Systems with nonholonomic (i.e., non-integrable) constraints are among the most complex systems to model and control. Various mechanical and electromechanical nonholonomic systems, such as a multifingered dextrous hand and a spacecraft/manipulator system are envisioned to be extensively used in the future.

The problem addressed in this thesis is the phenomenon of kinematic drift in nonholonomic systems. The drift is usually regarded as an undesirable and practically unacceptable phenomenon. The problem of kinematic drift in nonholonomic systems in general, and in nonholonomic robotic systems in particular, is formally stated and analyzed in the thesis. It is shown that drift generally occurs in nonholonomic systems because the dimensions of the input. configuration, and task (i.e.. Cartesian) spaces are, in general, not equal, and the kinematic relationships between such spaces are non-integrable. For instance, motion of a manipulator mounted on a free-flying platform affects the platform attitude (because of the angular momentum conservation law), and may lead to attitude drift.

In the thesis, two approaches for the drift compensation are presented. One approach is proposed for a general case of nonholonomic systems. The second approach is designed to compensate for kinematic drift in the particular case of multifingered robot hands, and it is motivated by the special structure of the multifingered nonholonomic system.

The proposed technique for controlling drift in the general case of nonholonomic systems is based on a new stable smooth dynamic feedback. It is shown in the thesis that the proposed dynamic feedback compares favorably with other comparable approaches in terms of a convergence rate, robustness, and overall response. The proposed feedback synthesis approach is less complicated than previous similar techniques, because certain complex symbolic operations. required by existing techniques, are avoided. Furthermore, it is demonstrated how particular feedback formulations resulted from the proposed general synthesis technique relate to feedback formulations proposed by other researchers. As an application of the proposed control technique, a solution for the kinematic drift in a nonholonomic spacecraft/manipulator system is developed.

Examples and numerical simulations are provided throughout for illustration.