Algebraic technique for the stiffness model reduction in elastostatic calibration of robotic manipulators

Alexandr Klimchik,Benoit Furet,Anatol Pashkevich

doi:10.1109/aim.2014.6878330

Abstract

The paper deals with elastostatic calibration of a serial industrial robot. In contrast to other works, all compliance sources associated with both links and joints elasticity are taken into account. Particular attention is paid to the model parameters identification using end-point measurements only. For such experimental setup, the model is transformed into the form suitable for calibration with the sufficient rank of the corresponding observation matrix. The main contributions are in developing algebraic, physical and heuristic techniques that allow user to obtain complete model with minimal number of parameters. The advantages of the developed approach are confirmed by an experimental study that deals with identification of the elastostatic model parameters for a 6 dof serial industrial robot.

Highlights

The paper deals with elastostatic calibration of a serial industrial robot
The main difficulty of elastostatic calibration is that direct application of the Virtual Joint Method (VJM)-based method gives excessive number of parameters whose impact in the robot positioning accuracy essentially differ
This paper further develops this research and pays particular attention to generation theoretically identifiable elastostatic model

Summary

METHODOLOGY OF ELASTOSTATIC IDENTIFICATION

To estimate the matrices describing elasticity of the manipulator components (i.e., compliances of the virtual springs presented in the VJM-based modeling [3]), the elastostatic model can be written as t. )T ηT η(A min π expression (7), where the observation matrices A(q j , w j | π) are computed for certain set of measurement configurations where η is the matrix of weighting coefficients that normalizes the measurement data, A j A(q j , w j | π) This minimization problem yields the following solution q j and loadings w j. It should be noted that this particularity is usually omitted in conventional robot calibration Another way to improve the identification accuracy is related to the proper selection of manipulator measurement configurations q j , j 1, m that is known as the calibration experiment planning [9], which directly influences on the observation matrices A(q j , w j | π) and on the covariance matrix (8).

MODEL REDUCTION

VIII. CONCLUSION