approximation are proposed to transform the former problem into a second-order cone programming problem with concave inequality constraints, which can be solved by existing methods with guaranteed convergence. The latter problem is equivalently rewritten into the same type of problem by applying variable redefinition and equivalent transformation of the objective function. An iterative algorithm of solving the two subproblems in sequence is designed to get a near-optimal solution of the original problem, and another algorithm is provided to improve the solution optimality. Rigorous analysis shows that the proposed algorithms are convergent. And numerical examples clearly demonstrate that they are much more reliable and efficient than existing algorithms.