Kinematic calibration of a 3-PRRU parallel manipulator based on the complete, minimal and continuous error model

Kinematic error model plays an important role in the kinematic calibration of robot manipulators. In order to guarantee the best calibration result, the error model should meet the requirements of completeness, minimality and continuity. For the conventional serial robots, these issues have been intensively studied and a consensus has been reached during the past decades. However, for parallel manipulators, the problem of minimality, namely the determination of identifiable parameters mainly relies on numerical studies. There is a lack of effective methods to analyze the parameters’ identifiability in the error modeling process. Besides, there is still no agreement on the formula of the maximum number of identifiable parameters. In our previous work, a complete, minimal and continuous error modeling approach for parallel manipulators has been proposed based on product of exponential (POE) formula and the equation that the maximal number of identifiable parameters 4r+2p+6 was proved. However, the correctness and effectiveness of this method in kinematic calibration have not been verified on any parallel manipulator or robot. Therefore, in this paper a kinematic calibration is conducted on a prototype of a 3-PRRU parallel manipulator based on the proposed error model. The method of validating the completeness and minimality are respectively given by numerical simulations. Furthermore, to illustrate the advantage of the proposed error model, the kinematic parameters of the prototype are also calibrated based on the conventional error model which is derived by means of differentiating the limbs’ inverse kinematics. By comparing the calibration results, it can be concluded that the error model satisfying the three criteria can better improve the positioning accuracy. In addition, since the calibration method is described uniformly, it can be applied to most parallel manipulators by referring to the calibration procedure this paper presented.