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 ofSE(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.

Industrial robots are characterized by good flexibility and a large working space, and offer a new approach for the machining of large and complex parts with small machining allowances (extra material allowed for subsequent machining). Parts of this type (such as aircraft skin parts, wind turbine blades, etc.) are easily deformed due to their large scale and low stiffness. Therefore, these parts cannot be directly machined according to the designed model. A feasible method is to plan a robotic machining path by using the point clouds of parts after clamping from onsite measurement which contains inherent defects of measurement such as noise points and abrupt points. In this article, a novel method is proposed to plan and optimize a robotic machining path that meets the requirements of smoothness, dexterity, and stiffness based on the point cloud from onsite measurement. The dual nonuniform rational B-spline curves of the machining path points and tool axis points are generated at first. Next, an objective function of smoothness optimization is established to filter out the local mutation of the path by considering the constraints of both the deformation energy and the deviation. Then, the objective function of robot postures optimization is established to optimize dexterity and Cartesian stiffness of a robot during the machining process. To show the feasibility of the proposed method, simulation and experiments are carried out. It is proved that the proposed method can generate a smooth machining trajectory. The stability of joint rotation and the rigidity and dexterity of the robot are improved during the machining process.