Intrinsic Repeatability: a new index for repeatability characterisation Jean-François BRETHE Groupe de Recherche en Electrotechnique et Automatique du Havre (GREAH) Le Havre University, BP540, 76058 Le Havre, FRANCE jean-francois.brethe@univ-lehavre.fr Abstract— The paper deals with the question of robot precision and how to characterise repeata- bility. Hence ISO and ANSI repeatability indexes advantages and drawbacks are analysed. A new intrinsic repeatability index is proposed that can estimate the robot endpoint position variability satisfying the non-bias and convergence conditions. Computation of this index is performed using sim- ulated straight and drifting trajectories. Influence of load on repeatability is studied using an ex- perimental determination of an angular covariance matrix. Therefrom intrinsic repeatability can be computed in every workspace location using only this covariance matrix and the stochastic ellipsoid theory. Index Terms— Stochastic Ellipsoids, Repeatability, Robot Accuracy, Industrial Robot I NTRODUCTION In the field of industrial robots, precision is an important issue. Precision is characterized by two different indicators: accuracy and repeatability. If the target is always the same, and the move is repeated several times, repeatability mea- sures the dispersion between final points. Accuracy char- acterises the distance between the cloud of points and the commanded position as explained in ISO9283 [1] or ANSI R15.05-1[2]. In the first section, robot precision indices are presented. Within them, the ISO and ANSI repeatability indices are compared. In the second section, we study the pros and cons of the two different approaches. The concept of a repeatability sphere is discussed. The repeatability estimation is analysed in a mathematical point of view concerning bias and convergence. The sample size and the drift influence are specified. In the third section, a new repeatability index is proposed to overcome some disadvantages of the usual procedures: it is called intrinsic repeatability index and can unify the ISO and ANSI approach. Simulations are made to illustrate the concept revealing intrinsic repeatability as a very good statistical estimator. In the fourth section, we give the main lines to evaluate intrinsic repeatability using only the covariance matrix. We display an experimental procedure to estimate the angular covariance matrix and show that it is possible to evaluate load influence on repeatability index from this covariance matrix. Then, it is possible to evaluate workspace location influence on the repeatability index. I. USUAL PRECISION I NDICES 1) Repeatability and accuracy: The estimation of indus- trial robot precision is based on a test where the robot is set up to attain a commanded point and come back, this cycle being repeated several times in the same conditions. Measurements of the final robot positions show that they are near the commanded point and all the final positions constitute a cloud of points. Precision is then declined in accuracy and repeatability as displayed in fig.1. In the ISO procedure, the distance between the mean of the different final positions and the commanded position will caracterise accuracy. The ANSI definition is slightly different as it considers different locations on a standard path. For each location, the distance between the final position and the commanded position, called the deviation is measured. The accuracy index is then the mean of all the deviations. Fig. 1. ISO approach of accuracy and repeatability 2) ISO and ANSI repeatability indices: The ISO definition of repeatability index is the formula REP ISO = D +3S D where D = q (x i − x) 2 +(y i − y) 2 +(z i − z) 2 is the ran- dom variable (RV) "distance between the point (x i ,y i ,z i ) and the barycentre ( x, y, z)". In this method, the repeatability is estimated at a given location. Therefore in order to evaluate repeatability variability in the workspace, it is necessary to estimate this repeatability index in different locations in the workspace. The ANSI definition is slightly different because three different locations distributed at the extremities and the middle of the standard path have to be considered and the 2010 IEEE International Conference on Robotics and Automation Anchorage Convention District May 3-8, 2010, Anchorage, Alaska, USA 978-1-4244-5040-4/10/$26.00 ©2010 IEEE 3849