Non-linear PID Controller for Trajectory Tracking of a Differential Drive Mobile Robot

The application of differential drive robots has grown from scientific research to broader industrial and commercial purposes. In order to Navigate the robot in difficult terrains, it must be well equipped with a robust controller with good path tracking ability and general stability. Typically, the wheeled mobile robot (WMR) can essentially be kinematically controlled by defining a route and determining the traveling time, speed and direction to get from one place to another. However, by ignoring the dynamic model of the robot, a purely kinematic model approach has been revealed to produce unrealistic results at higher speeds and loads. As a consequence, there are significant limitations to the applicability of solely kinematic systems to mobile robotics and hence, in recent years, there has been a trend towards the application of dynamic modelling. In this study, a simple but effective solution for the path tracking problem of a mobile robot using a PID controller is proposed. The method adopted is a trial and error technique with six tuning parameters for the robot to track a desired trajectory. The final mathematical derivation for a nonholonomic differential drive mobile robot was computationally simulated using MATLAB for both kinematic and dynamic models respectively. The controller was used to overcome the nonlinearity of the reference trajectory tracking as well as the speed of the DC motor adjustments. In order to evaluate the performance of the developed robot controller, tests were also carried out for different trajectories in terms of the initial and final conditions. The results show that the developed PID controller is responsive enough to be able to speed up when required to match the reference trajectory.