Abstract
The traditional Denavit–Hatenberg method is a relatively mature method for modeling the kinematics of robots. However, it has an obvious drawback, in that the parameters of the Denavit–Hatenberg model are discontinuous, resulting in singularity when the adjacent joint axes are parallel or close to parallel. As a result, this model is not suitable for kinematic calibration. In this article, to avoid the problem of singularity, the product of exponentials method based on screw theory is employed for kinematics modeling. In addition, the inverse kinematics of the 6R robot manipulator is solved by adopting analytical, geometric, and algebraic methods combined with the Paden–Kahan subproblem as well as matrix theory. Moreover, the kinematic parameters of the Denavit–Hatenberg and the product of exponentials-based models are analyzed, and the singularity of the two models is illustrated. Finally, eight solutions of inverse kinematics are obtained, and the correctness and high level of accuracy of the algorithm proposed in this article are verified. This algorithm provides a reference for the inverse kinematics of robots with three adjacent parallel joints.
Highlights
Robot kinematics includes forward and inverse kinematics, which are considered the basis of trajectory planning and motion control
Forward kinematics is about obtaining the pose of the end effector of robots by choosing a group of joint angles within the workspace, which correspond to a unique solution
According to the known pose of the end effector, the solving of all possible joint angles is regarded as inverse kinematics, for which there are multiple solutions
Summary
Robot kinematics includes forward and inverse kinematics, which are considered the basis of trajectory planning and motion control. Analytical, geometric, and algebraic methods in combination with the Paden–Kahan subproblem and matrix theory are adopted to solve the inverse kinematic problem of a type of 6-DOF industrial robot, whose three adjacent joint axes are parallel. The problems of singularity of the D-H and POE-based models are analyzed from the changes in the kinematic parameters that occur when the third joint axis of the OUR-1 robot exhibits a slight deviation with respect to the parallel axes. The mapping of the POE formula represents the smooth mapping from the Lie algebras to the Lie groups so that the singularity of the POE-based model can be handled effectively.[9] this model is regarded as a great option for application in kinematic calibration, by which the actual kinematic parameters are identified to improve the positioning accuracy of robots. Solving q5 and q6 Left-multiplying equation (11) by eÀ^x1q1 gives eÀ^x1q1 Á gst1 1⁄4 e^x2q2 e^x3q3 e^x4q4 e^x5q5 e^x6q6
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