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.

This paper presents and discusses the implementation results of a model-predictive control (MPC) scheme with friction compensation applied to trajectory following of an omnidirectional three-wheeled robot. A cascade structure is used with an inverse kinematics block to generate the velocity references given to the predictive controller. Part of the control effort is used to compensate for the effects of static friction, allowing the use of efficient algorithms for linear MPC with constraints. Experimental results show that the proposed strategy is efficient in compensating for frictional effects as well as for tracking predefined trajectories.

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.

A PID control for electric vehicles subject to input armature voltage and angular velocity signal constraints is proposed. A PID controller for a vehicle DC motor with a separately excited field winding considering the field current constant was tuned using controlled invariant set and multiparametric programming concepts to consider the physical motor constraints as angular velocity and input armature voltage. Additionally, the integral of the error, derivative of the error constraints, and λ were considered in the proposed algorithm as tuning parameters to analyze the DC motor dynamic behaviors. The results showed that the proposed algorithm can be used to generate control actions taking into account the armature voltage and angular velocity limits. Also, results demonstrate that a controller subject to constraints can improve the electric vehicle DC motor dynamic; and at the same time it protects the motor from overvoltage.

A novel descriptor observer structure is proposed in the context of discrete-time descriptor linear systems. On the basis of this new structure, the characterization of conditioned-invariant polyhedral sets with the purpose of limiting the estimation error is carried out. Limitation of the estimation error can be achieved by the computation of an as small as possible conditioned-invariant polyhedron, that contains the set of possible initial errors, and by a suitable output injection law. The approach is applied to an experimental tanks platform, for which a descriptor model is identified and validated. The obtained results confirm the merits of the proposed observer for applications in this kind of systems.