Modeling and hierarchical tracking control of tri-wheeled mobile robots

After exploring the structure of the dynamics derived by using the Appell equation, we propose a hierarchical tracking controller for a tri-wheeled mobile robot in this paper. With appropriately chosen privileged variables, the reduced equations are decoupled from the kinematic equations associated with the underlying nonholonomic constraints. This special character of the system makes it possible to separate the design into three levels: motion planning, kinematic, and dynamic. In the proposed scheme, a fuzzy inference engine in the kinematic level is used to update the desired trajectory computed in the motion-planning level. An adaptive sliding-mode controller is then adopted to track the new reference values of privileged variables in the dynamic level, which subsequently drives the nonprivileged variables. Simulation results show the effectiveness of such a tracking-control scheme, which concurrently takes kinematics and dynamics into consideration. All system variables can be tracked asymptotically to their desired values, which are assured by the skew-symmetric property of the Appell equation