Research On Methods Of Serial Mechanism Kinematic Calibration Based On Common Perpendicular Line Model

The serial mechanism represented by serial industrial robots and multi-axis CNC machine tools,is the cornerstone of high-end equipment manufacturing industry.Series industrial robots play an important role in improving the flexibility of the production line and improving the level of factory automation.On the other hand,multi-axis CNC machine tools,especially the five-axis CNC machine tools,can substantial increase efficiency and accuracy by simultaneously adjust the position and orientation of the tool in the processing process,which makes it Important base equipment in aerospace,energy,defense and other fields.Due to the widespread manufacturing and assembly errors,the serial mechanism needs to be calibrated to achieve desired performance.Product of Exponential(POE)formula is frequently used in serial mechanism kinematic calibration in recent years because of the inherent continuity.There are problems in traditional calibration method based on POE formula: firstly,the kinematics mode based on POE formula could not conveniently express the situation that axes deviate from the nominal configuration because the lack of parameters which to express mechanism kinematic pair axis movement.The error expression based on traditional POE formula does not comply with the lie algebra algorithm,which caused the additional introduction of normalization and orthogonalization to solve this problem in parameter identification.The whole calibration process of a robot is divided to two steps: the kinematic calibration and base frame calibration.The calibration process of the robot base frame is complex because it is difficult to be directly measured,meanwhile the calibration result is difficult to meet the requirements.This paper presents serial mechanism calibration method,based on common perpendicular line(CPL)model,to solve above problems.The main research work and innovations are as follows:(1)According to screw theory and adjoint transformation,the CPL transform is purposed,which expresses relationship between nominal twist and actual twist of kinematic pair by seeing them as line vectors.Further the serial mechanism kinematics model based CPL model is derived,and CPL kinematics model for the PUMA serial robots and table-tilting five-axis machine tool are established.(2)By analyzing the characters of the CPL transform,the number of equivalent robot kinematics error parameters based on the CPL model is put forward to be 4r(10)2 p+6,where r is the number of rotational joints,and p is the number of mobile joints.The use of CPL transformation avoid normalization and orthogonalization operation in the other kinematic calibration method which based on exponential product formula,and simplifies the operation in the process of calibration.Then the proposed calibration method is improved to accommodate the ball bar measurement,and make it suitable for five axis CNC machine tools kinematics calibration.(3)Propose the series robot calibration method without nominal parameter on the basis of the CPL model.This method combines the kinematics calibration and the base frame calibration into one step,calculate and get accurate kinematics model from topology of the robot and multiple sets of terminal position data at the specified coordinates.By using this method can replace the traditional robot factory calibration and base frame fast calibration method in production site,and significantly reduce robot pose error in the work frame caused by the rapid calibration,improve the overall accuracy.In addition,this method can also be used for kinematic calibration of multi-robot system,and get accurate kinematics model based on coordinate system for each robot,eliminate the basis frame transformation matrix.(4)The purposed method is used in the calibration tests for the PUMA serial robots and table-tilting five-axis machine tool.The experiment results demonstrate that the serial mechanism kinematics calibration method based on CPL model improved absolute position and pose accuracy for serial robots and NC machine tools successfully.Meanwhile,serial robot can be calibrated in any coordinate system,and the robot calibration and base frame calibration are simplified into one step,thus enhance the accuracy of the whole system.