# Study of Orientation Error on Robot End Effector and Volumetric Error of Articulated Robot
## 1 Introduction  
Articulated robots are being used in many areas where accuracy and kinematic performance can be crucial, for example in part assembly, drilling, deburring, and welding. These operations require performance that was needed on robot system. The major robot performance constraints are repeatability and accuracy, following by uptime, load capacity, velocity, and size of robot. The specifications quoted by the manufacturers, are generally not sufficient to determine the process capability of the robot required. Most of the time, manufacturers specify resolution, repeatability, and accuracy rather than pose, but pose is important for offline programming and process planning. Robots from the same production batch, with identical specifications, can demonstrate different characteristics when operated under different conditions (different loads, speeds, durations, temperature, etc.). Standardized testing and evaluation techniques are needed to examine the process capability of a wide variety of robots in order to make the appropriate selection [1; 2; 3; 4; 5; 6; 7]. During their life robots may require maintenance which may involve changing encoders etc. Unless a re-datuming technique is available then the accuracy could differ significantly from that achieved prior to the maintenance. To achieve the previous performance, re-teaching or re-datuming may be required [8; 9]. When the robot parameter does not coincide with the designer's intention, the error occurs between the taught position and the design data-based position. If the control parameter set up in the initial stage is applied to the robot hardware exactly, the robot system becomes a new one in accuracy perspective. To control the end effectors of an articulated robot to intended locations in general, controller for each driving axis are calculated based on modeling parameter. Therefore, the end effectors deviate from the expected position to have position and pose error when the actual kinematic parameter has error. The accuracy of an industrial robot can be improved through calibration [10; 11; 12]. There are two ways to address the position error of the robot. One is using the sensor and control technology and the other is calculating the robot parameter through measurement before modifying the control parameter of the controller. The first step is to choose the mathematical model that will improve the representation of the position and orientation of the robot end-effector. This mathematical model is a function of the robot joint angles and takes into account the error parameters that need to be modeled. The error parameters can be identified by measuring the complete pose or partial pose of the robot end-effector in a set of calibration robot configurations. Many measurement devices have been used for robot calibration or validation, such as: A touch probe and a reference artifact [13], a telescoping ball bar [14], a small-range 3D position measurement device such as a camera-based system, [15] acoustic sensors [16], a large-range 3D measurement device such as a laser tracker [17; 18; 19], and a 6D complete pose measurement device such as a camera-based system. [20]  
The robot parameter is calibrated to reduce the robot teaching time, failure cost, and operating the robot system efficiently as required works are increasingly diverse and complicated. Offline teaching can be done on a separate work area or the computer simulation result can be used for the robot rather instead of direct teaching. In other words, accurate robot system and exact geometric information of the target to work on is enough under offline program to efficiently produce an operation program for multiple robots and this can prevent malfunctioning and conflict during operation of the robot system. However, calibration of inaccurate robot parameters is needed to apply the offline programming to the industry. The parameters are used to build system model of the robot and work subject on the computer for the offline program and kinematic relationship.