# Influence of Drift on Robot Repeatability and Its Compensation
## 1 Introduction  
Contemporary industrial robots are precise machines. For a common industrial angular six-axis robot with a load capacity of up to 10 kg, a repeatability value of 0.025 mm is achievable. However, this value guaranteed by the manufacturers of those robots is valid only for the steady environment conditions. When the ambient temperature or temperature of the robot changes, the repeatability can drop to significantly worse values with a difference up to one order of magnitude. The value of repeatability is affected by many influences. The greatest one is the drift, caused by thermal expansion. It is the reason why, for many applications, robots must be pre-warmed before production can be started. The phenomenon, generally known as a drift, is defined by ISO 9283:1998 standard [1] as a shift of the position in time. The thermal expansion and its effect on repeatability is an issue accompanying any high precision device, and thus, there are solutions that describe possible compensation and calibration methods. Among the commercially available solutions, there can be found an AccuBeam: Robot Temperature Compensation system. It uses a twin beam laser and a rugged industrial sensor. Between production cycles, the robot automatically executes a \"Quick-Check\" measurement routine to assess overall system performance and to detect any drift of Tool Center Point (TCP) or crash of the robot. However, the presence of laser sensors in the workspace is required [2]. For special robot applications, such as honing of boreholes, Wiest AG offers an industrial solution of continuous compensation of the robot temperature drift with the help of the measuring technique LaserLAB [3]. Real-time compensation of 3 DOF ultra-high precision parallel robot, based on the use of a 6 DOF measuring system described in [4] effectively compensates the repeatabilityerror. A similar approach is used in real-time CNC thermal error compensation [5]. One of the approaches to solve the repeatability error is the calibration of the robot for a specific condition. The authors in [6] present a basic overview of robot calibration. Another solution suitable for industrial application is presented in [7] with the use of the finite element theory, which is utilized to create thermal distribution and deformation models of a measured system. A compensation system based on those models can reduce the final position error below 0.1 mm. Robot development centers, as well as university researchers, are working on drift minimization [8; 9]  
To obtain a reliable and robust model, a Grey Neural Network model with Convolution Integral methodology presented by [10] can be used. By using a neural network algorithm and camera-based measurement system, industrial robot calibration is performed in [11] resulting in significant improvement in precision compared to traditional analytical methods. There are other methods of measuring and increasing robot precision. According to [12], the joint errors can be compensated by identifying the joint deformation. With this information, the system can compensate for the predicted deviation caused by the joint stiffness error and the kinematic error by tens of percent. Real-time compensation of thermal error, based on an error distribution model, proposed by [13], can also increase the achievable level of robot precision, as was experimentally verified on a car-body assembly line. The theoretical prediction of the error distribution inside the robot working envelope is realized by using multiple vision sensors. A real-time error compensation can be achieved [14]. The [15] uses an advanced algorithm, such as Kalman filter and MOIFA data fusion, to increase robot precision. By the proposed methodology, an improvement in a range from 38% to 78% could be achieved. Another method of robot repeatability measurement is proposed by [16].