Mixed-integer trajectory optimization with no-fly zone constraints for a hypersonic vehicle

Abstract

This paper focuses on mixed-integer trajectory optimization of no-fly zones avoidance for a hypersonic vehicle. When there are multiple no-fly zones, the trajectory optimization problem has many local optimal solutions, and the performance of the solution depends on the selection of an initial guess. Essentially, the selection of the initial guess can be abstracted as a discrete path decision. To deal with this issue, this paper first integrates the discrete path decision and continuous trajectory optimization for no-fly zones avoidance and models these as a mixed-integer optimal control problem (MIOCP). As the corner stone, a creative directed graph is established to model the path decision problem, which is then formulated by integer constraints. Combined with the minimum effort optimal control problem (Problem 1), we form the MIOCP (Problem 2), thus integrating the path decision and trajectory optimization to improve global performance. Additionally, to solve the MIOCP, an effective iterative mixed-integer convex programming (IMICP) algorithm is customized by adding two ad-hoc techniques, relaxation and a proximity term, thus remedying the artificial infeasibility. Simulation results show that this approach is practically independent of the initial guess and has better performance than existing methods.