Mathematical and computer simulation of manipulators with nonlinear geometric constraint
Authors: Krasinsky A.Ya., Ilyina A.N., Krasinskaya E.M., Rukavishnikova A.S.
Published in issue: #4(76)/2018
DOI: 10.18698/2308-6033-2018-4-1757
Category: Mechanics | Chapter: Dynamics, Strength of Machines, Instruments, and Equipment
The article describes mathematical models and solution of stabilization problems of stationary motions for two manipulators with excessive coordinate and nonlinear geometric constraint in the electric drive: a rotating manipulator and a four-wheel mobile manipulator with elastic suspension. The method used here was developed earlier for holonomic and nonholonomic systems with differential constraints using the theory of critical (special) Lyapunov cases in the nonlinear stability theory. The dynamics of the mechanical part of the manipulators is described using equations in the form developed by M.F. Shulgin for systems with redundant coordinates that do not contain joining factor. The voltage at the armature winding of the actuating electric motor is used for control. The second Kirchhoff’s law describes the dynamics equation of the motor. The closed system is a system of indirect control. The control law is determined by solution of the linear-quadratic stabilization problem by the Krasovsky method for an isolated subsystem that does not include the critical variable corresponding to the zero root. Coefficients of controlling actions were found by solving the matrix algebraic Riccati equation using programs developed in the MATLAB system and taking into account the conditions imposed by the geometric constraint on the coordinate perturbations.
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