Dr inż. Maciej Gucma Pok. 343 (3p.)

Transcription

1 Dr inż. Maciej Gucma Pok. 343 (3p.)

2 Zaliczenie test! Ocena = moja + ocena P. Zieziuli / 2

3 Non sensitive to magnetic disturbances => can be used also in environment where the magnetic field is not available Mechanical gyroscopes based on conservation of momentum Measure the changes in linear or angular momentum Optical gyroscopes no moving parts Service free gravitation doesn t affect no need for gimbal mounting

4 There are two basic classes of rotation sensing gyros: Rate gyros the output is relative to the angular speed Rate integrating gyros Indicate the actual turn angle or heading The angle is relative => must be initiallly referenced to a known orientation

5 Classification according to bias drift Rate grade deg/h Tactical grade 0,01 10 deg/h Navigation grade <0,01 deg/h Mechanical, optical (fog, laser ring), MEMS (tuning fork, vibrating ring) Dynamic area: few Hz 500Hz

6 Based on conservation of momentum Continuous angular movement Mm. flywheel gyroscope Oscillatory angular momentum Employ a torsionally suspended mass oscillating back and forth at its natural frequency Continuous linear momentum Steady stream of fluid, plasma or electrons, which tend to maintain its established velocity Oscillatory linear momentum a set of discret masses moving back and forth along a straightline path ( tai ) (tuning fork rate gyro) In robotics most relevant are optical and MEMS

7 A rapidly spinning wheel or sphere with big inertia causes agyroscopic presession, when turned Rotor is rotated with electrical motor Rotor on supported by low friction bearings and mounted in a gimbal Both axis of the gimbal are perpendicular to the rotating axis The rate of precession is proportional to the torque T applied to the rotating mass: T = Iwhere T = applied input torque I = rotational inertia of rotor = rotor spin rate = rate of precession

8 special configuration of the rate integrating flywheel gyroscope If spinning axis is along the meridian (north south) no tilting (precession) occurs => if tilting occurs the axis is no more along the meridian By adding a weight as gravity reference a two axis gyroscope will become a north seeking instrument The function is dependent upon four principles: Gyroscopic inertia Gyroscopic presession Earth s rotation Earth s gravitational pull Not suitable for robots (size, weight, price, initialization time, shock and vibration sensitivitoes, power consumption etc.)

9 Mechanical tuning fork gyro is one of the most popular and low cost gyroscopes in land based mobile applications Simple Reliable The tines of a tuning fork are oscillating towards and away from one another (magnetic coils, piezoelectric oscillator) Any rotation of the gyro assembly about the vertical axis caused induced Coriolis forces acting on the tines (in horizontal plane) => this torsional vibration is proportional to the rate of turn Possible vibrational elements: strings, triangular and rectangular bars, cylinders and hemispheres

10 Tuning fork and support structure chemically etched from a single wafer of Piezoelectric quartz upper (drive) tines are actively driven by an oscillator towards and away from one another each tine will experience a Coriolis force when fork is rotated Coriolis forces cause a vibrating torsional torque Pick-up tines react to the vibrating torsional torque The vibration signal of pickup tines is demodulated into a DC signal, which is proportional to the rotation rate

11 One axix piezoelectric rate gyro Ceramic elements symmetrically on a triangular metal bar bar is made to vibrate in the X direction at its natural frequency the rotation around Z axis introduces a Coriolis force that causes a vibration in Y direction at the same frequency Rotation rate is proportional to the amplitude of the induced vibration iny direction

12 Triangular bar is made to vibrate with piezoelectric elements on right and left the third element is a feedback for the oscillator circuit the same drive elements measure the induced Coriolis force Rotation rate is the difference between the drive elements For robotics power consuption, size, price => one of the most used components drift (temperature,magnetic)

13 Tactical grade available Japan, USA Best in silicon 0.1 deg/h proto Further improvements expected Also optical MEMS under development

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16 Sagnac Effect Passive Ring Resonator Gyro (Fiber Gyro) Active Ring Resonator (Laser Gyro) Applications Future

17 First experiments concerning light propagation in rotating media were carried out by F. Harress in George Sagnac published his results in 1913 and is credited with the effect since Harress made numerous errors in interpretation of his experiment A thought experiment: R ct R R t t 2 2 c R ct 2R Rt t 2 4R Lc( t t) c L 8 2 c A 2R c R

18 A more realistic situation is an N sided regular polygon: L ( MoM M M )cos 1' o 1 ( MM o MM) R 1' o 1 MM o 1' MM o 1 c c L L c R 2 A cos c A Aenc L c c L 8A 2 c 8 c A, A 1 r 2 dr L c

19 Let us put in some numbers: d=10 cm, A = 45 cm 2, = 633 nm, = 15 deg/hr =7.3*10 5 rad/s = 4.2*10 8 rad B. Pogany experimented with an 80 kg device trying to rotate at 1600 rpm. He reported that all optical parts were damaged due to vibration by 600 rpm. Michelson used 5 miles of evacuated sewer pipes to measure the rotation of the Earth.

20 To increase effective area, we can wind N loops of fiber optic cable. 2 LD c L ND The output intensity is modulated by the phase shift between the two beams. I I o ( 1 cos( ))

21 The dynamic range of the device is easily configurable using the length and the diameter of the fiber loop. c 2LD For example, = 850 nm, L = 1 km, D = 10 cm = 73 deg/s For 1 rad sensitivity deg/h For example, = 850 nm, L = 100 m, D = 3 cm = 2400 deg/s For 1 rad sensitivity deg/h

22 Fundamental Limitations Sensitivity is limited by shot noise that goes as the square root of the power. The power received at the detector decreases with fiber length: P P e L o However, the Sagnac effect increases with the length of the fiber. These two competing effects set the length of the fiber for a given sensitivity. For a sensitivity of 10 3 deg/h, L is roughly few kilometers.

23 Thermal Noise Time dependent temperature gradient along the length of the fiber can introduce spurious phase shifts due to the temperature dependence of the index of refraction and the cable. T 2 nl c T 24NA For t = 1 h, D = 20 cm, L = 1.56 km, dn/dt = 10 5 / 0 C, = 5*10 7 / 0 C, n=1.45, and calculated shot noise limit of deg/h, T needs to be 6.7*10 3 / 0 C. Use fibers with smaller dn/dt dnc ( nc ) t dt Wind the coil such that equidistant points from fiber center are physically close to each other.

24 Polarization and Birefringence Single mode fibers permit transmission of two orthogonal polarizations Mechanical stresses can cause power transfer between polarizations and birefringence which changes the wave velocity. The result is a superposition of two interference patterns that lead to poor contrast and fringe shifts. Polarizers were initially used to suppress the weak polarization Polarization preserving fibers with high birefringence is used to suppress the weak polarization.

25 Backscatter and Beam to Filter Coupling Backscatter at the output input couplers can interfere with the main beams creating parasitic interferometers. A reasonable criterion is that the reflected power should be on the order of the intrinsic Rayleigh scattering. Since in a 1 m long, single mode fiber, the approximate value for the backscattered power is 60 db, the reflected power at the input/output interface should be less than 10 6 times the beam power. Antireflective coating on fiber surfaces is not enough as a solution. Immersion cell to reduce index of refraction step. Production of fibers with slanted end faces

26 v Optical Kerr Effect CW Electric fields of the counter propagating beams can cause changes in the index of refraction that is nonreciprocal if E 1 and E 2 are not equal (I 1 /I 2 = 10 4 leads to 10 3 deg/h shifts, Bergh et. al.1982). c [ ( E E ] / o A clever way to eliminate this problem is a square wave modulation v CCW c [ 2 2 ( E 2 2 E ] / o

27 Introduce an active laser medium into the cavity. This effectively converts phase changes to frequency changes. L m m c L L cl L c A L 4 ( ) 2 L The intensity is modulated at the beat frequency: d=10 cm, A = 45 cm 2, = o 633 nm, = 15 deg/hr =7.3*10 5 rad/s = 7 Hz I I( 1 cos( 2 t))

28 Null Shift The beat frequency is nonzero even when =0 Langmuir flow: In active laser media, neutral atoms along the center of the discharge move toward the cathode while the atoms near the walls move toward the anode. Since the lasing light is concentrated in the center, the two counter propagating beams see opposite motion for the lasing medium and hence different index of refraction (Fressnel drag). Use two discharge tubes

29 Mode Locking Backscattering in the optical path (mirrors) weakly couples the counter propagating beams. If the beat frequency gets smaller than a threshold value, the modes oscillate at the same frequency, eliminating the beat note. S bsin where and S A 4 L b or o For S<b, there is a stable solution where TH b/s 400 deg/h for b=10 3 rad/s S arcsin( ) b

30 Constant Bias Add a large constant bias such that within the operating range S+>b, where is the bias. Problem is that we need to keep a large bias very stable and know its value very precisely to be able to subtract it later on. Mechanical rotation is not stable enough Faraday effect: Applying a magnetic field parallel to the direction of propagation leads to polarization rotation by angle =VBd. However, the rotation is the same for in either direction leading to a frequency shift: c L ( c 2 ) L VBd

31 Alternating Bias Alternate bias in positive and negative directions. Over each cycle the net bias averages out eliminating the need to know the amplitude very precisely. S bsin cos( t) >>b The solution of this differential equation shows that there are dead bands centered at the multiples of the dither frequency with width: bj r ( )

32 Dead spaces can be made very small since by choosing large 2 1 / 2 r J r 2 4 ( ) ( ) cos( )

33 Currently CII is world s largest laser gyro with approximate area of 1m 2 Made out of one solid piece of Zerodur using HeNe as the active lasing medium Sensitivity of 10 7 Earth rotations over many hours: 10 8 rad/s/hz 1/2 Can detect 12 Hz oscillations in the earth s rotation axis due to the moon (60 cm daily motion at the poles) Currently designing a 367 m 2 gyro with estimated sensitivity of rad/s/hz 1/2

34 Navigation Geophysics Relativity Symmetry testing Quantum Field Theory

35 For matter waves, the phase shift equation is modified as, 2!!! atom 4A 4MA v h Gustavson et. al. 1996: A = 22 mm 2, sensitivity of 2*10 8 rad/s/hz 1/2 photon Mc Mc 10 h h 10 Space based: HYPER (European Space Agency) Space Matter Wave Gyroscope (Jet Propulsion Laboratory)

36 Chow W., et. al., The ring laser gyro, Rev. Mod. Phys, 1985, 57, 61 Lefevre, H., The Fiber Optic Gyroscope, (Artech House) 1993 Gustavson, T, et. al., Precision Rotation Measurements with an Atom Interferometer Gyroscope, Phys. Rev. Lett., 1996, 71, 2046 Bergh, R., et. al., Compensation of the optical Kerr effect in fiber optic gyroscopes, Opt. Lett., 1982, 7, 6 Stedman, G., Ring laser tests of fundamental physics and geophysics, 1997, Rep. Prog. Phys., 60, 615 Loukianov, D., et. al. (ed.), Optical Gyros and their Application, RTO AGARDoraph 339, 1999

37 Most promising sensors in the mobile robotics in near future two laser beams are rotating opposite directions in a closed loop when the beams are combined the rotation rate and direction can be calculated from the interference fringes Five basic principles: Active optical resonator Passive optical resonator Open loop fibre optic interferometer (anal.) Closed loop fibre optic interferometer (digit.) Fibre optic resonator

38 Active optical resonator Resonator is a laser itself (active) If gyro is rotated counterclock wise direction, the counter clock wise beam is travelling slightly longer than the opposite beam The change in the path length is proportional to the rotation rate In very small rotation rates there is a dead band because of frequency lock in

39 Laser ring gyroscope 0,001 deg/h standard, in use!!! Suitable for robots except price

40 Modular Azimuth Positioning System (MAPS) Complete stand alone navigation system Three sub units: Dynamic Reference Unit (DRU) Inertial Sensor Assembly (ISA) Inertial processor Navigation processor Control and Display Unit (CDU) Vehicle motion sensor (VMS)

41 VMS is optical incremental encoder, which is connected to vehicle s odemeter cable Inertial Sensor Assembly has three laser ring gyroscopes and three acceleration sensors Inertial sensor pairs (gyro + acceleration senasor) are located perpendicular to each other The initialization of heading is made by measuring the components of earth s rotation from stationary vehicle

42 New design of three axis active optical resonator in order to reduce size Six mirrors in the center of cubic faces Three mutually orthogonal laser ring gyros which are using the same mirrors Gyros are functionally independent The whole structure inside a monolithic class ceramic block No cross-talk between the axis was noticed in the tests

43 Laser source is outside of the ring cavity no frequency lock problem The passive structures also eliminates the problems arising from changes in the gain of refraction of the medium Changes in the gain change the length of the optical path

44 Polarization maintaining single mode fiber is employed to ensure the two counter propagating beams in the loop follow identical paths in the absence of rotation When gyro is rotated the rate of rotation is proportional to the phase shift between the beams (Sagnac phase shift)

45 + low price + not sensitive to shocks and vibrations + not sensitive to gravity nor accelerations + short initialization time + good sensitivity + the geometry of the fiber coil is not critical + no need to control the length of the optical path very long single mode fiber the dynamic area is small comparing to ring laser gyros drift caused by the analog components Suitable for low cost applications where best performance is not required Heading of (robots, cars) Tilt and roll sensing

46 Hitachi Cable Ltd. is manufacturing one axis open loop fiber optic gyroscopes Hitachi gyros are used in mobile robotics and automotive applications Demonstrated Gyro Hitachi FOG X Drift ~ 5 deg/hour

47 Fiber optic gyroscope 0,01 deg/h Can be produced in a smaller size in principle (looses precision though) 3 (or 2) built in would be very tight.

48 For more sophisticated applications like aircraft navigation Digital signal processing is more complicated than analog, which is used in open loop systems Benefit comparing to open loop systems: Not sensitive to light source intensity variations Not sensitive to gains of single components=>very small drift ~ 0,001 0,01deg/h Linearity and stability depend only from the phase transducer

49 Developed from Passive Ring Resonators A passive Resonant cavity is formed from multiturn closed loop of optical fiber Frequency modulated light is injected from input coupler reliable Long life Short initialization time Light small amount of fiber highly coherent laser source extremely low-loss fiber components

50 F=ma Moving mass capacitive, inductive, resistive Integrated Circuit Gravity is the problem Can be used for gravity sensing as a static position sensor.

51 built on a single monolithic IC two capacitor plates series connected form a capacitive divider with the moving center plate which is connected to the moving mass

52 sensor plates are driven differentially (180 phase shift) by a 1MHz square wave when sensor is in rest the centerplate output is zero when accelerated the centerplate moves and creates a mismatch between the two capacitances output amplitude varies as function of the acceleration