A novel nonlinear control law with trajectory tracking capability for nonholonomic mobile robots: Closed-form solution design

A novel nonlinear robust trajectory tracking control law for nonholonomic mobile robot is presented in this paper. This approach can be applied to generate trajectory tracking control commands on nonholonomic mobile robot movement. The design objective is to specify one nonlinear robust control law that satisfies the H₂ performance, for the nonlinear trajectory tracking control of nonholonomic mobile robot. In general, it is hard to obtain the closed-form solution from this nonlinear trajectory-tracking problem. Fortunately, because of the skew symmetric property of the trajectory tracking system of the nonholonomic mobile robot and adequate choice of state variable transformation, the H₂ trajectory-tracking problems can be reduced to solving one nonlinear time varying Riccati-like equations. Furthermore, one closed-form solution to this nonlinear time varying Riccati-like equation can be obtained with very simple forms for the preceding control design. Finally, there are two practical testing conditions: circular and square like reference trajectories are used for performance verifications.