Flexible Final-Time Stochastic Differential Dynamic Programming for Autonomous Vehicle Trajectory Optimization

In this article, the problem of autonomous vehicle trajectory optimization with flexible final time is concerned under the consideration of stochastic disturbances. Stochastic differential dynamic programming (SDDP) has been widely applied to address this type of problem due to its fast convergence and capability to handle model errors. Typically, traditional SDDP is designed with a deterministic final time, which is mainly assigned based on expert experiences. However, this may limit the implementation of this approach. To deal with this issue, we define the final time as a new optimal variable and propose an enhanced version of SDDP, named flexible final-time SDDP. The stochastic dynamic system is then characterized as a deterministic one with random state perturbances. An unscented transform approach is utilized to cope with the perturbed expected values. To verify the effectiveness of the proposed approach, a 3-D missile trajectory optimization problem is tested as an example. The simulation results show that the proposed method is able to address the stochastic trajectory optimization problem and can provide stronger robustness compared to other algorithms.