Trajectory tracking of mobile robots using hedge-agebras-based controllers

This research aims to design controllers based on the hedge-algebras (HA) theory to control differential robots that track reference trajectories. First, the HA-based controller (denoted as HA controller) is synthesized by selecting a suitable qualitative control rule base for the investigated model as a rule-based optimization problem. Then, the optimal HA-based controller (denoted as oHA controller) is established based on the problem of simultaneously optimizing the rule base, the reference interval of variables, and the fuzzy parameters of the variables. Optimization problems aim to minimize the distance between the robot and the reference trajectory. The optimization problems in this study use the Balancing composite motion optimization (BCMO) algorithm. A controller based on fuzzy set theory (denoted as FC controller) with the same parameters as the HA controller is also included for comparison. The simulation results show that the HA and oHA controllers demonstrate many advantages over the FC controller regarding reference trajectory tracking ability, calculation time, and control robustness. The main contribution of this work consists of (i) The development of a novel HA, oHA approaches to control a mobile robot to follow reference trajectories accurately; (ii) Providing optimal global-based BCMO in terms of minimal tracking error with computational efficiency; (iii) The investigation of one control rule base for HA and oHA controllers, which is effective for many different reference orbits; (iv) The development of a robust controller that adapts to the robot’s geometric parameters changes; (v) The proposed controllers have superior performance results compared to controllers based on fuzzy set theory in terms of position error between the robot and the reference trajectory, control action calculation time, and robust ability to change robot parameters.