Forbes, A B

Hughes, E B

Jamshidi, Jafar

Maropoulos, Paul

Mileham, Antony R

Muelaner, Jody E

Wang, Z

The indoor Global Positioning System (iGPS) is an innovative measurement system consisting of a network of Rotary-laser automatic theodolites (R-LATs) which provide a factory wide coordinate measurement system. The primary benefits of the system are that a theoretically unlimited number of sensors are able to simulatiously detect position using signals from a common network of transmitters and that the sensors are able to automatically regain connection to the network following a disruption of the line of sight. The basic functionality of this system is described together with a brief overview of work to verify its performance

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        Citation for published version:Muelaner, JE, Wang, Z, Jamshidi, J, Maropoulos, P, Mileham, AR, Hughes, EB & Forbes, AB 2008, 'iGPS - AnInitial Assessment Of Technical And Deployment Capability' Paper presented at 3rd International Conference onManufacturing Engineering, Kallithea of Chalkidiki, Greece, 1/10/08 - 3/10/08, pp. 805-810.Publication date:2008Link to publicationUniversity of BathGeneral rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Download date: 07. Dec. 2019Proceedings of the 3rd International Conference on Manufacturing Engineering (ICMEN), 1-3 October 2008, Chalkidiki, GreeceEdited by Prof. K.-D. Bouzakis, Director of the Laboratory for Machine Tools and Manufacturing Engineering (ΕΕΔΜ),Aristoteles University of Thessaloniki and of the Fraunhofer Project Center Coatings in Manufacturing (PCCM),a joint initiative by Fraunhofer-Gesellschaft and Centre for Research and Technology Hellas, Published by: ΕΕΔΜ and PCCM 805   iGPS - AN INITIAL ASSESSMENT OF TECHNICAL  AND DEPLOYMENT CAPABILITY   J. E. Muelaner1, Z. Wang1, J. Jamshidi1, P. G. Maropoulos1, A R Mileham1, E. B. Hughes2, A. B. Forbes2  1. Department of Mechanical Engineering, The University of Bath, Bath, UK 2. National Physical Laboratory, Teddington, UK   ABSTRACT The indoor Global Positioning System (iGPS) is an innovative measurement system consisting of a network of Rotary-laser automatic theodolites (R-LATs) which pro-vide a factory wide coordinate measurement system. The primary benefits of the system are that a theoretically unlimited number of sensors are able to simulatiously detect position using signals from a common network of transmitters and that the sensors are able to automatically regain connection to the network following a dis-ruption of the line of sight. The basic functionality of this system is described to-gether with a brief overview of work to verify its performance.  KEYWORDS: iGPS, Indoor GPS, Infrared GPS, Constellation 3Di, Metrology   1. INTRODUCTION  iGPS essentially consists of a network of automatic theodolites employing triangulation to auto-matically generate positional measurements at a single receiver. In this way a highly adaptable large scale coordinate measurement machine is created able to provide factory wide measure-ment. The system is best understood by first considering the function of an individual transmit-ter-sensor pair which constitutes a Rotary-laser automatic theodolite (R-LAT). An R-LAT transmitter mounts a rotating head on a stationary body as shown in Figure 1. The rotating head sweeps two fanned laser beams through the working volume, while the stationary body delivers a strobe with a single pulse for every other revolution of the head. The fanned la-ser beams are inclined at 30 degrees to the horizontal and offset by 90 degrees to one another /1/ as shown in Figure 1. The receiving sensor detects the pulse of light from the strobe and both of the fanned laser beams as they sweep past. These optical signals are the only form of    Figure 1: R-LAT Transmitter. 806 3rd ICMEN – 2008 communication between the transmitter and sensor. The timing differences between pulses of light reaching the sensor are used to calculate the azimuth and elevation angles, this is ex-plained in detail in Section 2. The novel functionality of R-LATs provides a number of advantages to a coordinate measure-ment network. Since all communication is one-way, a very large number of sensors are able to simultaneously detect signals from a single network of transmitters. This massive scalability through one-way broadcasting is similar to the Global Positioning System in which satellites broadcast timing signals to receiver units. Transmitters are continuously scanning the entire measurement volume and therefore they do not have to track a target as is the case with theodolites and Laser Trackers. Therefore there is no requirement to re-aim the transmitter fol-lowing a disruption in the line of sight. The sensor component of an R-LAT is able to detect sig-nals coming from a wide range of angles, typically 360 degrees in azimuth and at least plus/minus 30 degrees in elevation. This is in contrast to the corner cube reflectors used with Laser Trackers which have an acceptance angle of less than ±45 degrees in all directions.  The cumulative effect is that a sensor can move around various line of sight obstructions losing and regaining connection to transmitters with relative ease. A point can be located by a single sensor as long as the sensor receives optical signals from at least two different transmitters. Each transmitter is configured to rotate at a slightly different speed; typically approximately 3,000 rev/min. It is this difference in speed which allows the system to differentiate between the signals from different transmitters /1/. If more than two transmitters are visible it is possible to apply some form of least squares fitting to the redundant data in order to reduce the uncertainty of the coordinate measurements. The network setup must include a procedure to determine the relative transmitter positions. The standard way of achieving this for any measurement system employing triangulation is by using bundle adjustment /2/. The flexibility of operation facilitated by the system has considerable potential for use within the aerospace sector and other large scale manufacturing sectors. R-LAT networks have been demonstrated in industrial applications including positioning robots, the alignment of laser pro-jection /3/ and the jigless assembly of aircraft structures /4/. The R-LAT network can be compared to other multi-station metrology networks. Automatic theodolites /5/ have been used to demonstrate the concept of automatic triangulation while con-siderable work has been carried out to demonstrate the advantages of multilateration using spe-cially constructed tracking interferometers /6/ and industrial laser trackers in applications such as the assembly of spacecraft structures /7/. Multilateration generates positions based on dis-tance or displacement measurements from multiple stations to a single measurement sensor. The Anglescan positioning system /8/ probably has the most in common with R-LATs. In the Anglescan system a fixed laser is swept across the horizon by a rotating mirror, the laser is re-turned to the instrument by a retroreflector allowing a pulse of light to be detected at the trans-mitter. This is a two dimensional navigation system. None of these systems are able to offer the flexibility of operation provided by an R-LAT network.   2. MATHEMATICAL MODEL  The equations relating the azimuth and elevation angle to the timing signals received by the sensor can be derived by consideration of the two fanned lasers sweeping past the sensor and the strobe illuminating the sensor. If a vector is located so that it is normal to the first fan when that fan crosses the sensor (at t1) and a second vector is similarly located so that it is normal to the second fan at t2 then a third vector which is orthogonal to the first two will give the direction from the transmitter to the target sensor. Constructing the vectors normal to the fans when these fans are aligned with the x-axis and then rotating the vectors around the z-axis will give the vectors at t1 and t2 (n1 and n2 respec-tively). The rotation around the z-axis is simply calculated from the time difference between the strobe and the fan illuminating the sensor, multiplied by the angular velocity (ω). The vectors to fan 1 at t1 and to fan 2 at t2 are therefore given by; Logistics in Manufacturing 807  Figure 2: Parameters used in Construction of Vector Describing Target Direction   ⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡−⋅⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡−=1111111cossin01000cossin0sincosααaaaan  ( 1 ) ⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡−⋅⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡−=2222222cossin01000cossin0sincosααaaaan  ( 2 ) where a1 is the rotation of fan 1 about the z-axis from the time of the strobe illuminating the sen-sor (t0) to the time of the fan passing the sensor (t1) and a2 is the rotation of fan 2 from t0 to t2 and α1 and α2 as defined in Figure 2.  ( ) ω⋅−=011tta  ( 3 ) ( )0022αω −⋅−= tta  ( 4 )  The vector giving the direction from the sensor to the origin is then simply the cross product of n1 and n2 and from this vector it is straightforward to calculate the azimuth and elevation angles. The azimuth angle is the angle about the z-axis to the sensor target while the elevation angle is the angle from the x-y plane to the target. An interesting implication of this model is that measurements of the azimuth angle taken using an R-LAT will always be considerably more accurate than measurements of elevation.   3. VERIFICATION STRATEGY  The accuracy of the R-LAT system is difficult to quantify since despite reports of accuracies bet-ter than those for a laser tracker /4/ there has been little work published to independently verify this performance. Since uncertainties in the coordinate measurements provided by a triangula-tion network propagate from the uncertainties in the individual angular measurements, the first step in assessing the accuracy of the system is to determine the uncertainties of an individual R-LAT. Standards in existence for the verification of coordinate measurements include the ISO 10360 standard for coordinate measuring machines /9/ and the ASME B89 standard for Laser Trackers /10/. These standards have in common low level tests designed to isolate sub-systems followed by high level tests using the complete system in a more realistic manner. Initial testing of the individual R-LAT is in keeping with this principle of isolating sub-systems. Unfortunately the only 808 3rd ICMEN – 2008 available standards for testing theodolites are somewhat vague and “are not proposed as tests for acceptance or performance evaluations…”/11/. A test procedure was therefore designed to ensure the comparison of the measured angles with a calibrated reference angle. The test procedure involves mounting the transmitter on a high precision rotary table ( Figure 3) with the sensor mounted in a fixed position at an appropriate distance which was known approximately. The initial azimuth angle of the sensor is measured and the transmitter is then rotated through a known reference angle using the rotary table. A second angle is meas-ured and this provides the difference between the two measured angles which can then be compared with the rotary table reference.    Figure 3: Experimental Setup  In order to ensure the validity of the reference angle the transmitter must be mounted coaxial to the rotary table. A calibration procedure was designed to reduce deviation from the coaxial. This involved mounting a reference cylinder to the rotating head of the transmitter, the reference cyl-inder was moved radially on the centering base to adjust the concentricity and jacked-off the centering base to adjust the parallelism of the axes. A dial gauge was used to measure the ra-dial deflection of the reference cylinder as the transmitter head was rotated in order to adjust the position of the reference cylinder until it was coaxial within the measurement limits of the dial gauge. The rotating head was then fixed and the rotary table was rotated to adjust the position of the transmitter until the transmitter was coaxial with the rotary table. Combining the uncertain-ties arising from this procedure with the uncertainty inherent to the rotary table the expanded uncertainty at a 95% confidence level for the uncertainty in the reference azimuth angle is ap-proximately 0.5 arc seconds.   4. INITIAL RESULTS AND FURTHER WORK  Initial results indicate that measurements of azimuth can be made with an expanded uncertainty of approximately 0.5 arc seconds at a 95% confidence level. This level of accuracy is only ob-tained when measurements are averaged over at least 2 seconds as shown in figure 4. This angular uncertainty relates to an uncertainty in coordinate measurements of approximately 25 μm at a range of 10 m. Since this is at the same level as the experimental calibration it is likely that the actual performance of the R-LAT is better than this, all we can say with any confidence is that the R-LAT is at least as accurate as indicated by these tests. There are a number of possible directions for further work. Improved accuracy of the current experimental design would provide interesting results on the actual azimuth performance of the system. Investigation of the accuracy throughout the working volume at different ranges and elevation would also be interesting. Logistics in Manufacturing 809 012340 1 2 3 4Sampling Duration (s)Uncertainty (arc sec)Test 3aTest 3bTest 3cTest 3dTest 3e  Figure 4: Uncertainty in Azimuth at 95% Confidence against Sampling Duration  Similar tests for the accuracy of elevation angle would be desirable but also difficult to realize. The mathematical model combined with the existing results show that the expanded uncertainty in elevation must be lower than 0.5 arc seconds. In order to provide any new information the tests would therefore have to have a calibration uncertainty of considerably less than this.   The third area suggested for further work is testing to verify the coordinate measurement capa-bility of the complete system.   5. ACKNOWLEDGEMENTS  The work has been carried out as part of the EPSRC, IdMRC at the Mechanical Engineering Department of the University of Bath, under grant No. EP/E00184X/1. The authors wish to thank Ian Whitehead and John Walford from Rotary Precision Instruments for their technical inputs.    6. REFERENCES                                                 1.  Hedges, T.M., Takagi, H., Pr-latt, T., Sobel, M.J. 2003, Position Measurement System and Method Using Cone Math Calibration. United States Patent US 6,535,282 B2 Mar. 18, 2003 2. Triggs, B., MCLauchlan, P., Hartley R., Fitzgibbon, A., 1999, Bundle Adjustment - A Modern Synthesis, In: Vision Algorithms: Theory and Practice, International Workshop on Vision Al-gorithms, Corfu, Greece, September 21-22, 1999 Proceedings, Series: Lecture Notes in Computer Science , Vol. 1883 3.  Sell, C., 2005, On the right lines, In: Engineer, v 293, n 7680, Jul 25, 2005, p 30, Centaur Publishing Ltd. 4.  Sharke, P., 2003, Measuring across space and time; Large-scale metrology moves GPS in out of the rain, In: Mechanical Engineering, v 125, n 1, January, 2003, p 48 810 3rd ICMEN – 2008                                                                                                                                                           5.  Gottwald, R., 1988, SPACE – An Automated non-contact 3-D-measuring-system for indus-trial applications, In: 7th Int. Conf. Robot Vision and Sensory Controls. Feb 2-4, 1988, Zurich, Switzerland 6.  Hughes, E.B., Wilson, A., Peggs, G.N., 2000, Design of a high-accuracy CMM based on multi-lateration techniques, In: Manufacturing Technology, v 49, n 1, 2000, p 391-394, Hall-wag Publishing Ltd 7.  Maropoulos, P.G., Zhang, D., Rolt, S., Chapman, P., Rogers, B. C., 2006, Integration of Measurement Planning with Aggregate Product Modelling for Spacecraft Design and As-sembly, In: Journal of Engineering Manufacture, Proceedings of the Institution of Mechani-cal Engineers, Part B., Vol. 220, 1687-1695. 8.  Sprent, A., 1983, The Anglescan Positioning System, In: Technical Papers - 25th Australian Survey Congress: Observing New Directions, Melbourne, Australia, Inst of Surveyors 9.  ISO 10360-2:2002. Geometric Product Specifications Acceptance & Reverification tests for coordinate measuring machines (CMM) – Part 2: CMMs used for measuring size. ISO 10.  ASME B89.4.19. Performance Evaluation of Laser-Based Spherical Coordinate Measure-ment Systems. ASME 11.  ISO 17123-1:2002. Optics and optical instruments - Field procedures for testing geodetic and surveying instruments - Part 1: Theory. ISO 

iGPS - An Initial Assessment Of Technical And Deployment Capability

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iGPS - An Initial Assessment Of Technical And Deployment Capability

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