In this article a novel performance improvement scheme is being presented for the problem of designing a trajectory tracking controller for non-holonomic mobile robots with differential drive. Based on the robot kinematic equations, an error dynamics controller is being utilized for allowing the robot to follow an a priori defined reference path, with a desired velocity profile. The main novelty of this article stems from the utilization of a gradient based adaptive scheme that is able to adapt the controller's gain ruling the rising and settling time of the robot and up to now has been ad-hoc selected. The proposed adaptation scheme is based on the robot's path tracking errors and is able to provide an on-line adjustment for the performance improvement, independently of the selected path type. Multiple experimental test cases, including the movement of the robot on various path profiles, prove the efficacy of the proposed scheme.