On control for double-link manipulator with elastic joints

In the paper the problem on stabilization of program motion for two-link manipulator with elastic joints is solved. Absolutely rigid manipulator links are connected by elastic cylindrical joint and via the same one the first link is fixed to the base. Thus, the manipulator can perform motion in a vertical plane. Motions of the manipulator are described by the system of Lagrange equations of the second kind. The problem on synthesis of motion control of such a system consists in the construction of the laws of change of control moments that allow the manipulator to carry out a given program motion in real conditions of external and internal disturbances, inaccuracy of the model itself. In this paper the mathematical model of controlled motion of the manipulator is constructed for the case of the control actions in the form of continuous functions. Using vector Lyapunov functions and comparison systems on the base of the cascade decomposition of the system we justified the application of these control laws in the problem of stabilization of the program motion of the manipulator. The novelty of the results is to solve the problem of stabilization of nonstationary and nonlinear formulation, without going to the linearized model. The graphs for the coordinates and velocities of the manipulator links confirm the theoretical results.