Global exponential tracking control of a mobile robot system via aPE condition

This paper presents the design of a differentiable, kinematic control law that achieves global asymptotic tracking. In addition, we also illustrate how the proposed kinematic controller provides global exponential tracking provided the reference trajectory satisfies a mild persistency of excitation (PE) condition. We also illustrate how the proposed kinematic controller can be slightly modified to provide for global asymptotic regulation of both the position and orientation of the mobile robot. Finally, we embed the differentiable kinematic controller inside of an adaptive controller that fosters global asymptotic tracking despite parametric uncertainty associated with the dynamic model. Experimental results are also provided to illustrate the performance of the proposed adaptive tracking controller.