# Influence of the Approach Direction on the Repeatability of an Industrial Robot
## 1 Introduction  
Industrial robots and manipulators are generally considered to be universal systems that can be operated in any industrial conditions, in any way. However, the purpose of the manipulator is given by the mounted tool--its installation considerably limits the versatility of the manipulator. In industrial conditions, it is the rule that the manipulator is a part of a single-purpose machine, production line, or other equipment. In these cases, it is usually possible to operate only in a specific way, usually performing one specific task cyclically. Therefore, in cases where it is necessary to increase the precision of the manipulator, it may be not necessary to increase the absolute accuracy in the entire working envelope of the robot, but it might be sufficient to increase repeatability only for specific targets. In terms of industrial manipulator precision, two different values are generally addressed--accuracy and repeatability. Accuracy is the ability of the robot to reach a tool center points (TCPs) programmed pose with respect to the robot's base frame. Repeatability is ability of the robot to return its TCP (tool center point) to the same position, repeatedly from the same direction. The accuracy of the manipulator is affected by several external influences. In addition to temperature, manufacturing inaccuracies, shaft deflection and clearances in bearings and gearboxes, it can be, for example, the fact that the resolvers (or encoders) are located at the beginning of the drive unit, and therefore, do not detect an error that occurs on the motor and gearbox [1]. Repeatability is caused by clearances, resolution of position sensors, thermal expansion, and other influences. It doesnot include the coordinate system setting errors, other than the modelled arm length, manufacturing, and assembly deviations (e.g., non-perpendicularity or non-parallelism of joints and guides). While absolute accuracy can vary by up to 15 mm [2] compared to the ideal model in the case of large manipulators, and it is necessary to use an external device, such as a laser tracker for measuring and increasing accuracy, repeatability is usually in the range of tenths to hundredths of a mm [1]. However, it depends on the operating conditions a lot. The values given by the manufacturer usually apply to a steady state under ideal conditions and for a new manipulator. Nevertheless, there are applications in which an ordinary level of repeatability may not appear to be sufficient, especially for less rigid robot structures. For example, ABB offers the Absolute Accuracy and CalibWare Option for its robots [2]. This functionality aims to eliminate the difference between an ideal manipulator in a Computer-aided design (CAD) environment and the real robot installed on a factory site. The correction solves not only the mechanical properties and inaccuracies of the particular manipulator but also deviations caused by an inaccurately defined payload. An advantage is also the interchangeability of the robot \"piece by piece\" if necessary, as the accuracy of robots, calibrated by this method, is consistent. The difference between an ideal virtual and a real manipulator is usually in the range of 8-15 mm, depending on the type of robot and the concurrence of manufacturing tolerances and deviations. This technique uses a laser tracker to measure accuracy at one hundred targets within the entire robot workspace, based on this measurement, calibration within the entire robot working envelope is provided. The resulting accuracy is generally 0.5 mm, but typically not lower [2]. Calibration methods based on the use of a laser tracker [3; 4] are commonly used in industrial applications. Further research in this field focuses for example on an additional increase of accuracy of this method by making a big number of measurements (in the order of tens of thousands) as described in [5].