Preconditioned Distributed Trajectory Optimization Algorithm using Differential Dynamic Programming
Yunzhuo Wang, Koji Tsumura · 2020
Trajectory optimization and model predictive control is demanding but challenging for distributed and time-critical system that consists of a large number of dynamic subsystems with sparse physical interactions. The classic dual gradient ascent method suffers from the slow convergence when the system is not well-scaled. This paper proposes a Jacobi-preconditioned dual gradient ascent method that fully exploits the idea behind Differential Dynamic Programming to compute the ascent direction in a distributed and recurrent manner at a linear time-cost with respect to the length of the time horizon. Moreover, we propose a method to compute a fixed step size for the preconditioned dual gradient ascent step that can guarantee global convergence property under certain assumptions. A numerical experiment shows that our proposed algorithm improves performance and robustness to ill-scaled problems over the ordinary non-preconditioned dual ascent algorithm. This algorithm has great potential applications in power grid, chemical plants, and cooperative systems of drones.