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

Control of underactuated systems with non-holonomic constraints has been an issue interest in recent years. These 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 positioning second-order chained form system using simple approach based on linear algebra is proposed. The law formulated by setting two the six variables trajectories, while other four calculated assuming equations exact solution, ensuring error tends zero. stability proposed demonstrated through Khalil Lemma, simulations show performance controller.