A Unified Error Transmission Model Of Robot Manipulators Considering Both Kinematic And Deformation Errors

Error modeling plays an important role during the design, manufacturing and usage of robot manipulators. It is the fundamental to reveal the principle of error transimission, predict the accuracy performance of end-effector, and identify-and-compensate the kinematic errors of the links. Therefore, it is a key issue to establish an accurate and efficient errod model during the research and development of high-precision robot manipulators.Kinematic errors and structural deformations are two main aspects which influence the end-effector’s positioning accuracy of robot manipulators. Since they are caused by manufacturing inaccuracies and external forces respectively, they are separatedly taken account into the geometric error modeling and the structural stiffness mapping in existing methods. However, the kinematic errors and structural deformations of the links will be coupled when there exists overconstraint in the robot manupulators. And the deformation errors can not be determined only according to external load, but also depend on the links’ kinematic imperfections.To this end, this dissertation presents a unified approach to the modeling of transimissions for both kinematic errors and structural deformations in robot manipulators. Based on a uniformed representation of kinematic errors and structural deformations, analytical methods are proposed to decompose the redundant, independent and overconstrained error components in their transimission models. Then, accuracy analysis and kinematic calibration can be performed succussfully to the robot manipulators to improve their accuracy performances. In addition, the effectiveness and efficiency of the proposed approach are verified by several experiments and appliactions. The main contribution of this dissertation can be concluded as follows: □ Transmission principle of kinematic errors in open-chained mechanismsBased on the local POE formula, the error transmission model which satisfyies the completeness, minimality and continuity requirements can be derived for an arbitrary open chained mechanism. Then, the criterion for the determination of the identifiable kinematic errors is developed and the redundant error component can be eliminated in analytical manner. So that the inherent principles of the kinematic errors transmission and accumulation in these serial mechanisms can be revealed. □ Equivalent joint errors model for the structural deformations of linksAccording to the decomposition and synthesis of spatial stiffness matrices, elastic open-chained mechanisms are modeled to simulate the ‘force-defelection behavior’ of the links in robot manipulators. On this basis, the links’ compliance and deformation errors can be integrated within the equivalent flexible joints. And the kinematic errors and structural deformations can be established in a unified model in which an overall jacobian matrix can be derived to transform both kinemaric and structural errors from joint space to the workspace. It provides the possibility to isolate the links’ coupled deformations with the kinematic imperections in overconstraint subspace. □ Unified transmission model for both kinematic and deformation errorsBy modeling the kinematic errors and structural deflections as the flexible joints’ offset errors and elastic deformations, a unified transmission model can be derived readily for both kinematic errors and structure deformations in serial robot manipulators. Based on the dual property between the covariant and contravariant basis, a closed-form algorithm is proposed to eliminate the passive joints’ coordination errors which results in a unified error model for the manipulators with closed-loop topology considering both kinematic and deformation errors. In addition, the extendibility of the proposed method to over-constrained mechanisms is also conducted. □ Interface propagation algorithm for the exact output error bound predictionAccording to the uncertainties of the error sources, an interface propagation algorithm is proposed based on the Minkowski rule for the morphological addition of the errors’ influence sets. Consequently, the exact output error bounds of the robot manipulators can be determined efficiently and the performance of the robot’s positioning accuracy can be evaluated in a more systematical and accurate way.In addition, the proposed method has been applied to the error modeling, accuracy analysis and kinematic calibration/compensation of several industrial robot manipulators, such as a generic 6-DOF serial robot, a 6-DOF parallel coordination device and a spatial 3-DOF parallel forming manipulator. The results show the effectiveness and efficiency of the proposed method in the error modeling, accuracy analysis and precision enhancement for the robot manipulators considering both kinematic errors and structural deflections, and with either serial or closed loop structures.