Constrained Parameterized Differential Dynamic Programming for Waypoint-Trajectory Optimization

Unmanned aerial vehicles (UAVs) are required to pass through multiple important waypoints as quickly as possible in courier delivery, enemy reconnaissance and other tasks to eventually reach the target position. There are two important problems to be solved in such tasks: constraining the trajectory to pass through intermediate waypoints and optimizing the flight time between these waypoints. A constrained parameterized differential dynamic programming (C-PDDP) algorithm is proposed for meeting multiple waypoint constraints and free-time constraints between waypoints to deal with these two issues. By considering the intermediate waypoint constraints as a kind of path state constraint, the penalty function method is adopted to constrain the trajectory to pass through the waypoints. For the free-time constraints, the flight times between waypoints are converted into time-invariant parameters and updated at the trajectory instants corresponding to the waypoints. The effectiveness of the proposed C-PDDP algorithm under waypoint constraints and free-time constraints is verified through numerical simulations of the UAV multi-point reconnaissance problem with five different waypoints. After comparing the proposed algorithm with fixed-time constrained DDP (C-DDP), it is found that C-PDDP can optimize the flight time of the trajectory with three segments to 7.35 s, 9.50 s and 6.71 s, respectively. In addition, the maximum error of the optimized trajectory waypoints of the C-PDDP algorithm is 1.06 m, which is much smaller than that (7 m) of the C-DDP algorithm used for comparison. A total of 500 Monte Carlo tests were simulated to demonstrate how the proposed algorithm remains robust to random initial guesses.