Velocity and torque feedback control of a nonholonomic cart

A framework for designing and analysing velocity and torque feedback controls for a nonholonomic wheeled-cart is presented. A stability analysis of a set of nonlinear systems, the equations of which encompass all stable linear invariant systems, is first proposed. This analysis is then applied to the design and analysis of feedback controls for the wheeled-cart. The control inputs are either the cart's motorized wheels angular velocities (velocity control) or the torques applied to those wheels (torque control). Various control objectives are discussed and sufficient conditions for asymptotic convergence of the proposed controls are given. Among other results, the existence of smooth feedback controls that stabilize the cart at a desired position and orientation is established. This result does not contradict earlier non-existence results because the stabilizing controls depend not only on the robot's configuration variables but also on the exogeneous time variable.