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.

Multirobot systems have shown great potential in dealing with complicated tasks that are impossible for a single robot to achieve. One essential problem encountered in cooperatively working of the multirobot systems is the unknown initial transformation relationships from hand to eye, base to base, and flange to tool. In this article, the problem of multicoordinates calibration for a dual-robot system is formulated to a matrix equation AXB = YCZ. A novel approach for simultaneously solving the unknowns in equation AXB = YCZ is proposed, which is composed of a closed form method based on the Kronecker product and an iterative method which converts the calculation of a nonlinear problem to an optimization problem of a strictly convex function. The closed form method is used to quickly obtain an initial estimation for the iterative method to improve the efficiency and accuracy of iteration. In addition, a series of conditions on the solvability of the problem are proposed to guide the operators to select appropriate robot attitudes during the calibration process. To show the feasibility and superiority of the proposed iterative method, two other calibration methods are chosen to be compared to the proposed method through simulation and practical experiments. The comparison results verify the superiority of the proposed method in accuracy, efficiency, and stability.

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.

Free-form surface matching that aligns measured points with a design model is a common problem in manufacturing automation. In this paper, an iterative variance-minimization matching (VMM) method is proposed to address measured points that have measuring defects, such as uneven/open point distributions and measuring noise. The basic idea is that the objective function is defined as the variance of the closest distance from each measured point to the design model, and the measuring defects are considered by incorporating an average distance item into the objective function. Using the defined average distance item, a strategy for analyzing the effect of measuring defects on VMM and existing methods is presented. It is shown that the VMM method does not easily become trapped in a local optimum when measuring defects exist. To consider convergence speed and convergence stability, a new distance based on the first-order point-to-point distance and point-to-tangent distance is developed and used in the objective function. To demonstrate the availability of the proposed method, quadratic convergence and positive definiteness are theoretically analyzed. The proposed method is efficient and insensitive to measuring defects and is useful for shape matching tasks involving free-form surface features.