Stabilization of non-holonomic mobile robots using Lyapunov functions for navigation and sliding mode control

Mobile robots with non-holonomic kinematics have three degrees of freedom for planar motion, but there are only two control inputs available. The stabilization problem for such robots is known not to be solvable via smooth time-invariant feedback. The authors propose to utilize a Lyapunov function to prescribe a set of desired trajectories to navigate the robot to a specified configuration. Ideal tracking of the prescribed trajectories is achieved by exploiting the invariance property and the order reduction property of sliding mode control. The mobile robot is shown to be exponentially stabilizable for a class of quadratic Lyapunov functions