Optimal control on special Euclidean group via natural gradient algorithm

Considering the optimal control problem about the control system of the special Euclidean group whose output only depends on its input is meaningful in practical applications. The optimal control considered here is described as the output matrix is as close as possible to the target matrix by adjusting the system input. The geodesic distance is adopted as the measure of the difference between the output matrix and the target matrix, and the trajectory of the control input obtained in the process is achieved. Furthermore, some numerical simulations are shown to illustrate our outcomes based on the natural gradient descent algorithm for optimizing the control system of the special Euclidean group.