Principles for implementing servo-constraints in nonholonomic mechanical systems

The problem of implementing servo-constraints in nonholonomic mechanical systems is considered. An attempt is made to outline the theoretical principles for composing equations of motion of nonholonomic mechanical systems with servo-constraints, to set the conditions for implementing servo-constraints, and to indicate the features of the introduction of control forces implementing the motion program from the point of view of their practical realization. In contrast to nonholonomic constraints, the method of implementation is important for servo-constraints. To illustrate the principles outlined in this study, a mathematical algorithm for controlling a wheeled two-link robot (driving trolley and trailer) with a differential drive is constructed using servo-constraints. Nonholonomic constraints are also imposed on the wheels of the system. On the basis of the joint solution of the equations of motion in quasi-velocities and time derivatives of nonholonomic and servo-constraints, the equations of motion of the wheeled robot are obtained. The dynamics of the wheeled robot is studied when a motion program is set that allows pursuing a target. The dynamics of the wheeled robot is studied when a motion program is set that controls the angle of deviation of the trailer from the driving trolley axis. The results are illustrated graphically.