SUMMARY: Model predictive control (MPC) theory has gained attention with the recent increase in the processing power of computers that are now able to perform the needed calculations for this technique. This kind of control algorithms can achieve better results in trajectory tracking control of mobile robots than classical control approaches. In this paper, we present a review of recent developments in trajectory tracking control of mobile robot systems using model predictive control theory, especially when nonholonomicity is present. Furthermore, we point out the growth of the related research starting with the boom of mobile robotics in the 90s and discuss reported field applications of the described control problem. The objective of this paper is to provide a unified and accessible presentation, placing the classical model, problem formulations and approaches into a proper context and to become a starting point for researchers who are initiating their endeavors in linear/nonlinear MPC applied to nonholonomic mobile robots. Finally, this work aims to present a comprehensive review of the recent breakthroughs in the field, providing links to the most interesting and successful works, including our contributions to state-of-the-art.

Trajectory tracking for autonomous vehicles is usually solved by designing control laws that make the vehicles track predetermined feasible trajectories based on the trajectory error. This type of approach suffers from the drawback that usually the vehicle dynamics exhibits complex nonlinear terms and significant uncertainties. Toward solving this problem, this work proposes a novel approach in trajectory tracking control for nonholonomic mobile robots. We use a nonlinear model predictive controller to track a given trajectory. The novelty is introduced by using a set of modifications in the robot model, cost function, and optimizer aiming to minimize the steady-state error rapidly. Results of simulations and experiments with real robots are presented and discussed verifying and validating the applicability of the proposed approach in nonholonomic mobile robots.

Landing an unmanned aerial vehicle unmanned aerial vehicle (UAV) on top of an unmanned surface vehicle (USV) in harsh open waters is a challenging problem, owing to forces that can damage the UAV due to a severe roll and/or pitch angle of the USV during touchdown. To tackle this, we propose a novel model predictive control (MPC) approach enabling a UAV to land autonomously on a USV in these harsh conditions. The MPC employs a novel objective function and an online decomposition of the oscillatory motion of the vessel to predict, attempt, and accomplish the landing during near-zero tilt of the landing platform. The nonlinear prediction of the motion of the vessel is performed using visual data from an onboard camera. Therefore, the system does not require any communication with the USV or a control station. The proposed method was analyzed in numerous robotics simulations in harsh and extreme conditions and further validated in various real-world scenarios.