A Novel Dual-Robot Accurate Calibration Method Using Convex Optimization and Lie Derivative

凸优化 数学优化 机器人 工业机器人 数学 计算机科学 算法 人工智能 正多边形 几何学
作者
Cheng Jiang,Wenlong Li,Wenpan Li,Dongfang Wang,Lijun Zhu,Wei Xu,Huan Zhao,Han Ding
出处
期刊:IEEE Transactions on Robotics [Institute of Electrical and Electronics Engineers]
卷期号:40: 960-977 被引量:11
标识
DOI:10.1109/tro.2023.3344025
摘要

Calibrating unknown transformation relationships is an essential task for multi-robot cooperative systems. Traditional linear methods are inadequate to decouple and simultaneously solve the unknown matrices due to their intercoupling. This paper proposes a novel dual-robot accurate calibration method that uses convex optimization and Lie derivative to solve the dual-robot calibration problem simultaneously. The key idea is that a convex optimization model based on dual-robot transformation chain is established using Lie representation of SE(3). The Jacobian matrix of the established optimization model is explicitly derived using the corresponding Lie derivative of SE(3). To balance the influence of the magnitudes of the rotational and translational optimization variables, a weight coefficient is defined. Due to the closure and smoothness of Lie group, the optimization model can be solved simultaneously using Newton-like iterative methods without additional orthogonalization processing. The performance of the proposed method is verified through simulation and actual calibration experiments. The results show that the proposed method outperforms the previous calibration methods in terms of accuracy and stability. The actual experiments are used to compare the proposed method with two existing calibration methods, and the mean measurement error of a certified ceramic sphere is reduced from 0.9205mm and 0.5363mm to 0.4381mm, respectively.
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