Absolute Position Accuracy Analysis For 6R Robot Based On Interval Analysis And Screw Theory

The large-scale applications of industrial robots in modern factories improve productivity as well as quality of product significantly, which transmits conventional factories into unmanned ones. However, the end-effector of manipulator can not reach ideal destination because of the unavoidable errors in manipulator manufacture、 assembly、control and so on, this drawback has seriously limited the application of industrial robot where the operating accuracy is very high.The present method for improving absolute accuracy of industrial robot can be summarized as follows:first, the kinematic error model of industrial robot is constructed, then calibration method can be applied to obtain the deviation of kinematic parameters, last the deviations are used to compensate for each kinematic parameter. Although product-of-exponential formula (POE formula) has many advantages over the other kinematic modeling methods and interval analysis is more convenient than fuzzy theory and probability statistics theory in parameter error modeling, the extant research based on POE formula and interval analysis has some deficiency:1) The kinematic error model obtained by partial differentiating the parameters of POE formula is too complex for practical application; 2) The research combining POE formula and interval analysis has not been introduced into industrial robot precision analysis. Besides, the existing method is not efficient and the calculating result is not precise enough. The deficiency listed above is the motivation of this paper, which not only presents further analysis of absolute position accuracy for industrial robot through incorporating POE formula with interval analysis, but provides simulation and experiment verification as well.In order to analyze the absolute position accuracy of serial robot, some modified interval calculation rules are defined which are used to cooperate with POE formula to model robot kinematic, then, a closer extended interval kinematic model is obtained. After analyzing the hierarchy property of the extended interval kinematic model, a hierarchy interval kinematic model (HIKM) is proposed which can not only be extended to general serial robots but can also significantly reduce interval dependency. Later, an interval matrix refinement algorithm is provided to relieve the overestimation of HIKM result. Monte Carlo samples and the results of contrast simulation between the hierarchy interval kinematics and existing extended interval kinematics shows the presented kinematic error model can get as tight result as desired result more efficiently than existing one.Considering parameter uncertainties of robot kinematic model, the impact to the position accuracy of robot kinematic parameter errors based on POE formula have been analyzed. Interval analysis is used to cover the input errors of POE formula and 3 corresponding error models of serial manipulator are deduced. Considering the overestimation of interval calculation, the error models of corresponding interval parameters are handled with calculation transformation, which are verified by contrast experiment of Monte Carlo method. Then the impact factor of each parameter is calculated by least square method, the result shows among all the kinematic parameter errors, joint errors have the biggest impact to the position accuracy of robot while impact of the other input errors are quite small.In order to verify the theory, we execute our model on a 6R robot which performs tightening bolts in an automotive transmission assembly line. Considering design tolerance as well as measure accuracy of horizontal coordinate measuring machining (CMM), the interval parameters of 6R robot are set. After measuring the positioning distribution of end-effector for 6R robot and calculating the interval region of kinematic error model, the experiment points are totally enclosed by interval region obtained from kinematic error model, the maximum deviation of two distribution region becomes 0.6mm after interval matrix refinement, the analysis method is sufficient for practical application. Thus the proposed kinematic error model for serial robots and refinement algorithm is valid.According to the study, a kinematic error model based on POE formula and modified interval analysis which can easy to be extended to general serial robots is established, the kinematic error model is introduced into absolute position accuracy analysis of serial robots. Simulation and experimental results demonstrates the validation of the kinematic error model. The impact of kinematic parameter errors to absolute position accuracy are studied, which is efficient and convenient for practical design.