The accuracy of industrial robots is typically expressed by the position and posture errors of the robot's hand actuators, which is one of the main indicators reflecting the robot's performance. Current research on robot errors can be divided into several aspects: theoretical prediction of robot errors, experimental analysis of the causes and extent of robot errors, and research on compensation techniques specifically designed to avoid or reduce robot errors.
Currently, the main approach is to use analytical methods based on the solutions of robot forward kinematics to perform static error analysis on the position and orientation of the robot's hand actuator. Generally, vector and matrix algorithms are used, assuming the robot's mechanism parameters are known, including link lengths, joint hole center distances, and initial manufacturing errors, to analyze and study the accumulated errors in the hand's position and orientation. This analytical method typically treats the entire mechanism as a rigid body; therefore, it does not consider deformations that occur during motion, but only discusses and analyzes errors caused by changes in motion and errors caused by parameters such as mechanism length.
The problem of robot error was first proposed by A. Kuman and K.J. Waldron in 1978, more than twenty years after the birth of industrial robots. The following year, at the Fifth International Congress on Mechanisms and Machines (IFToMM), they presented a more comprehensive method for analyzing robot positional accuracy. Kuman and Waldron used two 3x3 transformation matrices and a three-dimensional translation column vector in the Denavit-Hartenberg coordinate system to form the coordinate transformation matrix between adjacent components. They assumed that the structural parameters of the object under study were known and error-free, and based on this, they established an expression for the positional error of the robot's end effector. At the Sixth International Congress on Mechanisms and Machines in 1983, Parakash and Kuman incorporated errors such as the length of the robot mechanism and the center distance of the joint holes into the overall error model and derived its expression.
In 1984, Wu Qihao applied Paul's method of motion analysis of robot mechanisms to the analysis of static errors, and derived the trend of the position error of the robot hand working unit in Cartesian space relative to the global coordinate system caused by the errors of structural parameters of components and joint motion variables.
The variation law of position error of the end effector. Zhang Qixian et al. applied the dynamic velocity algorithm of the BoboLev series mechanism, and used the robot Jacobi matrix to give a relatively simple mathematical relationship between the mechanism's length, hole center distance error and end effector position error, and used this as its transfer function. Its physical meaning is relatively clear, its versatility is strong, and its form is relatively simple, making it convenient for engineers to perform calculations and analyses with computers. These methods all use matrix transformations, and calculate the position error of the robot end effector through differentiation, multiplication, and quadrature between matrices.
K. Sugimoto, Huang Zhen, and others have employed the vector method to analyze and study the position error of robot end effectors. Unlike the matrix method, the vector method operates within an absolute coordinate system, propagating errors through vector multiplication and addition. Due to its characteristics, its model expression contains many partial derivatives, making it quite complex. Therefore, most methods based on the vector method for analyzing static errors typically employ various mathematical approaches to try and find a more unified expression for the partial derivative function of the robot's end effector's position deviation, linking it to a computer to reduce manual computation.
Xu Weiliang integrated the slight displacements and deviations of each part in the robot's initial state to construct a deviation model for the hand's position and posture. He then used statistical simulation—a probabilistic and mathematical statistical method—to calculate the deviations in the robot's hand's position and posture through random sampling. He further conducted a probabilistic analysis of the position and posture errors within the robot's achievable workspace. Based on this algorithm, he constructed a mathematical optimization model. This model uses the length of the mechanism components as the control parameter, the deviation as the objective function, and the absolute position and posture deviations meeting the given task requirements as a constraint.
Because the motion accuracy of industrial robots has a significant impact on their reliability in the production process, and sometimes even determines their survival in industrial manufacturing, it has received close attention from many scholars both domestically and internationally. Scholars have published numerous papers analyzing the causes of errors and actively seeking various methods to compensate for them. William K. Veitschegger constructed an error model using the least squares method combined with matrix partial differential equations and compensated for the deviations by designing iterative deviation compensation software; this method is algorithmically complex. Souji Inagaki focused on the impact of different parameter deviations in the robot's transmission parts on the hand's deviations; however, due to the use of advanced sensing technology to collect data, this method increased the robot's production cost. Broderick analyzed the pose of each link of the robot using the robot's pose shape matrix and calculated its geometric parameters, but lacked a good method to solve the inverse kinematics problem, thus affecting error compensation. Currently, most literature on robot error analysis and compensation involves the derivation of complex mathematical formulas, with less attention paid to the comprehensive error analysis and compensation of robot position and posture caused by multiple factors.
