Quasi-Static Compliance Calibration of Serial Articulated Industrial Manipulators

This article presents a procedure for the quasi-static compliance calibration of serial articulated industrial manipulators. Quasi-static compliance refers to the apparent stiffness displayed by manipulators at low-velocity movements, i.e., from 50 to 250 mm/s. The novelty of the quasi-static compliance calibration procedure lies in the measurement phase, in which the quasi-static deflections of the manipulator’s end effector are measured under movement along a circular trajectory. The quasi-static stiffness might be a more applicable model parameter, i.e., representing the actual manipulator more accurately, for manipulators at low-velocity movements. This indicates that the quasi-static robot model may yield more accurate estimates for the trajectory optimization compared with static stiffness in the implementation phase. This study compares the static and apparent quasi-static compliance. The static deflections were measured at discretized static configurations along circular trajectories, whereas the quasi-static deflections were measured under circular motion along the same trajectories. Loads of different magnitudes were induced using the Loaded Double Ball Bar. The static and quasi-static displacements were measured using a linear variable differential transformer embedded in the Loaded Double Ball Bar and a Leica AT901 laser tracker. These measurement procedures are implemented in a case study on a large serial articulated industrial manipulator in five different positions of its workspace. This study shows that the measured quasi-static deflections are bigger than the measured static deflections. This, in turn, indicates a significant difference between the static and apparent quasi-static compliance. Finally, the implementation of the model parameters to improve the accuracy of robots and the challenges in realizing cost-efficient compliance calibration are discussed.

New identification method for computer numerical control geometric errors

To address the problems of the low accuracy of geometric error identification and incomplete identification results of the linear axis detection of computer numerical control (CNC) machine tools, a new 21-item geometric error identification method based on double ball-bar measurement was proposed. The model between the double ball-bar reading and the geometric error term in each plane was obtained according to the three-plane arc trajectory measurement. The mathematical model of geometric error components of CNC machine tools is established, and the error fitting coefficients are solved through the beetle antennae search particle swarm optimization (BAS–PSO) algorithm, in which 21 geometric errors, including roll angle errors, were identified. Experiments were performed to compare the optimization effect of the BAS–PSO and PSO and BAS and genetic particle swarm optimization (GA–PSO) algorithms. Experimental results show that the PSO algorithm is trapped in the local optimum, and the BAS–PSO is superior to the other three algorithms in terms of convergence speed and stability, has higher identification accuracy, has better optimization performance, and is suitable for identifying the geometric error coefficient of CNC machine tools. The accuracy and validity of the identification results are verified by the comparison with the results of the individual geometric errors detected through laser interferometer experiments. The identification accuracy of the double ball-bar is below 2.7 µm. The proposed identification method is inexpensive, has a short processing time, is easy to operate, and possesses a reference value for the identification and compensation of the linear axes of machine tools.

A method for identifying and predicting the geometric errors of a rotating axis

To improve the machine tool accuracy, an integrated geometric error identification and prediction method is proposed to eliminate the positioning inaccuracy of tool ball for a double ball bar (DBB) caused by the rotary axis’ geometric errors in a multi-axis machine tool. In traditional geometric errors identification model based on homogenous transformation matrices (HTM), the elements of position-dependent geometric errors(PDGEs) are defifined in the local frames attached to the axial displacement, which is inconvenient to do redundance analysis. Thus, this paper proposed an integrated geometric error identification and prediction method to solve the uncertainty problem of the PDGEs of rotary axis. First, based on homogeneous transform matrix (HTM) and multi-body system (MBS) theory, The transfer matrix only considering the rotary axes is derived to determine the tool point position error model. Then a geometric errors identification of rotary axis is introduced by measuring the error increment in three directions. Meanwhile the geometric errors of C-axis are described as position-dependent truncated Fourier polynomials caused by fitting discrete values. Thus, The geometric error identification is converted to the function coefficient. Finally, the proposed new prediction and identification model of PDGEs in the global frame are verified through simulation and experiments with double ball-bar tests.