A Fast Algorithm for Inverse Kinematic Analysis of Robot Manipulators

Abstract

To solve the inverse kinematics problem, we obtain with little effort a reduced and complete set of equations by a conve nient choice of end-effector frame and application of rotation orthogonality. This approach does not require computation of the forward kinematics and can be used with manipulators of any geometry, although it is most efficient when applied to orthogonal manipulators, a class of robot arms defined in this paper. For manipulators requiring numerical techniques, but for which knowledge of one joint variable allows closed- form solutions of the remaining joint variables, an iterative inverse kinematic method, simple and fast enough to be suitable for real-time manipulator control, has been devel oped. The concepts and techniques presented in this paper are illustrated with two examples. The iterative method devel oped here performs a kinematic inversion of a 6-degree-of- freedom manipulator with no closed-form solutions in less than 30 ms using a desktop computer, an order of magnitude faster than times found in the literature.

Freeing the Serial Mechanism Designer from Inverse Kinematic Solvability Constraints

“…In a sense, our method could be considered a hybrid method, as it is partially an analytical solution method and partially a numerical solution method. This method is similar to the one presented by Manseur and Doty (1988). Their method required the first joint to be rotational and iterated over that joint angle.…”

Two optimization algorithms for solving robotics inverse kinematics with redundancy

“…where G is either (5) or (6), and Ω is the domain of θ 2 . In other words, the redundancy in the inverse kinematics mapping is removed.…”

A kinematic analysis of the gmf a-510 robot: An introduction and application of groebner basis theory

“…Formally called the Denavit-Hartenberg Matrix, this matrix algebra technique is preferred by engineers because of its simplicity and repetition, to obtain an inverse kinematics solution for a robot manipulator. Tsai et al [29], Huang [11], Manseur and Doty [19] developed iterative procedures (also referred to as continuing methods) to obtain a solution. These methods required rigorous calculations that did not necessarily converge to a correct solution.…”