# Design and Evaluation of a New Fuzzy Control Algorithm Applied to a Manipulator Robot
## 1 Introduction  
The performance of mechanical and routine tasks, as well as the speeding-up of processes in which precision cannot be overlooked, are just two of the most outstanding features that have made industrial robots the most preferred tool for increasing productivity and reducing operational costs. For a robot to perform a specific movement, a control device that ensures the completion of this movement is essential. Despite the utmost importance of control in manipulator robots, control is still an issue that poses several practical and theoretical challenges to the field, due to the complex dynamic of these robots and the need to achieve highly precise trajectory-tracking in the case of high-speed movements with variable loads [1, 2]. Manipulator robots are multivariable and non-linear dynamic systems. Therefore, obtaining mathematical models that both represent them and in which classic or modern control laws are satisfactorily applicable is difficult, as it is necessary to know the exact masses, inertias, and lengths of each link, as well as other characteristic parameters. Also, these robots face a series of uncertainties inherent to their practical application, such as internal friction or external disturbances. To solve such inconveniences, several control strategies have been proposed, among which the Proportional-Integral-Derivative (PID) method is widely accepted and extensively used in industrial robots. The success of this method is attributed to its simple structure and robust performance in a wide range of operating conditions. Furthermore, these controllers can minimize the steady-state error of a manipulator robot, but they are sensitive to the variation of parameters and uncertainties of the latter [3, 4, 5]. Conventional control techniques such as PID, adaptive control, and sliding mode control, among others, depend largely on precise mathematical modelling. These approaches may be adapted to robots operated in environments without uncertainty and with models that are exactly known; thus, the absence of an accurate analytical model makes it difficult to design an adequate controller [6, 7]. Nevertheless, operations in non-structured environments, where there always will be some degree of uncertainty, require robots to carry out tasks that are more complex [8; 9]. Fuzzy control is a control technique that belongs to the expert systems and that allows for controlling dynamic systems without any mathematical model. This characteristic makes fuzzy control suitable for complex processes that are difficult to model analytically, either because of the incomplete knowledge of the procedure or the unfeasibility of identifying the experimental model due to the unquantifiability of the process inputs and outputs. Thus, this technique may be understood as a mean that enables the conversion of a linguistic control strategy, which is based on the knowledge of an operator, into an automatic control strategy [10]. A controller based on fuzzy logic delivers fast and precise dynamic responses, allows for analyzing information through a true-and-false scale, and is generally robust, and tolerant to imprecisions and noise in the input data, among other characteristics. The logic programming of fuzzy controllers is governed by rules whose order is arbitrary and can be modified in number and type of membership function [11; 12]. Since its creation, fuzzy logic has been widely adopted by researchers to develop controllers for a wide variety of systems in different fields.