Finite-time posture stabilization of the unicycle mobile robot using only position information: A discrete-time sliding mode approach

The posture stabilization of a unicycle mobile robot is useful in executing parking and docking maneuvers. It becomes more advantageous to guarantee the posture stabilization in finite time for a battery operated robot, especially in an application involving multiple robots. This paper addresses the posture stabilization of the unicycle mobile robot in finite time, especially when only the position information is available. We adopt the reaching law approach and design a discrete-time sliding mode (DSM) controller by finitely discretizing the chained form of the unicycle, using the notion of multirate input sampling. Finite-time stabilization of the equilibria is achieved by using multirate piecewise continuous inputs. Furthermore, the control inputs are realized using multirate output-feedback (MROF) technique, wherein the states are estimated using the knowledge of the past fast output samples and immediate past control inputs. The proposed MROF-DSM strategy avoids undesirable chatter in the system response owing to the nonswitching-type controller and guarantees the stabilization in finite time. Simulations demonstrate the efficacy of the proposed method