Linear Algebra Based Control: Application to a second order chained form system

Control of underactuated systems with non-holonomic constraints has been an issue of interest in recent years. These systems are hard to control because their linearization makes them uncontrollable and current approaches generally involve complex calculations. In this manuscript, a controller for trajectory tracking and positioning for a second-order chained form system using a simple approach based on linear algebra is proposed. The control law is formulated by setting two of the six variables trajectories, while the other four are calculated assuming the equations system has an exact solution, and ensuring the error tends to zero. The stability of the proposed control system is demonstrated through the Khalil Lemma, and simulations show the performance of the controller.