3RRR Planar Parallel Robot Research Articles

Kinematic Modelling of a 3RRR Planar Parallel Robot Using Genetic Algorithms and Neural Networks

Kinematic modelling of parallel manipulators poses significant challenges due to the absence of analytical solutions for the Forward Kinematics (FK) problem. This study centres on a specific parallel planar robot, specifically a 3RRR configuration, and addresses the FK problem through two distinct methodologies: Genetic Algorithms (GA) and Neural Networks (NN). Utilising the Inverse Kinematic (IK) model, which is readily obtainable, both GA and NN techniques are implemented without the need for closed-loop formulations or non-systematic mathematical tools, allowing for easy extension to other robot types. A comparative analysis against an existing numerical method demonstrates that the proposed methodologies yield comparable or superior performance in terms of accuracy and time, all while reducing development costs. Despite GA’s time consumption limitations, it excels in path planning, whereas NN delivers precise results unaffected by stochastic elements. These results underscore the feasibility of using neural networks and genetic algorithms as viable alternatives for real-time kinematic modelling of robots when closed-form solutions are unavailable.

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

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.

Dynamic Filtered Path Tracking Control for a 3RRR Robot Using Optimal Recursive Path Planning and Vision-Based Pose Estimation

This study proposes a dynamic filtered path tracking control schema for a 3RRR planar parallel robot to reduce the positioning errors caused by various sources such as backlash in the mechanical system, system nonlinearities, uncertainties, and unknown disturbances. The optimal recursive algorithm is implemented absolutely in path planning based on the optimization problem. Compared to other methods, this algorithm not only helps the robot avoid singularities but also ensures the shortest movement distance of links thanks to the optimization in path planning. The vision system using the 3D Intel RealSense camera D435i is proposed to provide the visual measurement as feedback for the pose estimation of the 3RRR planar parallel robot. The unscented Kalman filter is designed to reduce the errors of the pose estimation due to the camera’s intrinsic parameters, the vibration of the mechanical system, and unknown noises. The establishment of important equations and parameters of the unscented Kalman filter is detailed in this study. The simulation, experiment, and comparison are conducted to verify the effectiveness and feasibility of the proposed approaches.

Optimization Design by Genetic Algorithm Controller for Trajectory Control of a 3-RRR Parallel Robot

In order to improve the control precision and robustness of the existing proportion integration differentiation (PID) controller of a 3-Revolute–Revolute–Revolute (3-RRR) parallel robot, a variable PID parameter controller optimized by a genetic algorithm controller is proposed in this paper. Firstly, the inverse kinematics model of the 3-RRR parallel robot was established according to the vector method, and the motor conversion matrix was deduced. Then, the error square integral was chosen as the fitness function, and the genetic algorithm controller was designed. Finally, the control precision of the new controller was verified through the simulation model of the 3-RRR planar parallel robot—built in SimMechanics—and the robustness of the new controller was verified by adding interference. The results show that compared with the traditional PID controller, the new controller designed in this paper has better control precision and robustness, which provides the basis for practical application.

Dimensional Synthesis of 3RRR Planar Parallel Robots for Well-Conditioned Workspace

In this paper an exhaustive singularity analysis of a 3RRR planar parallel robot is performed. The Jacobian matrix using the Screw theory is obtained and an effective method for singular configurations analysis based on a condition index of the Jacobian matrix is presented. Finally, a new similarity law that allows the workspace optimization free of singular configurations and the working mode selection is presented. Furthermore, MATLAB as a testing tool and programming language is used.

Modelling and Simulation of Inverse Kinematics for Planar 3-RRR Parallel Robot Based on SimMechanics

Parallel robots are widely used in the manufacturing industry. In this paper, a planar 3-RRR parallel robot is studied. The inverse kinematics mathematical model is established for this kind of mechanism. Furthermore, a physical simulation model is established by virtue of MATLAB/SimMechanics and a relevant inverse kinematics simulation is implemented at the assumption of known conditions of the end-effector of robot. Through inverse kinematics simulation, the motion rules of driving parts of the planar 3-RRR parallel robot are obtained, and visualization of simulation process is realized in the system. The simulation results show that this method is much more effective and convenient when a certain simulation is implemented for the parallel mechanisms. Meanwhile, it provides a theoretical foundation and a better analytical approach of simulation for the controller design and further analysis of complex multi-linkage mechanisms in the future.

Modelling and Simulation of Forward Kinematics for Planar 3-DOF Parallel Robot Based on Simulink

Parallel robots are widely used in the machinery industry. In this paper, a planar 3-RRR parallel robot is researched. The forward kinematics mathematical model is established for this kind of mechanism. On the basis of it, a relevant simulation is carried out through MATLAB/Simulink. Thus, the motion rules and stress state for all parts of the mechanism are described vividly The simulation results show that this method is much more effective and efficient when the simulation is implemented for a certain machine system. Meanwhile, it provides a theoretical foundation and a better analytical approach of simulation for the design and analysis of complex multi-linkage mechanisms in the future.

Joint forces in dynamics of the 3-RRR planar parallel robot

Recursive matrix relations for the complete dynamics of a 3-RRR planar parallel robot are established in this paper. Three identical planar legs connecting to the moving platform are located in the same vertical plane. Knowing the motion of the platform, we develop first the inverse kinematics problem and determine the positions, velocities and accelerations of the robot. Further, the inverse dynamic problem is solved using an approach based on the principle of virtual work. Finally, compact matrix equations and graphs of simulation for the input torques of three actuators, the external and internal joint forces are obtained.