Table 4 Identified kinematic errors and calibrated local frame poses
Related Figures (20)
Fig. 1. Two consecutive links: a dyad. L.-M. Chen et al. | Mechanism and Machine Theory 36 (2001) 1215-1239 Fig. 2. Forward kinematic transformation of an n-DOF serial robot. I.-M. Chen et al. | Mechanism and Machine Theory 36 (2001) 1215-1239 words, instead of simultaneously identifying the actual initial poses 7(0)", joint twists s*, and joint displacement q*, we only have a set of newly defined calibrated frame 7(0)° to be identified. By doing so, the kinematic calibration model can be greatly simplified. Without loss of generality, we also assume that the nominal and actual base frames coincide with the world frame. Therefore, Eqs. (10) and (11) can be simplified as I.-M. Chen et al. | Mechanism and Machine Theory 36 (2001) 1215-1239 “ig. 5. A 4-DOF SCARA type robot. Preseted kinematic errors I.-M. Chen et al. | Mechanism and Machine Theory 36 (2001) 1215-1239 Identified kinematic errors and calibrated local frame poses physical meaning and are not of one-to-one correspondence, the preseted kinematic errors at each of the dyads are not fully recovered. However, the success of the calibration simulation can be deduced from the results shown in Table 3, where the nominal, actual, and calibrated tool frame poses representing two arbitrarily selected robot postures are listed. The results show that under the calibrated parameters description, the actual (measured) poses can be precisely Table 2 Tool frame poses before and after calibration I.-M. Chen et al. | Mechanism and Machine Theory 36 (2001) 1215-1239 described. In other words, the calibration algorithm is successful in improving the pose accuracy of the tool frame. A further re-enforcement of the calibration results is from Fig. 6 which shows that the simulation yields a full recovery of kinematic errors at the tool frame. Both the quantified orientation and position deviations, as in Eqs. (31) and (32), are driven from the initial magnitude of 0.10746 and 0.026887 to values approximately zero. Since a SCARA type robot is made up of both prismatic and revolute joints, the simulation example shows that the proposed local POE (calibration) model is uniform for robot kinematic calibration regardless of the types of joints. Fig. 7. A singularity configuration. This example a gularity configura preset in such a w intersect at a poin kinematic parame peatability on the measurement nois error parameters by the traditional D-H model would be difficult due t he smooth change of the kinematic parameters which is able to hand In the same example, we finally illustrate the effect of the measur so shows the capability of the model in handling . We understand that with this ‘actual’ twist geome ers at this singularity configuration. However, our parameters changes at sin- ions of the robot. As indicated in Fig. 7, the kinematic errors are deliberately ay that the first two parallel axes of the robot configuration are misaligned to ry, the identification of the o the abrupt changes in the modeling technique allows calibration result. Form the viewpoint of comput e and robot repeatability can be simula le the singularity problem. ement noise and robot re- er simulation, both of the ed in a uniform way by adding uni- Fig. 9. Experimental setup for robot calibration. To further va app ications, a calibration exper idate the effectiveness and generality of the calibration algorithm for industrial iment is also conducted. The experimental setup consists of an articulated type coordinate measuring machine, SpinArm, by Mitutoyo of Japan, and a tree-type mod T for positioning measurement is 4 aver WOr 4 1 ular robot (to be calibrated) from Amtec GmbH of Germany, shown in Fig. 9. he Mitutoyo SpinArm is a 6-DOF articulated coordinate measuring machine. The accuracy +0.00008 m. The positioning accuracy of Amtec modular robots age at £0.01 m experimentally, which is significantly less than that of the SpinArm. The king envelope of SpinArm covers a hemisphere of 2.4 m in diameter. A simple cubic fixture 11, 4 1 1 rr oo, rf 414 Wa ve fr. - ae: | . yc eee As shown in Fig. 10, the tree-type modular robot has two branches: Branch | consists of 3 (RPR) joints and Branch 2 consists of 4 (RPRR) joints. In total the robot has 5 DOFs because joints 1 and 2 are the two common joints in branches | and 2. We will calibrate these two branches simultaneously by using the local POE calibration model. Fig. 10 shows the local frame assign- ment of the tree-type modular robot. Note that the two tool frames, frame 6 and frame 7, nor- mally coincide with their corresponding last link frames, frame 3 and frame 5, respectively. Based on Eq. (25) and the connecting sequence of the links and joints, the kinematic calibration model for this tree-structured robot can be written as I-M. Chen et al. | Mechanism and Machine Theory 36 (2001) 1215-1239 L-M. Chen et al. | Mechanism and Machine Theory 36 (2001) 1215-1239 a tree-type modular robot also shows an improvement of pose accuracy to the order of the robot repeatability. Hence, the proposed local POE model is a generic kinematic calibration method for open chain robots with serial or tree-typed geometries. This Local POE calibration model also has been successfully implemented in an object-oriented modular robot/industrial robot simulation
