Second-order sliding-mode control of a mobile robot based on a harmonic potential field

The problem of controlling an autonomous wheeled vehicle which must move in its operative space and reach a prescribed goal point avoiding the collision with the obstacles is dealt with. To comply with the nonholonomic nature of the system, a gradient-tracking approach is followed, so that a reference velocity and orientation are suitably generated during the vehicle motion. To track such references, two control laws are 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.