Contents I. Introduction
Trajectory following is a fundamental challenge of control theories. It forms the foundation of various applications in real life. For example, vehicle navigation [1], manipulator automation [2] and so on. To improve precision and reduce consumption during trajectory following task, many effective approaches have been proposed. In general, mainstream strategies for trajectory following problems can be categorized into two classes: the geometric and prediction-based approaches. The geometric approach is based on basic geometric calculation given current location and target location in cartesian space [3]. Robots can perfectly traverse the target location or keep reducing error gradually like the PID controller. This approach is easy to implement since it disregards the dynamic model of the robot. In terms of mobile robots control, Stanley method [4] and pure pursuit [5] are delegates of this approach and have been widely adopted in mobile robot tracking research [6], [7], [8], [9], [10]. Prediction-based approach predicts future states of the robot and implement convex optimization to minimize future error based on prediction [11]. It is a close-loop optimization control strategy, with the ability to deal with constraints explicitly. One representative is model predictive control [12]. For example, in [13], the authors successfully implemented an MPC controller for the high-speed tracking control of a 4WIS robot. Nonetheless, geometric approaches are too simple to deal with complicated situations in real life. Prediction-based methods are robust and can cope with uncertainties and nonlinearity, but are prohibitive in processing, especially when computational resources are limited.
