Inverse kinematics and path planning of manipulator using real quantifier elimination based on Comprehensive Gr\"obner Systems

TL;DR

This paper introduces a novel approach using Comprehensive Gr"obner Systems for inverse kinematics and path planning of a 3-DOF manipulator, enhancing efficiency and solution verification.

Contribution

It presents the first application of CGS-based quantifier elimination for inverse kinematics and path planning, improving computational efficiency and solution verification.

Findings

Effective verification of inverse kinematics solutions.

Enhanced efficiency in trajectory planning.

Successful application to a 3-DOF manipulator.

Abstract

Methods for inverse kinematics computation and path planning of a three degree-of-freedom (DOF) manipulator using the algorithm for quantifier elimination based on Comprehensive Gr\"obner Systems (CGS), called CGS-QE method, are proposed. The first method for solving the inverse kinematics problem employs counting the real roots of a system of polynomial equations to verify the solution's existence. In the second method for trajectory planning of the manipulator, the use of CGS guarantees the existence of an inverse kinematics solution. Moreover, it makes the algorithm more efficient by preventing repeated computation of Gr\"obner basis. In the third method for path planning of the manipulator, for a path of the motion given as a function of a parameter, the CGS-QE method verifies the whole path's feasibility. Computational examples and an experiment are provided to illustrate the effectiveness of the proposed methods.