Adjacent grids algorithm and dynamics programming realization for minimum time-to-climb trajectories

This paper deals with the minimum time-to-climb problem, as a basic function of an aircraft during executing the flight mission. After discussing the longitudinal equation of motion, the relationship between consumption time and other state variables is obtained by disposing the aircraft equations of dynamics and motion. Based on the relationship, the time interval between any adjacent grids in the vertical plane is figured out. Finally, the minimum time cost for climbing from one flight point to the target point is calculated by dynamic programming (DP) method. The numerical simulation shows that, the algorithm presented in this paper which based on adjacent grids and DP can find the optimal flight trajectory series which is realizable in designated flight envelope, and the time cost of obtained trajectory serried satisfies with the requirement.