## 1 Introduction  
Robot manipulators are widely used in industry to attain many duties such as welding, painting, pick and place task, etc. The construction of robot manipulators is characterized using their kinematic model parameters. However, experience has shown that industrial manipulators have much greater repeatability than accuracy [1]. Therefore, the utility of robot manipulators would be significantly enhanced if they were made to be as accurate as they are repeatable. In producing and assembly, many errors arise that could not be taken into account by the nominal geometric model. For that reason, there is a demand to create model-based robotic calibrations that depend on an error model that symbolizes the connection between the errors of geometric parameters and the end effector positioning errors. The kinematic calibration method has been widely researched by numerous studies [2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13] to describe the proper geometric model. [PERSON], [PERSON] et al. proposed one of the most fundamental calibration methods that is widely used. The DH model is based on homogenous transformation matrices. The model is a description of the kinematic relations between the links of a kinematic chain connected by 1 degree-of-freedom lower pair joints [6; 7; 8]. There are also other methods such as the zero-reference position model that is proposed by [PERSON] et al., which has been widely used by many studies [9; 14; 15]. Another fundamental model-based calibration method is the complete and parametrically continuous (CPC) model, which relies on the singularity-free line representation by [PERSON] et al. [10; 11]. [PERSON] and [PERSON] [12] employed the product of exponentials (POE) error model to robot calibration. This model has been adopted by several researchers [4; 13]. There have been some attempts to replace the least square estimation with the Kalman filter, particle filter, fuzzy theory, etc. [16; 17; 18]. However, those attempts did not seem to be very effective. In addition, the kinematic errors are not the only source of robot manipulator errors. [PERSON] et al. [19] used a PUMA 560 robot to determine that the most significant error sources for the robot were several nongeometric errors. [PERSON] and [PERSON] [20] studied an AID-900 robot and found that the geometric errors were responsible for approximately 95% of the measured error. [PERSON] et al. [21] and [PERSON] [22] reported that flexibility in joints and in links is responsible for 8-10% of the total position and orientation errors. Therefore, more recently, researchers have been devoted to the identification of compliance errors as well as kinematic errors in industrial robots [5; 20; 23], [PERSON] and [PERSON] [5] proposed a method for simultaneously identifying the kinematic and compliance parameter of the robot. The model-based calibration has been widely applied due to its fast computing and knowledge of error sources [5; 24; 25]. However, the accuracy of the model-based calibration method is dependent on the model accuracy. It is practically impossible to create a model that contains all the sources committing to the end effector errors. Some error sources such as gear backlash, temperature variation, and other errors are difficult to model correctly and completely. To archive further accuracy, nongeometric calibration has been widely studied for compensating for the sources of errors that could not be taken into account by geometric calibration [26; 27; 28; 29; 30; 31; 32; 33]. The conventional back-propagation neural network (BPNN) [34] is widely adopted by researchers [35] for compensating the unmodeled errors to increasing the precision of the robot. In robotic calibration processing, BPNN is usually employed to construct the relationship between the end effector position and the corresponding joint angle configuration [36; 37; 38; 39]. However, the conventional BPNN has some drawbacks such as getting stuck in local minima and slowing convergence [40].