Robotica95 - A Meta-study of PUMA 560 Dynamics

A Meta-study of PUMA 560 DynamicsPeter I. CorkeDivision of Manufacturing TechnologyCSIROPreston, 3072. Australia.andBrian Armstrong-HelouvryDepartment of Electrical Engineering and Computer ScienceUniversity of Wisconsin - MilwaukeeMilwaukee, Wisconsin 53201.

U.S.AJuly 18, 1994AbstractThis paper presents a meta-study of the kinematic, dynamic and electrical parametersfor the PUMA 560 robot. Parameter values which have been reported in the literature aretransformed to a single system of units and coordinates, and dierences in the data andmeasurement techniques are discussed. New data have been gathered and are presentedwhere the record was incomplete.11 IntroductionResearch on visual servoing at CSIRO1 led to a need to implement dynamic-model-based control.The robot platform was a PUMA 560, for which there is a substantial literature.

Ratherthan re-implementing sophisticated model estimation experiments, the necessary dynamic modelparameters were sought in the literature.2{10 Presented here are numerical comparisons of datafound in these reports.In the absence of denitive data from the manufacturer, researchers have pursued manyapproaches to estimating this data. The techniques used vary widely and include estimationfrom geometric data,7,5 direct disassembly and measurement2 and unattributed incidental datain tables. More recently there has been considerable literature related to time-domain identication techniques for manipulators such as the Puma 260,11 MIT Direct Drive arm,12 the CMUDD-II arm,13,14 and a Manutec R3.15 Apart from Mayeda,16 there have been no reports onthis approach for the Puma 560. The authors attribute this to the low velocity and accelerationcapabilities of the PUMA 560 which preclude accurate determination of inertial parameters.Online model-based controllers for the Puma 560 have been reported by a number of authors,see An et al.17 for a discussion of reports through 1988, and Leahy et al.18 for an experimentalcomparison of several model-based control structures.

Principally these controllers have beenbased on model data from the sources cited here. However, as shown below, there is considerablevariation in the model data available for the PUMA 560 robot. The success of the model-basedcontrollers may be interpreted as a demonstration of the robustness of model-based controlapproaches when applied to the relatively slow and rigid PUMA 560 manipulator.Bringing together results from the literature involves more than might meet the eye. Thevalues of dynamic parameters depend upon the choice of coordinate frames in which they areexpressed, whether inertia is given in a center-of-gravity or axis-of-rotation frame, and uponthe choice of physical units. Principally because there are two Denavit-Hartenberg conventionsin use19,20 and within each convention there are user-dened degrees of freedom arising fromparallel axes and zero pose, no two reports of PUMA dynamics present their results in exactlycomparable systems of coordinates.Toward the goal of bringing together a complete and consistent set of kinematic, dynamicand electrical parameters of the PUMA 560, data presented in the above cited papers, along withnew data from the original manufacturers and from CSIRO measurements, have been translated2into a single system of coordinates and units.

With the data in a directly comparable form,several things may be accomplished:1. Gaps which may exist in some reports may be lled in using data available elsewhere.2. It is possible to compare results. In some cases it is possible to identify outliers in thedata; and where consensus can be established among reports, it will give condence thatthe data are reliable.3. By looking at the spread in reported parameters, it is possible to assess the challengeposed by accurate dynamic parameter identication.In medicine or the natural sciences it is common for several research groups to repeatreported experiments and for the data to be ultimately compared and contrasted in a metastudy, that is a study of studies. In these elds a measurement needs to be made several timesbefore it is fully trusted. In engineering we do less of this, but the PUMA 560 arm presentssomething of a unique opportunity to assess the challenges to accurate parameter identicationby observing the degree of variation among reported values.

This paper then is a meta-studyof PUMA 560 dynamic characteristics.In this paper, a table will be given for each group of parameters showing data reported in theliterature translated into a single system of coordinates. Additionally, new data, particularlyelectrical parameters, are presented.

Throughout the rest of the paper sources will be referredto by the keys given in Table 1.1.1 A note on coordinate framesTwo dierent systems for coordinate frame assignment are now in use:1. Denavit-Hartenberg (DH) assignments where frame i has its origin along the axis ofjoint i + 1, as described by Paul21 and Lee.4,32. Modied Denavit-Hartenberg (MDH) assignments where frame i has its origin alongthe axis of joint i, as described by Craig.20 This form will be used here as the basis forcomparison.To permit direct comparison, PUMA 560 parameters from the source papers have beentranslated to a single system of coordinates.

The modied Denavit-Hartenberg representation20is used, with frame assignments and zero-angle pose as shown in Figure 1.32 A Comparison of Kinematic ParametersThe kinematic models of the 11 sources must be considered in order to transform the inertialparameters into a single system of coordinates. Five sets of kinematic parameters are comparedin Table 2. Each set of parameters must be taken in the context of the axis and angle conventionsin the cited paper. However there is clearly some variation in the link lengths and osets citedby various authors. These could conceivably reect changes to the design and manufacture ofthe robot with time.

Some comments on these parameters are:The modied Denavit-Hartenberg representation has 5 length parameters compared tofour in the standard representation. By inspection we can see that D2MDH + D3MDH D3DH , and Armstrong's data thus agrees closely with both Tarn and Lee.Paul81 apparently gives an incorrect sign for A3.

The sign of A3 in Paul86 is correct dueto the denition of the zero-angle pose.The i values given by Paul86 are negative compared to Paul81 and Lee. This is due tothe denition of a right-handed conguration for the zero-angle pose in Paul86.The value of D3 from Paul86 is given as 125.4, which is signicantly lower than the otherreported values.Lee alone gives a value for D6, which is the distance from wrist center to the ange plate.Thus Lee places the T6 coordinate frame on the ange, while all others consider it as thecenter of the wrist.3 A Comparison of Inertial Parameters3.1 Link massReported values for link mass are presented in Table 3. Armstrong's data were determined bydismantling the robot and weighing the components. Paul81's paper provides only \normalizedmass" gures with link 6 being assigned a relative mass of 1.

The gures are simply normalizedversions of the \Plato areas" given in the same table. In the table we have equated the massof link 3 with Armstrong's value. Tarn's data are from estimation and measurement of thecomponents of each link and are consistently higher than Armstrong's.3.2 Link center of gravityLink center-of-gravity values are given in Table 4. Paul81's values are given without explanation,but examination seems to indicate that uniform distribution of mass within the links is assumed.This, however, is unlikely given the monocoque construction technique and the heavy motors at4one end of each of links two and three.

Tarn used a combination of measurement and estimationfor each component within the link to determine the overall value for the link. Armstrong useda knife edge balance to determine the center-of-gravity of the disassembled links directly.3.2.1 Cross-check via gravity loadingSince gravity is a dominant dynamic eect, a comparison of the gravity loading coecientsmay be more meaningful than link mass and center of gravity values alone. The equations ofthe gravity loading terms are given in Table A7 of Armstrong. The coecients of the gravityloading terms are evaluated and compared in Table 5.

There is close agreement between themagnitudes of the coecients from Armstrong and those used in RCCL. The sign dierence onjoints 1 and 3 is likely to be due to the sign of the gear ratios,8 which are negative for thosejoints. The values used within RCCL were obtained by an experimental procedure as describedby Lloyd for a PUMA 2609 (Private communication, J.Lloyd, Mc Gill University, Canada).3.3 Link moments of inertiaTable 6 gives the moments of inertia about the center of gravity for each link. Tarn's inertialvalues are reported relative to the joint axes. Using Tarn's center of gravity parameters fromTable 4, the inertial values have been translated to the center of gravity representation for Table6.

Radii of gyration are reported in Paul81. Using the values for link mass reported in Table3, these have been translated to inertia. Since the inertia and location of center of gravityof link 1 are not separately identiable in the manipulator dynamics, the value presented byArmstrong as Izz1 is the combined inuence in link coordinates, that is, Izz1[Link Coordinates] =Izz1[Center of Gravity] + m1(s2x1 + s2y1 ).Parameter values vary by 200% - 450% throughout Table 6.