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

This paper presents the design of a differentiable, kinematic control law that utilizes a damped dynamic oscillator with a tunable frequency of oscillation to achieve global asymptotic tracking. Provided the reference trajectory satisfies a mild persistency of excitation condition, we also illustrate how the proposed kinematic controller can be slightly modified to provide global exponential tracking. In addition, we illustrate how the proposed kinematic controller provides for global asymptotic regulation of both the position and orientation of the mobile robot; hence, a unified framework is provided for both the tracking and regulation problem.