A stable proportional–proportional integral tracking controller with self-organizing fuzzy-tuned gains for parallel robots

Francisco G Salas,Raymundo Juarez-Del-Toro,Ricardo P Parada,Jorge Orrante-Sakanassi

doi:10.1177/1729881418819956

Abstract

Parallel robots are nowadays used in many high-precision tasks. The dynamics of parallel robots is naturally more complex than the dynamics of serial robots, due to their kinematic structure composed by closed chains. In addition, their current high-precision applications demand the innovation of more effective and robust motion controllers. This has motivated researchers to propose novel and more robust controllers that can perform the motion control tasks of these manipulators. In this article, a two-loop proportional–proportional integral controller for trajectory tracking control of parallel robots is proposed. In the proposed scheme, the gains of the proportional integral control loop are constant, while the gains of the proportional control loop are online tuned by a novel self-organizing fuzzy algorithm. This algorithm generates a performance index of the overall controller based on the past and the current tracking error. Such a performance index is then used to modify some parameters of fuzzy membership functions, which are part of a fuzzy inference engine. This fuzzy engine receives, in turn, the tracking error as input and produces an increment (positive or negative) to the current gain. The stability analysis of the closed-loop system of the proposed controller applied to the model of a parallel manipulator is carried on, which results in the uniform ultimate boundedness of the solutions of the closed-loop system. Moreover, the stability analysis developed for proportional–proportional integral variable gains schemes is valid not only when using a self-organizing fuzzy algorithm for gain-tuning but also with other gain-tuning algorithms, only providing that the produced gains meet the criterion for boundedness of the solutions. Furthermore, the superior performance of the proposed controller is validated by numerical simulations of its application to the model of a planar three-degree-of-freedom parallel robot. The results of numerical simulations of a proportional integral derivative controller and a fuzzy-tuned proportional derivative controller applied to the model of the robot are also obtained for comparison purposes.

Highlights

Parallel robots are nowadays used in many high-precision industrial tasks, such as machining,[1,2] welding,[3,4] packaging,[5,6] as well as flight simulators[7] and telescopes.[8,9] These high-precision applications demand the implementation of position regulators, for point-to-point motion tasks, and tracking controllers, when the end-effector motion has to follow a prescribed trajectory of motion.[10]
Given the larger complexity of the dynamic models of parallel robots, and the need of improved robustness of the controllers before parameter variations or uncertainties, in this work, we propose a novel design of a two-loop P-proportional integral (PI) controller for tracking control of parallel manipulators
The approach that we address to carry out the stability analysis of the closed-loop system is considering the self-organizing fuzzy (SOF)-P-PI controller as a variable gains P-PI L controller, without taking into account the dynamics of the 0 tuning algorithm used for tuning the variable gains

Summary

Introduction

Parallel robots are nowadays used in many high-precision industrial tasks, such as machining,[1,2] welding,[3,4] packaging,[5,6] as well as flight simulators[7] and telescopes.[8,9] These high-precision applications demand the implementation of position regulators, for point-to-point motion tasks, and tracking controllers, when the end-effector motion has to follow a prescribed trajectory of motion.[10]. Such an algorithm will be described in a later section in this article. Let consider the dynamic model of a parallel robot in equation (7), together with the control law given by equations (9) to (11), where Fðq~; q~_Þ is a diagonal matrix of variable gains, and Kvp and Kvi are diagonal matrices of constant gains defined in equations (12) to (13). (see Garcia-Gamez et al.’s work[29])

R yp þ pffiffiffi 3 2

Conclusion