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A General Procedure to Evaluate Robot Positioning Errors

The School of Engineering and Architecture The Catholic University of America Washington, D.C. 20064

Edward B. Magrab

Precision Engineering Division Center for Manufacturing Engineering National Bureau of Standards Gaithersburg, Maryland 20899

A new, explicit, and complete formulation that describes the geometric errors due to both origin translation and misalign ments of axes in the positioning of an open-loop robot ma nipulator has been presented. The formulation does not use the usual Denavit-Hartenberg approach. The results clearly display the role of each quantity involved and allow easy physical interpretation of each error term. First, a general kinematic formulation for an ideal robot with an arbitrary number of links is developed. The geometric errors in axes locations and orientations are then shown to be skew coordi nate transformations with origin translations and are incor porated into the analysis using general tensor algebra. The final forms of forward and backward transformations contain up to 9 (N + 2) error parameters for a robot with N physical links. This theoretical formulation is applied to a specific six-degrees-of-freedom robot. It is observed that of the possi ble 72 errors in this robot, only 53 can independently contrib ute to the error at the end effector and are the only ones that can be determined by measurements made at the end effec tor. It is shown how a correlation matrix analysis can be used to isolate these 53 parameters. In addition. it is shown how, using a successive orthogonalization technique, one can eliminate from consideration error parameters (eight in the present case) that are too small to be significant but contrib ute to the ill-conditioning of the coefficient matrix. Applica tion of the procedure to computer-simulated data shows that the formulation and the numerical techniques developed here combine to form a powerful method to calibrate a robot.

The International Journal of Robotics Research, Vol. 6, No. 1, 59-74 (1987)
DOI: 10.1177/027836498700600105


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