Constraint stabilization application to chaplygin systems

The paper considers the problem of the dynamics control of nonholonomic Chaplygin systems. The control is executed by introducing additional forces that correspond to the problem goals given by both holonomic and nonholonomic constraints. The determination of the expressions for the control actions by means of Lagrange multipliers leads to the instability of the numerical solution of the dynamic equations of a closed system. An introduction of extra variables estimating the deviations from the constraint equations and a construction of the extended system allows solving the problem of the constraint stabilization. © 2018 IEEE.