Nonlinear control for first-order nonholonomic system with hardware restriction and disturbance

In this paper, the tracking controller for a firstorder nonholonomic system affected by friction is synthesized. A linear approximated system of this system does not ensure the controllability. The system cannot be stabilized by using linear time-invariant state feedback. Control Moment Gyroscope (CMG) is a first-order nonholonomic system. Furthermore CMG has hardware restriction of a motion range. In this research, the state equation of CMG is converted into a chained system which is a canonical form of nonholonomic systems. The tracking controller is synthesized based on a backstepping approach. The integrator is applied in the controller to eliminate a steady-state error caused by coulomb friction. The stability of the system with the integrator is guaranteed theoretically by a Lyapunov function. The effectiveness of the proposed method is illustrated by simulations.