On Feedback Linearization of Mobile Robots

A wheeled mobile robot is subject to both holonomic and nonholonomic constraints. Representing the motion and constraint equations in the state space, this paper studies the feedback linearization of the dynamic system of a wheeled mobile robot. The main results of the paper are: (1) It is shown that the system is not input-state linearizable. (2) If the coordinates of a point on the wheel axis are taken as the output equation, the system is not input-output linearizable by using a static state feedback; (3) but is input-output linearizable by using a dynamic state feedback. (4) If the coordinates of a reference point in front of the mobile robot are chosen as the output equation, the system is input-output linearizable by using a static state feedback. (5) The internal motion of the mobile robot when the reference point moves forward is asymptotically stable whereas the internal motion when the reference point moves backward is unstable. A nonlinear feedback is derived for each case where the feedback linearization is possible.