Differential Dynamic Programming Approach for Robust-optimal Low-thrust Trajectory Design Considering Uncertainty

Abstract: This paper proposes a robust-optimal trajectory design method for uncertain system to minimize the expected value of objective function. The basic idea is solving Stochastic Differential Dynamic Programming (SDDP), which solve optimal control problem to minimize the expected value of cost-to-go function, with Unscented Transform, which is used to estimate the expected value. Most recent studies have focused on the trajectory optimization assuming that the spacecraft can control their trajectory exactly as planed; however, the assumption is violated in the realistic operations where uncertain events, such as missed-thrust and navigation error, perturb the predetermined trajectory. Conventionally, experienced specialists empirically determine “margin” on optimal low-thrust trajectory by duty cycle or forced coast period. A proposed SDDP autonomously provides “margin” in optimization for future feedback as well. Numerical result by V-infinity leveraging problem shows that SDDP has better performance, in other words, expected value of objective function considering uncertainty is better, than conventional DDP when the system has uncertainty, since the result of SDDP has “margin” in optimal control for future feedback.