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On modeling of the dynamics of a mobile manipulator as a mechatronic system

The paper provides the method of the stability and stabilization of steady motion problem solution for mechanotronic systems with geometric constraints by the example of a four-wheeled mobile single-link manipulator. The manipulator, moving rectilinearly, must keep its clamp on a specified height. The manipulator clamp position is regulated by the link rotation by force of commutator motor of constant current with indirect excitation. As a control action, additional tension at the anchor engine is accepted. To construct an accurate mathematical model the manipulator is studied as a mechanotronic system with a redundant coordinate. For the mechanical part of the system, equations in M.F. Shul'gin's form are used. These equations being free from joining factors can be considered as a special case of the Voronetz equations for nonholonomic systems with integrable kinematic constraints. Then the first approximation of the disturbed motion equations is analyzed. Manipulator controllability at steady motion by means of additional tension at the anchor engine is confirmed. Coefficients of the optimal Lyapunov function and control law can be determined uniquely by solving linear-quadratic problems using N.N. Krasovsky's method. Computational solution can be founded with the Repin-Tretyakov procedure. Results of numerical computations are displayed.