Inverse Kinematics of Some General 6R/P Manipulators

TL;DR

This paper introduces an algorithm for solving inverse kinematics of various 6R and related manipulators using dual quaternions and algebraic geometry, enabling precise workspace analysis and solution computation.

Contribution

It develops a novel inverse kinematics algorithm for general serial manipulators based on the HuPf method and algebraic geometry techniques.

Findings

Successfully computes inverse kinematics solutions for complex manipulators.

Identifies workspaces of manipulator subchains as quasi-projective varieties.

Provides numerical examples demonstrating the algorithm's effectiveness.

Abstract

We develop an algorithm that solves the inverse kinematics of general serial 2RP3R, 2R2P2R, 3RP2R and 6R manipulators based on the HuPf algorithm. We identify the workspaces of the 3-subchains of the manipulator with a quasi-projective variety in $\mathbb{P}^7$ via dual quaternions. This allows us to compute linear forms that describe linear spaces containing the workspaces of these 3-subchains. We present numerical examples that illustrate the algorithm and show the real solutions.