Unified controller for both trajectory tracking and point regulation of second-order nonholonomic chained systems

In this article, a unified controller is developed for both trajectory tracking and point regulation of nonholonomic second-order chained systems. The controller design relies on converting the error model of second-order chained systems to the form of perturbed first-order nonholonomic integrator, followed by a dynamic state feedback control law steering the tracking error to origin exponentially. The proposed control law is universal for both trajectory tracking and point regulation, as the reference trajectories can be any one produced by bounded reference inputs. The control design approach is illustrated by application to a planar manipulator with two translational actuated joints and one revolute unactuated joint. Simulation results show the effectiveness of the proposed approach.