Robotica95 - A Meta-study of PUMA 560 Dynamics (779829), страница 2
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This may be taken as anindication of the diculty of obtaining accurate measurements of inertia. On the other hand,the range between the largest and smallest parameters is 105 , and so the 100:5 (or 300%)variability in published values of inertia is an order of magnitude less than the spread in theseparameters. Control based upon a model with 100:5 uncertainty in dynamic parameters isperhaps much better than control based upon no dynamic model at all.54 A Comparison of Motor ParametersThere are two types of PUMA 560, one built by Unimation (Danbury, CT) and the other byKawasaki (Japan). The two types are similar in most respects, but dierent servo motors areused. In each PUMA two sizes of servo motor are used; a larger motor for joints 1-3 and a smallermotor for joints 4-6.
The following sections compare data for the two most signicant motorparameters; torque constant and armature inertia. Information about other motor electricalparameters is given by Corke and Armstrong-Helouvry.224.1 Motor torque constantReported motor torque constants are presented in Table 7. These have been translated from theoriginal reports using gear ratio or knowledge of full motor current where necessary.
Strikingvariation is seen, given that motors 1-3 are identical, as are motors 4-6. The data reported inTable 7 are averaged and compared with data from the motor manufacturers in Table 8. Themanufacturers' data indicate that a higher torque constant in the wrist motors of the Kawasakimodel is one dierence between the robots. Considerable variation is also seen in Table 8.Communication with a robotics rm supporting PUMA's, (Private communication, F.
Pagano,AR2 Inc., Oxford, Connecticut, USA) indicates that the Unimation data are specicationsof a lower limit, and that variation of up to 20% above the specication is normal. A remagnetizing process is needed for motors with many hours of operation or that have experiencedseveral abrupt power shut-down events. Reduced motor magnetization, along with friction,perhaps accounts for the experimental data being consistently lower than the manufacturers'specications seen in Table 8.4.2 Armature inertiaMotor armature inertias are tabulated in Table 9. Armstrong's values for motor plus transmission inertia (load referenced) were determined by parameter identication experiments.
Here,they are divided by the gear ratio squared to give the values of armature inertia presented inTable 9 (motor referenced). From our knowledge of motor similarity, Armstrong's value formotor 2 seems anomalous. Armstrong's data for the wrist joint motor inertias is consistentlyhigher than the manufacturer's data.
This may be explained by the inertia of the shaft andexible coupling which cannot experimentally be separated from armature inertia.65 FrictionMachine friction will vary substantially between robots, and for a given robot with changesin temperature and lubrication. Due to the gear type transmission, joint friction also has asubstantial position dependence.23 A seven-parameter friction model has recently been proposed,23,24 but in the literature one most often nds Coulomb and viscous friction parametersreported. Typically, each parameter is dependent upon direction of motion, and has a component due to the motor and a component due to the transmission. Writing friction on the ithjoint in the form:8< f + B _ ; _ < 0Fi (t) = : i+ i+(1)fi + Bi _ ; _ > 0the Coulomb and viscous friction parameters are fi and Bi respectively, and is the jointangle.
These parameters are given in Table 10. The data give some impression of the variabilityencountered, though it should be stressed that the experimental approaches used may varywidely. The break-away friction level (the static friction) has been observed to be roughly 120%of the Coulomb friction level in the PUMA 560.236 DiscussionThe degree of variability found among reported values for each of the tabulated parameters isseen in Table 11. For each parameter, the normalized standard deviation is given by the squareroot of the variance between published values divided by the mean of those values.
The valuein Table 11 is then the mean of the normalized standard deviations within a table.Whereas the normalized standard deviation is an L2 measure, the ratio of extremal valuesis an L1 measure. It is the ratio of the largest value given for a parameter to the smallest,non-negligible value given. For each table, the largest such ratio is presented in Table 11.At the outset of this project, it was hoped that by comparing the data from several reports,consensus and thereby more reliable data could be obtained. And indeed, for each parameterand from each report there are data which are inconsistent with the others, and may be regardedas outliers.
Thus, by combining data from the 11 available reports, a more complete and reliablemodel is achieved.Rejecting outliers, however, is not equivalent to establishing consensus. And it is consensusamong several dierent measurements that would give condence in the correctness of the data.7Regarding Tables 2 through 10, it is clear that consensus values are not available, even forsuch basic parameters as link mass or coecients of the gravity loading model. In some cases,such as the electrical parameters, inter-robot variability has been identied and may accountfor the variations among reports.
In other cases, however, the observed variability stems fromchallenges to accuracy underlying the parameter measurement and estimation methods appliedto robots.As robots become more compliant the demands on the accuracy of the dynamic model willbe come more stringent, and obtaining accurate dynamic model parameters will be a priority.When the time comes that the literature can provide multiple reports of dynamic parametermeasurements taken with a new robot, these too should be translated into a single coordinateframe for comparison. Doing so will make possible assessment of consensus that exists and givecondence in the correctness of the data.AcknowledgmentsThe authors appreciate the eorts of Vaughan Roberts and Malcolm Good, who performedsome of the parameter identication work referred to for the CSIRO PUMA robot; and RonPerez, who provided many helpful comments on a draft of this manuscript.References[1] P.
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