Abstract
This article presents a solution of the inverse kinematics problem of 7-degrees-of-freedom serial redundant manipulators. A 7-degrees-of-freedom (7-DoF) redundant manipulator can avoid obstacles and thus improve operational performance. However, its inverse kinematics is difficult to solve since it has one more DoF than that necessary for reaching the whole workspace, which causes infinite solutions. In this article, Gröbner bases theory is proposed to solve the inverse kinematics. First, the Denavit–Hartenberg model for the manipulator is established. Second, different joint configurations are obtained using Gröbner bases theory. All solutions are confirmed with the aid of algebraic computing software, confirming that this method is accurate and easy to be implemented.
Highlights
E solution of the forward kinematic problem is independent of the geometry of the robot. e same does not occur with the inverse kinematics problem since the procedure to obtain the equations depends exclusively on the geometric configuration of the robotic manipulator
When using the Grobner bases theory for the solution of inverse kinematics of 7-degrees-of-freedom serial redundant manipulators, one notes in the tests performed during this research that it is computationally efficient since the equations produced for determination of seven variables are mathematically simpler to be solved
E original equations that model the inverse kinematics of these manipulators cannot be solved at once using the solve command in MAPLE
Summary
Two well-known classic problems in the kinematics of robotic manipulators are forward and inverse kinematics. E solution of the forward kinematic problem is independent of the geometry of the robot. Denavit and Hartenberg [1] presented a convention to standardize the reference coordinate systems for spatial links; after ten years, the same authors developed the algorithm for solving the forward and inverse kinematics problems of articulated systems [2]. An alternative method for the solution of inverse kinematics will be used in this article, namely, Grobner bases theory. With the help of algebraic computing software, all these solutions can be calculated, including cases which are not so solved using matrix algebra or geometric applications due to the complexity of the geometry of some manipulator robots
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