1、Designation: E2919 13Standard Test Method forEvaluating the Performance of Systems that Measure Static,Six Degrees of Freedom (6DOF), Pose1This standard is issued under the fixed designation E2919; the number immediately following the designation indicates the year oforiginal adoption or, in the cas
2、e of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope1.1 PurposeIn this test method, metrics and proceduresfor collecting and analyzing data to dete
3、rmine the performanceof a pose measurement system in computing the pose (positionand orientation) of a rigid object are provided.1.2 This test method applies to the situation in which boththe object and the pose measurement system are static withrespect to each other when measurements are performed.
4、Vendors may use this test method to establish the performancelimits for their six degrees of freedom (6DOF) pose measure-ment systems. The vendor may use the procedures described inSection 9.2 to generate the test statistics, then apply anappropriate margin or scaling factor as desired to generate t
5、heperformance specifications. This test method also provides auniform way to report the relative or absolute pose measure-ment capability of the system, or both, making it possible tocompare the performance of different systems.1.3 Test LocationThe methodology defined in this testmethod shall be per
6、formed in a facility in which the environ-mental conditions are within the pose measurement systemsrated conditions and meet the users requirements.1.4 UnitsThe values stated in SI units are to be regardedas the standard. No other units of measurement are included inthis standard.1.5 This standard d
7、oes not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM St
8、andards:2E456 Terminology Relating to Quality and StatisticsE2544 Terminology for Three-Dimensional (3D) ImagingSystems2.2 ASME Standard:3ASME B89.4.19 Performance Evaluation of Laser-BasedSpherical Coordinate Measurement Systems2.3 ISO/IEC Standards:4JCGM 200:2012 International Vocabulary of Metrol
9、ogyBasic and General Concepts andAssociated Terms (VIM),3rd editionJCGM 100:2008 Evaluation of Measurement DataGuideto the Expression of Uncertainty in Measurement (GUM)IEC 60050-300:2001 International ElectrotechnicalVocabularyElectrical and Electronic Measurements andMeasuring Instruments3. Termin
10、ology3.1 Definitions from Other Standards:3.1.1 calibration, noperation that, under specifiedconditions, in a first step, establishes a relation between thequantity values with measurement uncertainties provided bymeasurement standards and corresponding indications withassociated measurement uncerta
11、inties and, in a second step,uses this information to establish a relation for obtaining ameasurement result from an indication. JCGM 200:20123.1.1.1 Discussion(1) A calibration may be expressed by a statement, calibra-tion function, calibration diagram, calibration curve, or cali-bration table. In
12、some cases, it may consist of an additive ormultiplicative correction of the indication with associatedmeasurement uncertainty.(2) Calibration should not be confused with either adjust-ment of a measuring system, often mistakenly called “self-calibration,” or verification of calibration.(3) Often, t
13、he first step alone in 3.1.1 is perceived as beingcalibration.3.1.2 maximum permissible measurement error, maximumpermissible error, and limit of error, nextreme value of1This test method is under the jurisdiction of ASTM Committee E57 on 3DImaging Systems and is the direct responsibility of Subcomm
14、ittee E57.02 on TestMethods.Current edition approved May 1, 2013. Published June 2013. DOI: 10.1520/E2919-13.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the sta
15、ndards Document Summary page onthe ASTM website.3Available from American Society of Mechanical Engineers (ASME), ASMEInternational Headquarters, Three Park Ave., New York, NY 10016-5990, http:/www.asme.org.4Available from American National Standards Institute (ANSI), 25 W. 43rd St.,4th Floor, New Yo
16、rk, NY 10036, http:/www.ansi.org.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1measurement error, with respect to a known reference quantityvalue, permitted by specifications or regulations for a givenmeasurement, measuring instrume
17、nt, or measuring system.JCGM 200:20123.1.2.1 Discussion(1) Usually, the terms “maximum permissible errors” or“limits of error” are used when there are two extreme values.(2) The term “tolerance” should not be used to designate“maximum permissible error.”3.1.3 measurand, nquantity intended to be meas
18、ured.JCGM 200:20123.1.3.1 Discussion(1) The specification of a measurand requires knowledge ofthe kind of quantity; description of the state of thephenomenon, body, or substance carrying the quantity, includ-ing any relevant component; and the chemical entities in-volved.(2) In the second edition of
19、 the VIM and IEC 60050-300,the measurand is defined as the “quantity subject to measure-ment.”(3) The measurement, including the measuring system andthe conditions under which the measurement is carried out,might change the phenomenon, body, or substance such thatthe quantity being measured may diff
20、er from the measurand asdefined. In this case, adequate correction is necessary.(a) Example 1The potential difference between theterminals of a battery may decrease when using a voltmeterwith a significant internal conductance to perform the measure-ment. The open-circuit potential difference can be
21、 calculatedfrom the internal resistances of the battery and the voltmeter.(b) Example 2The length of a steel rod in equilibriumwith the ambient Celsius temperature of 23C will be differentfrom the length at the specified temperature of 20C, which isthe measurand. In this case, a correction is necess
22、ary.(4) In chemistry, “analyte,” or the name of a substance orcompound, are terms sometimes used for “measurand.” Thisusage is erroneous because these terms do not refer toquantities.3.1.4 measurement error, error of measurement, and error,nmeasured quantity value minus a reference quantity value.JC
23、GM 200:20123.1.4.1 Discussion(1) The concept of “measurement error” can be used both:(a) When there is a single reference quantity value torefer to, which occurs if a calibration is made by means of ameasurement standard with a measured quantity value havinga negligible measurement uncertainty or if
24、 a conventionalquantity value is given, in which case the measurement error isknown, and(b) If a measurand is supposed to be represented by aunique true quantity value or a set of true quantity values ofnegligible range, in which case the measurement error is notknown.(2) Measurement error should no
25、t be confused with pro-duction error or mistake.3.1.5 measurement sample and sample, ngroup of obser-vations or test results, taken from a larger collection ofobservations or test results, that serves to provide informationthat may be used as a basis for making a decision concerningthe larger collec
26、tion. E4563.1.6 measurement uncertainty, uncertainty ofmeasurement, and uncertainty, nnon-negative parametercharacterizing the dispersion of the quantity values beingattributed to a measurand based on the information used.JCGM 200:20123.1.6.1 Discussion(1) Measurement uncertainty includes components
27、 arisingfrom systematic effects, such as components associated withcorrections and the assigned quantity values of measurementstandards, as well as the definitional uncertainty. Sometimesestimated systematic effects are not corrected for but, instead,associated measurement uncertainty components are
28、 incorpo-rated.(2) The parameter may be, for example, a standard devia-tion called standard measurement uncertainty (or a specifiedmultiple of it) or the half width of an interval, having a statedcoverage probability.(3) Measurement uncertainty comprises, in general, manycomponents. Some of these ma
29、y be evaluated by Type Aevaluation of measurement uncertainty from the statisticaldistribution of the quantity values from series of measurementsand can be characterized by standard deviations. The othercomponents, which may be evaluated by Type B evaluation ofmeasurement uncertainty, can also be ch
30、aracterized by stan-dard deviations evaluated from probability density functionsbased on experience or other information.(4) In general, for a given set of information, it is under-stood that the measurement uncertainty is associated with astated quantity value attributed to the measurand. A modific
31、a-tion of this value results in a modification of the associateduncertainty.3.1.7 precision, ncloseness of agreement between inde-pendent test results obtained under stipulated conditions. E4563.1.7.1 Discussion(1) Precision depends on random errors and does not relateto the true value or the specif
32、ied value.(2) The measure of precision is usually expressed in termsof imprecision and computed as a standard deviation of the testresults. Less precision is reflected by a larger standard devia-tion.(3) “Independent test results” means results obtained in amanner not influenced by any previous resu
33、lt on the same orsimilar test object. Quantitative measures of precision dependcritically on the stipulated conditions. Repeatability and repro-ducibility conditions are particular sets of extreme stipulatedconditions.3.1.8 rated conditions, nmanufacturer-specified limits onenvironmental, utility, a
34、nd other conditions within which themanufacturers performance specifications are guaranteed atthe time of installation of the instrument. ASME B89.4.193.1.9 reference quantity value and reference value,nquantity value used as a basis for comparison with values ofquantities of the same kind. JCGM 200
35、:20123.1.9.1 DiscussionE2919 132(1) A reference quantity value can be a true quantity valueof a measurand, in which case it is unknown, or a conventionalquantity value, in which case it is known.(2) A reference quantity value with associated measure-ment uncertainty is usually provided with referenc
36、e to:(a) Amaterial, for example, a certified reference material;(b) A device, for example, a stabilized laser;(c) A reference measurement procedure; and(d) A comparison of measurement standards.3.1.10 registration, nprocess of determining and applyingto two or more datasets the transformations that
37、locate eachdataset in a common coordinate system so that the datasets arealigned relative to each other. E25443.1.10.1 Discussion(1) A three-dimensional (3D) imaging system generallycollects measurements in its local coordinate system. When thesame scene or object is measured from more than one posi
38、tion,it is necessary to transform the data so that the datasets fromeach position have a common coordinate system.(2) Sometimes the registration process is performed on twoor more datasets that do not have regions in common. Forexample, when several buildings are measured independently,each dataset
39、may be registered to a global coordinate systeminstead of to each other.(3) In the context of this definition, a dataset may be amathematical representation of surfaces or may consist of a setof coordinates, for example, a point cloud, a 3D image, controlpoints, survey points, or reference points fr
40、om a computer-aided drafted (CAD) model.Additionally, one of the datasets ina registration may be a global coordinate system (as in3.1.10.1(2).(4) The process of determining the transformation ofteninvolves the minimization of an error function, such as the sumof the squared distances between featur
41、es (for example, points,lines, curves, and surfaces) in two datasets.(5) In most cases, the transformations determined from aregistration process are rigid body transformations. This meansthat the distances between points within a dataset do notchange after applying the transformations, that is, rot
42、ations andtranslations.(6) In some cases, the transformations determined from aregistration process are nonrigid body transformations. Thismeans that the transformation includes a deformation of thedataset. One purpose of this type of registration is to attempt tocompensate for movement of the measu
43、red object or deforma-tion of its shape during the measurement.(7) Registration between two point clouds is sometimesreferred to as cloud-to-cloud registration, between two sets ofcontrol or survey points as target-to-target, between a pointcloud and a surface as cloud-to-surface, and between twosur
44、faces as surface-to-surface.(8) The word alignment is sometimes used as a synony-mous term for registration. However, in the context of thisdefinition, an alignment is the result of the registration process.3.1.11 true quantity value, true value of a quantity, and truevalue, nquantity value consiste
45、nt with the definition of aquantity. JCGM 200:20123.1.11.1 Discussion(1) In the error approach to describing measurement, a truequantity value is considered unique and, in practice, unknow-able. The uncertainty approach is to recognize that, owing tothe inherently incomplete amount of detail in the
46、definition ofa quantity, there is not a single true quantity value but rather aset of true quantity values consistent with the definition.However, this set of values is, in principle and practice,unknowable. Other approaches dispense altogether with theconcept of true quantity value and rely on the
47、concept ofmetrological compatibility of measurement results for assess-ing their validity.(2) In the special case of a fundamental constant, thequantity is considered to have a single true quantity value.(3) When the definitional uncertainty associated with themeasurand is considered to be negligibl
48、e compared to the othercomponents of the measurement uncertainty, the measurandmay be considered to have an “essentially unique” truequantity value. This is the approach taken by JCGM 100 andassociated documents in which the word “true” is considered tobe redundant.3.2 Definitions of Terms Specific
49、to This Standard:3.2.1 absolute pose, npose of an object in the coordinateframe of the system under test.3.2.2 degree of freedom, DOF, nany of the minimumnumber of translation or rotation components required tospecify completely the pose of a rigid body.3.2.2.1 Discussion(1) In a 3D space, a rigid object can have at most 6DOFs,three translation and three rotation.(2) The term “degree of freedom” is also used with regardto statistical testing. It will be clear from the context in whichit is used whether the term relates to a statistical test or th
