SOLVING THE INVERSE KINEMATICAL PROBLEM OF A ROBOT ARM BY USING GROEBNER BASIS

Alisya Masturoh,Bambang Hendriya Guswanto,Triyani Triyani

doi:10.20884/1.jmp.2021.13.1.4428

Alisya Masturoh, Bambang Hendriya Guswanto + Show 1 more

Open Access

https://doi.org/10.20884/1.jmp.2021.13.1.4428

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Abstract

The inverse kinematical problem of a robot arm is a problem to find some appropriate joint configurations for a pair of position and direction of a robot hand which is represented by a polynomial equations system. The system is solved by employing Groebner basis notion. Thus, the appropriate joint configurations for a pair of position and direction of the robot hand are obtained.

Highlights

Groebner basis of a polynomial ideal is a spanning subset of the ideal causing the leading term of any non-zero element of the ideal can be divided by one or more leading terms of the elements of Groebner basis
Groebner basis is employed to solve polynomial equations system. This notion can be applied to robotics problems such as inverse kinematical problems
This paper studies how Groebner basis is used to solve an inverse kinematical problem for a robot arm with three segments

Summary

INTRODUCTION

Groebner basis of a polynomial ideal is a spanning subset of the ideal causing the leading term of any non-zero element of the ideal can be divided by one or more leading terms of the elements of Groebner basis. Groebner basis is employed to solve polynomial equations system (see [1,2]) This notion can be applied to robotics problems such as inverse kinematical problems. Inverse kinematical problem is a problem to find some appropriate joint configurations for a pair of position and direction of a robot hand. This paper studies how Groebner basis is used to solve an inverse kinematical problem for a robot arm with three segments. We obtain all combinations of joints settings satisfying certain position and direction of the robot hand which solves the polynomial equations system of the reduced Groebner basis reperesenting the inverse kinematical problem. The solvability of the polynomial equations system of the reduced Groebner basis representing the inverse kinematical problem for the robot arm with three segments is discussed. All combinations of joints settings satisfying certain position and direction of the robot hand are mentioned

METHODS

RESULTS AND DISCUSSION

CONCLUSION