Robotica95 - A Meta-study of PUMA 560 Dynamics (779829), страница 3
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An, C. G. Atkeson, J. D. Griths, and J. M. Hollerbach, Model based control of arobot manipulator. MIT Press (1989).9[18] M. Leahy, D. Bossert, and P. Whalen, \Robot model-based control: An experimental casestudy", Proc. IEEE Int. Conf. Robotics and Automation 1982{87 (1990).[19] R. S. Hartenberg and J. Denavit, \A kinematic notation for lower pair mechanisms basedon matrices", Journal of Applied Mechanics 77, 215{221 (1955).[20] J.
J. Craig, Introduction to Robotics. Addison Wesley (1986).[21] R. P. Paul, Robot Manipulators: Mathematics, Programming, and Control. Cambridge,Massachusetts: MIT Press (1981).[22] P. Corke and B. Armstrong-Helouvry, \A search for consensus among model parametersreported for the PUMA 560 robot", Proc. IEEE Int. Conf. Robotics and Automation(1994).[23] B. Armstrong-Helouvry, Control of Machines with Friction.
Kluwer (1991).[24] B. Armstrong-Helouvry, \Stick slip and control in low-speed motion", IEEE Trans. Autom.Control 38, No. 10, 1483{1496 (1993).[25] V. Hayward and R. P. Paul, \Robot manipulator control under UNIX | RCCL: a RobotControl C Library", Int. J. Robot.
Res. 5, No. 4, 94{111 (1986).[26] B. Armstrong, Dynamics for Robot Control: Friction Modelling and Ensuring ExcitationDuring Parameter Identication. PhD thesis Stanford University (1988).10Figure 1: Frame assignments made according to the modied Denavit-Hartenberg convention.11Table 1: Keys to principal sources used in the text.KeySourceArmstrongLeePaul81Paul86TarnBreakingAwayUnimationKawasakiRCCLMUCSIROArmstrong et al.2Fu, Gonzalez and Lee,3 and also Lee.4Paul, Rong and Zhang.5Paul and Zhang.6Tarn et al.7\Breaking Away from Val" a memo describing operationsof the Unimation servo system in some detail.8A data sheet of unknown origin but purporting to befrom Unimation, listing dynamic parameters of motorsand links.A data sheet of motor specications obtained from thelocal (CSIRO) Kawasaki robot distributor.Source code of RCCL software.9,25Measurements taken on University of Melbourne'sKawasaki 560.10Measurements taken on CSIRO Division of Manufacturing Technology's Unimate 560.12Table 2: Comparison of kinematic constants.Paul81i-90090-90900Ai043220000Paul86Di0014943200i900-9090-900Ai0431.819.1000LeeDi00125.4431.800Tarni-90090-90900Ai0431.8-19.1000i-90090-90900Ai0431.8-20.32000Di0149.090433.07056.25ArmstrongDi00150.05431.100i 10-90090-9090Ai 100431.8-20.300Di0243.5-93.4433.100Each is specied in terms of the coordinate frames of the cited paper ( in degrees, A and Dare in mm).13Table 3: Link mass values (kg).Parameter Armstrong Paul81 Tarnm1m2m3m4m5m617.404.800.820.350.094.4310.24.801.180.320.131413.022.45.01.20.620.16Table 4: Link center of gravity (mm).Parameter Armstrong Paul81 Tarnsx1sy1sz1sx2sy2sz2sx3sy3sz3sx4sy4sz4sx5sy5sz5sx6sy6sz6686-160-701400-1900000321508002160-260-216000-20000001004-3091035-4020-4140-3-860-1-10003Table 5: Comparison of gravity coecients (Nm).Parameter ArmstrongTarnRCCLg1g2g3g4g5-37.2-20.8 37.196 (CP21)-8.44-7.51 -8.44 (CP30)1.021.10 -1.023 (CP20)0.2490.390 0.248 (CP22)-0.0282 0.00455 -0.028 (CP50)16Table 6: Link moments of inertia.Parameter ArmstrongIxx1Iyy1Izz1Ixx2Iyy2Izz2Ixx3Iyy3Izz3Ixx4Iyy4Izz4Ixx5Iyy5Izz5Ixx6Iyy6Izz60.3500.1300.5240.53966.0 e-312.5 e-386.0 e-31.80 e-31.80 e-31.30 e-3300 e-6300 e-6400 e-6150 e-6150 e-640 e-6TarnPaul811.1000.1951.1100.0260.1770.1950.4030.5880.9691.8860.9651.47074.8 e-3 324.0 e-37.3 e-3 17.0 e-375.6 e-3 324.0 e-35.32 e-3 3.83 e-35.20 e-3 3.83 e-33.37 e-3 2.50 e-3487 e-6 216 e-6482 e-6 216 e-6572 e-6 348 e-6123 e-6 437 e-6123 e-6 437 e-658 e-613 e-6Moments of inertia about the center of gravity | load referenced (kg m2).17Table 7: Experimental motor torque constants | motor referenced (Nm/A).Parameter Armstrong CSIRO Paul81 MUK1K2K3K4K5K60.1890.2190.2020.0750.0660.0660.2230.2260.2400.0690.0720.066180.2550.2200.2390.0780.0700.0790.2020.2580.2450.0950.1010.089Table 8: Comparison of average experimental values and manufacturer data (Nm/A).Source Kbase KwristArmstrongCSIROPaul81MURCCLTarnUnimationKawasaki0.2030.2300.2380.2350.2540.2590.2600.258190.0690.0690.0760.0950.0900.097Table 9: Motor inertia | motor referenced (kg m2).Parameter Armstrong Unimation Tarn Kawasaki CSIROJm1Jm2Jm3Jm4Jm5Jm6291e-6409e-6299e-635e-635e-633e-6200e-6 198e-6200e-6 203e-6200e-6 202e-618e-6 18.3e-618e-6 18.3e-618e-6 18.3e-620200e-6200e-6200e-620e-620e-620e-626e-6Table 10: Measured friction values for three PUMA 560s.Parameter Armstrong26 CSIROB1B1+f1f1+B2B2+f2f2+B3B3+f3f3+3.454.94-8.268.438.537.67-11.3412.773.023.27-5.575.93MU Motor6.27 3.856.40 3.20-29.8 -6.7427.0 7.248.89 22.111.7 24.7-8.30 -13.014.7 15.95.31 5.592.91 4.33-5.87 -4.567.37 4.19-6.146.14-10.610.6-5.265.26Coulomb friction, fi (Nm), viscous friction, Bi (Nms/rad).
Superscripts indicate direction ofrotation.21Table 11: Degree of variability in reported values of the PUMA 560 parameters.ParameterTable Normalized Ratio ofStandard ExtremalDeviation ValuesKinematics22.7%1.20Link Mass329%2.93Center of Gravity4124%10.70Gravity Coecients527%6.20Moments of Inertia666%4.52Motor Torque711%1.53Armature Inertia929%2.06Friction Parameters1040%4.4222.
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