Algebraic methods for computing inverse kinematics

Abstract

Abstract. Inverse kinematics computation is one of the challenging topics in robot control and simulation. The description of the kinematics of a robot leads to an algebraic system of equations when trigonometric functions are avoided by certain substitutions. Solving the inverse kinematics problem can so be reduced to solving a system of algebraic equations. In order to keep numerical errors small, one should try to transform the system of equations into an equivalent but 'simpler' one by some algebraic method. GrC3bner bases are an algebraic technique that transform algebraic equations into a 'standard form', the Gr0bner basis, that has certain properties concerning the solvability and the solutions of an algebraic system of equations. In this paper, we give an introduction to the formulation of the kinematic equations and to the method of Gr0bner bases, and discuss how Gr6bner bases can be applied to this specific class of problems.

Analysis of computational efficiency for the solution of inverse kinematics problem of anthropomorphic robots using Gröbner bases theory

“…Note that the S-polynomial is produced to cancel the leading terms of the polynomials involved. The Buchberger's algorithm receives as input a finite set F ¼ f 1 ; f 2 ; Á Á Á ; f n f gof polynomials and provides a set G, which is a Gröbner basis of F: According to Stifter, 19 this algorithm can be described as follows.…”

“…Stifter 19 presented an algorithm to solve the IK of a 2R robot using Gröbner bases theory. The author presented a brief list of subjects that were not yet fully resolved but that could play an essential role in applying Gröbner bases theory for solving the problem of IK.…”

A Metaheuristic Optimization Approach to Solve Inverse Kinematics of Mobile Dual-Arm Robots

“…However, the proposed approach can also be applied to solve non-coordinated manipulation tasks. Some classical methods to compute the inverse kinematics of robot manipulators are closed-form methods and numerical approaches [3,4]. There is no guarantee of finding a closed-form solution with algebraic methods.…”

Inverse Kinematics of Redundant Manipulators Formulated as Quadratic Programming Optimization Problem Solved Using Recurrent Neural Networks: A Review

“…For manipulators with larger number of DOF, one possible solution is to split the problem into smaller parts and make calculations with geometrical approach, 11 (2) algebraic. [12][13][14][15][16][17][18][19][20][21][22] Algebraic methods are used to obtain closed-form solutions. The kinematic equations of the manipulator are transformed into higher degree polynomial and then all the roots of the polynomial are determined, and (3) iterative.…”