Practical Linearization Control of Nonholonomic Unicycles

Due to underactuation, the states of nonholonomic systems cannot be steered toward any direction of the state space. This note takes unicycles as an example and demonstrates a new idea of control design for nonholonomic systems. More precisely, we apply state transformation technique and external dynamic oscillator, and convert an underactuated nonholonomic unicycle into a fully-actuated and linearizable one. A control law, capable of tracking and stabilization uses, is then constructed. The tradeoff therein is that the tracking/stabilization errors can only be steered into the neighborhood of the origin rather than converging to zero. Numerical simulations are carried out to validate the proposed control scheme.