An Improved Differential Dynamic Programming Approach for Computational Guidance

Differential dynamic programming (DDP) is a well-recognized method for computational guidance due to its fast convergence characteristics. However, the original DDP requires a predefined final time and cannot handle nonlinear constraints in optimization. This prohibits the application of DDP to autonomous vehicles due to the heuristic nature of setting a final time beforehand and the existence of inherent physical limits. This chapter revisits DDP by dynamically optimizing the final time via the first-order optimality condition of the value function and using the augmented Lagrangian method to tackle nonlinear constraints. The resultant algorithm is termed flexible final time-constrained differential dynamic programming (FFT-CDDP). Extensive numerical simulations for a three-dimensional guidance problem are used to demonstrate the working of FFT-CDDP. The results indicate that the proposed FFT-CDDP provides much higher computational efficiency and stronger robustness against the initial solution guess, compared with the commercial-off-the-shelf GPOPS toolbox.