Control of a 3-RRR Planar Parallel Robot Using Fractional Order PID Controller

Abstract

3-RRR planar parallel robots are utilized for solving precise material-handling problems in industrial automation applications. Thus, robust and stable control is required to deliver high accuracy in comparison to the state of the art. The operation of the mechanism is achieved based on three revolute (3-RRR) joints which are geometrically designed using an open-loop spatial robotic platform. The inverse kinematic model of the system is derived and analyzed by using the geometric structure with three revolute joints. The main variables in our design are the platform base positions, the geometry of the joint angles, and links of the 3-RRR planar parallel robot. These variables are calculated based on Cayley-Menger determinants and bilateration to determine the final position of the platform when moving and placing objects. Additionally, a proposed fractional order proportional integral derivative (FOPID) is optimized using the bat optimization algorithm to control the path tracking of the center of the 3-RRR planar parallel robot. The design is compared with the state of the art and simulated using the Matlab environment to validate the effectiveness of the proposed controller. Furthermore, real-time implementation has been tested to prove that the design performance is practical.

Mathematical Modeling and Kinematic analysis of 3-RRR Planar Parallel Manipulator

“…PKMs are closed-loop systems that can be outfitted with prismatic or revolute actuators [50]- [52]. Such machines include separate sequential chains in which a fixed base is associated with a moving platform [28]. PKMs can be arranged into different types in the literature [29], and the structure of such PKMs can be developed dependent on 3-RRR and 3-RPR planar parallel robots.…”

Social spider optimization algorithm for tuning parameters in PD-like Interval Type-2 Fuzzy Logic Controller applied to a parallel robot

“…The design parameters FOPID controller is optimized using the bat optimization algorithm for better improvement of controller’s performance. 20 Liu focused on the solution of the singularity problem in Redundant Parallel Manipulator. Three kinds of redundant methods are developed and discussed.…”

Application of fractional theory in quantum back propagation neural network

“…Many scientists have also conducted in‐depth research on the application of fractional order, such as the realization of the fractional‐order controller, 6 and the application in mechanics and physics 7,8 . In recent years, various domestic and foreign magazines have systematically introduced the application of fractional calculus theory in various fields, including medicine, 9–11 biology, 12–14 mechanical control, 15–17 signal processing, 18–20 image processing, 21–23 diffusion process, 24–26 and autonomous robot control 27–29 …”

“…7,8 In recent years, various domestic and foreign magazines have systematically introduced the application of fractional calculus theory in various fields, including medicine, [9][10][11] biology, [12][13][14] mechanical control, [15][16][17] signal processing, [18][19][20] image processing, [21][22][23] diffusion process, [24][25][26] and autonomous robot control. [27][28][29] Neural network is an important area of the application of fractional-order theory. 30 Using the theory of fractional calculus and the method of generalized Gronwall Bellman inequality, a finite time stability criterion is established, which shows that the stability of Caputo fractional distributed delay neural network depends on the time delay and the order of Caputo fractional derivative in finite time.…”