The inverse kinematics of a 7R 6-degree-of-freedom robot with non-spherical wrist

Abstract

The 7R 6-degree-of-freedom robots with hollow non-spherical wrist have been proven more suitable to spray painting. However, the inverse kinematics of this robot is still imperfect due to the coupling between position and orientation of the end-effector. In this article, a reliable numerical iterative algorithm for the inverse kinematics of a 7R 6-degree-offreedom robot is proposed. Based on the geometry of the robot, the inverse kinematics is converted into a onedimensional iterative research problem. Since the Jacobian matrix is not utilized, the proposed algorithm possesses good convergence, even for singular configurations. Moreover, the multiple-solution problem in the inverse kinematics is also discussed. By introducing three robot configuration indicators which are prespecified by a user, the correct solution could be chosen from all the possible solutions. In order to verify the accuracy and efficiency of the proposed algorithm, several simulations are implemented on a practical 7R 6-degree-of-freedom painting robot. The result shows that the proposed algorithm is more advantageous for a continuous trajectory.

Kinematic Calibration of a 7R 6-DOF Robot With Non-spherical Wrist Using Laser Tracker

“…The kinematic error model is a mathematical relationship between the kinematic errors and the pose of EE. As shown in Figure 1 (a), it is the virtual prototype of a 7R 6-DOF robot with non-spherical wrist which has been proved to be advantageous in painting application due to wider range of motion of the wrist [28]. The 4R 3-DOF wrist of the 7R 6-DOF robot has 4 revolute joints, the second and third of which are coupled with the relation 65 =  − .…”

“…The robot researched in this paper is a 7R 6-DOF robot as shown in Figure 1, which is not a purely open-loop structure, but rather contains a 4R 3-DOF non-spherical wrist with a coupling joint to increases motion flexibility [28]. This special wrist great increase the complexity and difficulty of calibration.…”

Finite-Time Output Feedback Control for a Rigid Hydraulic Manipulator System

“…There exists ∈ (0, 1) such that, for every ∈ (1 − , 1), the origin is a globally finite-time-stable equilibrium for system (2) under the feedback control law…”

“…In the past years, robotic system related control problem has been investigated more and more widely for robots application value [1,2]. In addition to rapid responses and high power-to-weight ratios [3][4][5][6][7][8][9][10], a great many robots are driven by hydraulic actuators.…”

The investigation of trajectory control for an anthropomorphic manipulator attached to a vehicle

“…A comparative study of several methods based on the Jacobian matrix [2], clarified that the modified Levenberg-Marquardt method is much better for a large set of random configurations, but may lose convergence compared to Jacobian transpose and pseudocode inverse methods. For solving real-time IK without using the Jacobian matrix, numerical and analytical mathematical tools based on the end-effector position were proposed, but without mentioning the solution time consumption [3]. A similar method for (2n+1) DoF hyper-redundant manipulator arm was also applied [4].…”