Iterative Optimal Control Syntheses Illustrated on the Brockett Integrator

Abstract

In this paper, we investigate computational methods for synthesizing optimal control inputs for nonholonomic control systems. We use the Brockett integrator as a benchmark example to illustrate different aspects of the computational trajectory optimization problem. The main result of this paper is the establishment of a rather attractive iterative scheme for practically constructing optimal control inputs. The functionality and efficiency of the proposed iterative scheme are illustrated on different optimal steering problems centered around the Brockett integrator.