Optimal Control of Manipulator

When solving the problem of optimal performance for manipulative robots, the scientific team headed by F. L. Chernousko actively uses the Pontryagin maximum principle. The application of the maximum principle is complicated by the nonlinearities of controlled systems of manipulation robots. Therefore, when using it, the original mathematical model is replaced with a simpler one. These substitutions made it possible to analytically solve the problems of finding the switching points of relay controls for individual models of manipulation robots. In this paper, when finding the switching moments of relay controls for a manipulating robot, the original nonlinear controlled system is used. The problem is reduced to the problem of the existence of a solution to the boundary value problem for a controlled nonlinear system in the selected class of permissible controls that guarantee the arrival of the manipulator in the final position with zero speeds.