AI summary
Problem
The lack of a direct, closed-form conversion method between Product of Exponentials (POE) and Complete and Parametrically Continuous (CPC) kinematic models complicates robot calibration and parameter identification across different conventions.
Approach
The paper formulates and proves three lemmas using Lie group theory to decompose POE joint twists into CPC parameters, yielding a systematic algorithm for exact parameter mapping.
Key results
- Proves exact conversion lemmas for revolute, prismatic, and helical joints
- Develops Algorithm 1 for systematic POE-to-CPC parameter extraction
- Validates conversion accuracy numerically on a PUMA 560 robot
- Provides a unifying framework for comparing calibration results across kinematic conventions
Why it matters
Allows robotics researchers and engineers to flexibly select and convert between kinematic models for calibration and control without sacrificing mathematical rigor or accuracy.
Abstract
This paper presents an analytical framework for parameter conversion between Complete and Parametri- cally Continuous (CPC) and Product of Exponentials (POE) kinematic models of serial-chain mechanisms. The approach, grounded in Lie group and algebra theory, formulates and proves three key lemmas to enable exact POE-to-CPC pa- rameter conversion. Building upon established POE-DH and CPC-DH transitions, the proposed framework facilitates flexible model selection based on application-specific needs, independent of the initial parameterization. Primarily designed for robot calibration, this method also serves as a unifying tool for comparing and analyzing calibration results across different kinematic conventions. The framework’s effectiveness is demon- strated through numerical validation on the PUMA 560 robot, confirming its accuracy and practical applicability.