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- 1. copyright 2011 controltrix corp www. controltrix.comHand held motion tracking usingMEMS gyros and accelerometer forgaming applicationswww.controltrix.com
- 2. copyright 2011 controltrix corp www. controltrix.com• Accelerometers (acc) measure acceleration• Gyroscopes (gyro) measure angular velocity• Integrated MEMS may have 3 axis gyro + 3 axis acc• MEMS have low cost compared to other types of gyro /acc• The MEMS device is Clamped to the object (strap down)(Unlike gyro stabilized system which give direct values)• Measurements are with respect to object and not with earth• Complex/Vector /coordinate computation for absolute valuesIntro
- 3. copyright 2011 controltrix corp www. controltrix.com• Objective : Measure angles(orientation) in 3D in real time• 3D Angle (orientation) is mapped to screen object motion• Integrating(accumulating) angular velocity gives angulardisplacement• Integration causes drift• Accumulation errors diverging results to ∞ loss of syncExampleMPU 6000 has angular velocity error of 20 degrees/s .After 9 sec, the object may point opposite !!!Intro.
- 4. copyright 2011 controltrix corp www. controltrix.com• Essentially an inertial measurement system• Attitude Heading Reference systems (AHRS) used in aircraft• Best systems drift ~ 1Km /hr and few degrees/hr• Cost ~ US$ 100K ,weight ~ few Kg• Aircraft has auxillary systems like GPS, magnetometer• Augment inertial measurements (keep drift negligible)• Objective : emulate AHRS in a few US$ , < 100 gmIntro..
- 5. copyright 2011 controltrix corp www. controltrix.com• To overcome drift filtering is used• Filtering removes DC offset in measurement but….Creates a side effect of homing• A Stationary object the measured anglesdrift towards 0 with time. (still better than drifting to ∞)• To fix homing some thresholding is done but……It causes slow movements not accurately tracked…..Approach and limits
- 6. copyright 2011 controltrix corp www. controltrix.com• Only relative motion tracked ..screen object and handheld.ExampleThe directionality of motion is correct, butA 90 degree counter clockwise followed by 90 degree clockwiseis never initial position.• Cannot Track pure translation motion• Slow movements are not properly tracked.• Below a certain limit the system essentially rejects data as noiseLimits
- 7. copyright 2011 controltrix corp www. controltrix.com• Auxiliary angular position data to periodically recalibrate(accelerometer and magnetometer)• Remove unbounded drift• Even noisy, jumpy, low bandwidth, low sample rate data is good• Real time data fusion• Sensor data fusion algorithm to compute best estimate• Kalman filter or Modified Kalman filterWhat is required ?
- 8. copyright 2011 controltrix corp www. controltrix.com• Accelerometer measures gravity ‘g’ (always down) when stationary• Gravity is absolute reference direction and magnitudeAccelerometer featuresFig: The accelerometermeasures the component ofthe acceleration due togravity acting on each of thethree axes. Thesecomponents aretrigonometrically related tothe angle of inclination
- 9. copyright 2011 controltrix corp www. controltrix.com• 3 components provide crude estimatefor roll and pitch• Simple vector math required• Doesn’t help with YawExampleNorth and east pointing is indistinguishable / give samereadingsAccelerometer features.
- 10. copyright 2011 controltrix corp www. controltrix.com• Magnetometer (mag) measures axial magnetic field strength (B)• 3 axis magnetometer measures in all 3dimensions• Absolute reference is local earthmagnetic field• 2 Angles (pitch and yaw) can be measured(assuming 0 magnetic dip/perfectly horizontal)• Doesn’t help with rolle.g. any roll about the magnetic line axis will give same readingsMagnetometer features and utility
- 11. copyright 2011 controltrix corp www. controltrix.com• Combining both acc and mag all 3 angles can be found but…• Earths magnetic field is rarely horizontal dip is non 0• More computation required to account for dip• Calibration of magnetometer to get local dip initiallyMagnetometer features and utility.
- 12. copyright 2011 controltrix corp www. controltrix.com• One to one mapping of all rotational motion• Extremely intuitive gaming experience for role playing game• Perfect synch /small tracking error (ref: simulation)• Accurate tracking of slowest possible movements (No drift)• Inspite of noise/ jumpy acc /mag based angle sensing• Very smooth operation (limited by display frame rate)Proposed method advantages
- 13. copyright 2011 controltrix corp www. controltrix.com• Future of gaming• Auto calibration for acc and mag• Unlike filtering , method acts like a filter but without the lag• Virtually 0 lag filter• Performance can be easily tweaked (ref. appendix)• Minimal tuning/ trial and error• Tracking Pure translation is still not possible but…..• Hand movements are seldom pure translationProposed method advantages.
- 14. copyright 2011 controltrix corp www. controltrix.com• Acceleration and velocity are measured using noisy sensor• Direct velocity measurement is noisy ( v m/s)• Acceleration is measured witha = 0.1 m/s2offset = 0.2 m/s2 (DRIFT)Superposed sine wave driveAmplitude A = 3 m/s2,frequency f = 0.05 HzSample time Ts = 0.1 sProblem specifics
- 15. copyright 2011 controltrix corp www. controltrix.com• Example from a different problem , but math is same• Replace Velocity with angle (from acc and mag )in deg• Replace Acceleration with angular velocity (gyro data in deg/s)• Sample time is 0.01 s timescale units change to 0.1s• Total simulated time 20 s (instead of 200 as shown)Mapping to our system
- 16. copyright 2011 controltrix corp www. controltrix.comMeasured velocity noisy data(True velocity is smooth sine wave of amp 10, period 20 s/ 10 cycles (2 s for our handheld system)
- 17. copyright 2011 controltrix corp www. controltrix.comvelocity estimation error (v^ - v) vs timeSim results std Kalman filter
- 18. copyright 2011 controltrix corp www. controltrix.comerror = v^ – v vs timeSim results of proposed solution
- 19. copyright 2011 controltrix corp www. controltrix.com• Velocity estimation techniques using sensor fusion• MEMS -Accelerometer• MEMS gyroAppendix
- 20. copyright 2011 controltrix corp www. controltrix.comVelocity Estimation from noisyMeasurementsSensor fusion using modified Kalman filter
- 21. copyright 2011 controltrix corp www. controltrix.comConsider a vehicle moving• Desired to measure the velocity accurately• Velocity is directly measured but is noisy• Acceleration also measured using onboard accelerometers• Integrating acceleration data gives velocity• Offset errors in acc./random walk cause drift in velocityStandard solution• Kalman filter with optimal gain K for sensor data fusion• Estimate by combining velocity and acc. MeasurementObjective
- 22. copyright 2011 controltrix corp www. controltrix.com• Acceleration and velocity are measured using noisy sensor• Direct velocity measurement is noisy( v m/s)• Acceleration is measured witha = 0.1 m/s2offset = 0.2 m/s2 (DRIFT)Superposed sine wave driveAmplitude A = 3 m/s2,frequency f = 0.05 HzSample time Ts = 0.1 s• Simulated time = 200s - 400sProblem specifics
- 23. copyright 2011 controltrix corp www. controltrix.comMeasured velocity noisy data(True velocity is smooth sine wave of amp 10, period 20 s)
- 24. copyright 2011 controltrix corp www. controltrix.com• No matrix calculations• Easier computation, can be easily scaled• Equivalent to Kalman filter structure (easily proven)• No drift (the error converges to 0)• Estimate accelerometer drift in the system by default• Drift est. for calib. and real time comp. of accelerometersAdvantages
- 25. copyright 2011 controltrix corp www. controltrix.com• Can be modified easily to make tradeoff between driftperformance (convergence) and noise reduction• Systematic technique for parameter calculations• No trial and errorAdvantages.
- 26. copyright 2011 controltrix corp www. controltrix.comSl No Metric Kalman Filter Modified Filter1. Drift •Drift is a major problem(depends inversely on K)•Needs considerablecharacterization.(Offset,temperature calibrationetc).•Guaranteed automatic convergence.•No prior measurement of offset andcharacterization required.•Not sensitive to temperature inducedvariable drift etc.2. Convergence •Non-Zero measurementand process noisecovariance required elseleads to singularity•Always converges•No assumptions on variances required•Never leads to a singular solution3. Method •Two distinct phases:Predict and update.•Can be implemented in a few singledifference equation or even incontinuum.Comparison
- 27. copyright 2011 controltrix corp www. controltrix.comComparison.Note: The right column filter is a super set of a standard Kalman filterSl No Metric Kalman Filter Modified Filter4. Computation •Need separate statevariables for position,velocity, etc which adds morecomputation.•Highly optimized computation.•Only single state variable required5. Gain value/performance•In one dimension,•K = process noise /measurement noise. dt• ‘termed as optimal’•Gains based on systematic designchoices.•The gains are good thoughsuboptimal (based on tradeoff)6. Processor req. •Needs 32 Bit floating pointcomputation for accuracyand plenty of MIPS/computation•Easily implementable in 16 bitfixed point processor 40MIPS/computation is sufficient
- 28. copyright 2011 controltrix corp www. controltrix.comvelocity estimation error (v^ - v) vs timeSim results std Kalman filter
- 29. copyright 2011 controltrix corp www. controltrix.comerror = v^ – v vs timeSim results of proposed solution
- 30. copyright 2011 controltrix corp www. controltrix.com• MEMS - Micro electro-mechanical systems• Simplest MEMS devices possible, consisting of little more thana cantilever beam with a proof mass (also known as seismic mass).• Under the influence of external accelerations the proof massdeflects from its neutral position. This deflection is measured in ananalog or digital manner.MEMS ACCELEROMETER
- 31. copyright 2011 controltrix corp www. controltrix.comMEMS ACCELEROMETER.
- 32. copyright 2011 controltrix corp www. controltrix.com• Most commonly, the capacitance between a set of fixed beamsand a set of beams attached to the proof mass is measured.This method is simple, reliable, and inexpensive.• Integrating piezo-resistors in the springs to detect springdeformation, and thus deflection, is a good alternative• For very high sensitivities Quantum tunneling is also used;this requires a dedicated process making it very expensive.MEMS ACCELEROMETER..
- 33. copyright 2011 controltrix corp www. controltrix.com• Most micromechanical accelerometers operate in-plane,i.e. they are designed to be sensitive only to a direction in theplane of the die.• By integrating two devices perpendicularly on a single die a 2-axisaccelerometer can be made• By adding an additional out-of-plane device 3-axes can bemeasured. Such a combination may have much lowermisalignment error than 3 discrete models combined afterpackaging.MEMS ACCELEROMETER...
- 34. copyright 2011 controltrix corp www. controltrix.comMEMS GYROSCOPE• Almost all reported micro machinedgyroscopes use vibrating mechanicalelements (proof-mass) to sense rotation• They have no rotating parts that require bearings, and hence theycan be easily miniaturized and batch fabricated usingmicromachining techniques• All vibratory gyroscopes are based on the transfer of energybetween two vibration modes of a structure caused byCoriolis acceleration
- 35. copyright 2011 controltrix corp www. controltrix.com• Coriolis acceleration is an apparent acceleration that arisesin a rotating reference frame and is proportional to the rate ofrotationMEMS GYROSCOPE.
- 36. copyright 2011 controltrix corp www. controltrix.comMEMS GYROSCOPE..• In general, gyroscopes can be classified intothree different categories based on theirperformance: inertial grade, tactical - grade, and rate-gradedevices.• Tuning fork gyroscopes contain a pair of masses that are drivento oscillate with equal amplitude but in opposite directions.When rotated, the Coriolis force creates an orthogonal vibrationthat can be sensed by a variety of mechanisms.
- 37. copyright 2011 controltrix corp www. controltrix.com• The Draper Lab gyro, figure 2, uses comb-type structures to drivethe tuning fork into resonance, and rotation about either in-plane axis results in the moving masses to lift, a change that canbe detected with capacitive electrodes under the mass.MEMS GYROSCOPE...
- 38. copyright 2011 controltrix corp www. controltrix.comMEMS GYROSCOPE….• Vibrating-Wheel Gyroscopes have a wheel that is driven to vibrateabout its axis of symmetry, and rotation about either in-plane axisresults in the wheel’ s tilting, a change that can be detected withcapacitive electrodes under the wheel, Figure 3. It is possible tosense two axes of rotation with a single vibrating wheel.
- 39. copyright 2011 controltrix corp www. controltrix.com• Wine Glass Resonator Gyroscopes. A third type of gyro is the wineglass resonator. Fabricated from fused silica, this device is alsoknown as a hemispherical resonant gyro.• Researchers at the University of Michigan have fabricatedresonant-ring gyros in planar form.• In a wine glass gyro, the resonant ring is driven to resonance andthe positions of the nodal points indicate the rotation angle.• The input and output modes are nominally degenerate, but due toimperfect machining some tuning is required.MEMS GYROSCOPE.....
- 40. copyright 2011 controltrix corp www. controltrix.comThank Youwww.controltrix.com

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