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

Calibrating unknown transformation relationships is an essential task for multirobot cooperative systems. Traditional linear methods are inadequate to decouple and simultaneously solve the unknown matrices due to their intercoupling. This article 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 special Euclidean group in 3 dimensions [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 0.9205 and 0.5363 to 0.4381 mm, respectively.

I. Introduction

Multirobot systems offer several advantages, including efficiency, scalability, and flexibility [1], [2], [3]. Multirobot systems are capable of performing more complex collaborative tasks, particularly for large-scale, intricate structures, compared to single-robot systems. Multirobot equipment has been widely used in various industries, including aviation, aerospace, automotive, and other sectors. Boeing and KUKA have collaborated in developing a multirobot machining system that is a component of fuselage automated upright build for Boeing 777 and 777X aircraft [4]. Airbus also employs comparable automated fuselage structure production lines for the A320 family aircraft [5], with over 20 robots involved in manufacturing the airplane's longer sections. With the support of the European Union's Clean Sky 2 program, Fraunhofer IFAM develops a multirobot assembly system for manufacturing a lighter aircraft fuselage of the future made of thermoplastic fiber-reinforced plastics [6], [7], as shown in Fig. 1. The coordination among multirobots is essential in typical engineering applications, particularly in determining each robot's coordinate relationship. Fig. 1.

Fraunhofer IFAM develops a multirobot assembly system for manufacturing a lighter aircraft fuselage of the future made of thermoplastic fiber-reinforced plastics (FRP) [6].