Gradient tracking based second order sliding mode control of a wheeled vehicle

The present paper deals with the problem of making a three-wheeled vehicle move in its operative space reaching prescribed goal points with the desired orientation, and avoiding the collision with obstacles. To comply with the nonholonomic nature of the system to be controlled, a gradient tracking approach is followed, so that a reference velocity and orientation are suitably generated during the vehicle motion. To track such references a multi-input control law is designed by suitably transforming the system model into a couple of auxiliary second order uncertain systems, relying on which second order sliding modes can be enforced. As a result, the control objective is attained by means of a continuous control law, so that the problems due to the so-called chattering effect, such as the possible actuators wear or the induction of vibrations, typically associated with the use of sliding mode control, are circumvented.