Geometric Error Modeling And Its Engineering Application In Robotic Machining

The application of industrial robots in machining large complex parts is limited to machining errors.The major factors are geometric errors,including robot pose error,hand-eye pose error,workpiece pose error and tool pose error.For example,the positioning error of empty-loaded robot is mainly caused by kinematic errors;The geometric error caused by weak stiffness is larger than that of machine tool;The constraints of singularity,collision avoidance,joint limits and reachable workspace also increase the complexity of robotic machining.Thus,above factors are considered in this paper.The research objects include robot,workpiece,tool and vision sensor.Machining error modeling,parameters identification and poses optimization are studied to reduce the machining error.A variety of theories of reducing machining error are proposed.The achieved contributions include:(1)Modeling of both kinematic chain and machining error in robotic machining system.The kinematic chain of the robotic machining system is constructed.The influence of geometric parameters on machining errors is studied;A curvature-adaptive machining error model is proposed.The point-to-point and point-to-tangent errors are unified in this model to improve the calculation accuracy of machining error;Combining kinematic chain and machining error model,the mapping models between machining error and kinematic errors/joint stiffness/workpiece pose error/tool pose error are established.The mapping models are the theoretical basis of both parameters identification and pose optimization in next chapters.(2)Hand-eye identification based on kinematic errors compensation.A method of solving initial values of kinematics parameters/hand-eye parameters using Kronecker product is proposed;The mapping model between kinematic errors/hand-eye errors and robot positioning error is established.A method based on compensating kinematic errors is proposed to identify hand-eye parameters,which can reduce the effect of kinematic errors on hand-eye parameters.A differential motion method of iteratively solving the optimal orthogonal matrix is proposed to avoid the uncertainty error caused by the multi-solutions of Schmidt method.The proposed method is suitable for the orthogonalization of general non-standard rotation matrix.(3)Workpiece pose identification by considering measurement defects.A new point cloud matching method based on minimizing variance is proposed to avoid the ICP/TDM's matching distortion(tangential slip and unbalanced tilt)caused by the measurement defects,such as non-closed shape,non-uniform density and Gauss noise,etc.The equivalent sufficient condition of the proposed method and TDM method is proved.The condition is that the sum of line vectors(Plücker coordinates)of measured points is zero.The second-order fast convergence of the proposed method and the stability on measurement defects /Gauss noises/ tangent slip are verified by experiments.The proposed matching method is applied to the location and inspection of 14 types of blades.(4)Tool pose identification based on machining error estimation of free-form surface.The mapping model between workpiece/tool pose errors and the machining error of surface is established.The objective function of squared sum of the deviation between actual and estimated machining error is defined.The pose error identification problem is converted to the point cloud matching.Compared with existing static construction methods,1)the proposed method reflects the tool pose error caused by chatter,force deformation and rotation axis error,etc;the proposed method is not limited to the shape of the workpiece.It is very suitable for the pose identification of general surface,such as nuclear blade and wing skin.(5)Modeling of pose optimization based on machining error minimization.A method of compensating overall machining errors is proposed by fine-tuning tool/workpiece coordinate system.This method avoids modifying target points to reduce the overall machining errors.The objective function of machining error minimization is proposed with the constraints of joints limit/motion singularity/collision avoidance/reachable workspace.The proposed method is general and applicable to control various machining errors,such as normal depth(grinding and milling),tangential sliding(making hole)and angle inclination(cutting edge).(6)Based on above researches,the parameter identification software for robotic machining system is developed for grinding and cutting edge application.The identified parameters include kinematic parameters,hand-eye parameters,workpiece pose and tool pose.The effectiveness of the proposed machining error control method is verified by the the actual machining of the standard cylinder.Finally,the proposed method is applied to grind 2 types of blades and trimm 4 types of wing skins.After grinding,front/rear edge radii,concave/convex surface distances,maximum thickness and roughness are controlled within the tolerance.The wings skins after cutting satisify the processing requirement.