Kinematic Calibration of Articulated Arm Coordinate Measuring Machines and Robot Arms Using Passive and Active Self-Centering Probes and Multipose Optimization Algorithm Based in Point and Length Constrains

The kinematic modeling of articulated arm coordinate measuring machines (AACMM) has inherited both the previous developments in the field of robot arms and manipulators, and their calibration and parameter identification techniques, given the similarity of their mechanical characteristics. Traditional approaches to the problem of kinematic parameters identification in both cases use an objective function in terms of quadratic sum of errors of measurement or positioning, formulated as the euclidean distance between the points materialised by a gauge or measuring instrument, and the points obtained through the kinematic model. By capturing data at various positions in the workspace, those approaches follow a resolution scheme that involves indirect optimization, such as the Moore-Penrose pseudoinverse or other methods for solving systems of linear equations to obtain the set of kinematic model parameters which minimize the error in the positions considered. This chapter first presents a review of developments and state of the art concerning the kinematic modeling of robot manipulators and AACMM, as well as aspects to consider regarding the influence of the model chosen on the subsequent parameters identification procedure. Secondly an optimization algorithm based on an objective function that considers terms related to the accuracy and repeatability is shown. This algorithm follows a pure optimization scheme from data obtained through probing several spheres of a ball-bar gauge placed at several positions in the working range for both systems. In addition to the distance errors from the nominal coordinates of the gauge, it is possible to optimize the repeatability from the captured pose values for the same sphere in several arm orientations. To capture data, a passive self-centering probe and an active self-centering probe are used to directly probe the center of each sphere for a large number of arm orientations, and also to analyze the effect of probing force in the identification process and the generalization of the error results for any arm position and orientation. Experimental results of the capture and identification technique are presented with both probes linked to a Faro AACMM, as well as 14

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