Handheld device motion tracking using MEMS gyros and accelerometer

copyright 2011 controltrix corp www. controltrix.com
Hand held motion tracking using
MEMS gyros and accelerometer for
gaming applications
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 values
Intro

• Objective : Measure angles(orientation) in 3D in real time
• 3D Angle (orientation) is mapped to screen object motion
• Integrating(accumulating) angular velocity gives angular
displacement
• Integration causes drift
• Accumulation errors  diverging results to ∞  loss of sync
Example
MPU 6000 has angular velocity error of 20 degrees/s .
After 9 sec, the object may point opposite !!!
Intro.

• 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 gm
Intro..

• To overcome drift filtering is used
• Filtering removes DC offset in measurement but….
Creates a side effect of homing
• A Stationary object the measured angles
drift 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

• Only relative motion tracked ..screen object and handheld.
Example
The directionality of motion is correct, but
A 90 degree counter clockwise followed by 90 degree clockwise
is never initial position.
• Cannot Track pure translation motion
• Slow movements are not properly tracked.
• Below a certain limit the system essentially rejects data as noise
Limits

• 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 filter
What is required ?

• Accelerometer measures gravity ‘g’ (always down) when stationary
• Gravity is absolute reference direction and magnitude
Accelerometer features
Fig: The accelerometer
measures the component of
the acceleration due to
gravity acting on each of the
three axes. These
components are
trigonometrically related to
the angle of inclination

• 3 components provide crude estimate
for roll and pitch
• Simple vector math required
• Doesn’t help with Yaw
Example
North and east pointing is indistinguishable / give same
readings
Accelerometer features.

• Magnetometer (mag) measures axial magnetic field strength (B)
• 3 axis magnetometer measures in all 3
dimensions
• Absolute reference is local earth
magnetic field
• 2 Angles (pitch and yaw) can be measured
(assuming 0 magnetic dip/perfectly horizontal)
• Doesn’t help with roll
e.g. any roll about the magnetic line axis will give same readings
Magnetometer features and utility

• 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 initially
Magnetometer features and utility.

• 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

• 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 translation
Proposed method advantages.

• Acceleration and velocity are measured using noisy sensor
• Direct velocity measurement is noisy ( v m/s)
• Acceleration is measured with
a = 0.1 m/s2
offset = 0.2 m/s2 (DRIFT)
Superposed sine wave drive
Amplitude A = 3 m/s2,
frequency f = 0.05 Hz
Sample time Ts = 0.1 s
Problem specifics

• 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

Measured velocity noisy data
(True velocity is smooth sine wave of amp 10, period 20 s/ 10 cycles
 (2 s for our handheld system)

velocity estimation error (v^ - v) vs time
Sim results std Kalman filter

error = v^ – v vs time
Sim results of proposed solution

• Velocity estimation techniques using sensor fusion
• MEMS -Accelerometer
• MEMS gyro
Appendix

Velocity Estimation from noisy
Measurements
Sensor fusion using modified Kalman filter

Consider 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 velocity
Standard solution
• Kalman filter with optimal gain K for sensor data fusion
• Estimate by combining velocity and acc. Measurement
Objective

• Acceleration and velocity are measured using noisy sensor
• Direct velocity measurement is noisy
( v m/s)
• Acceleration is measured with
a = 0.1 m/s2
offset = 0.2 m/s2 (DRIFT)
Superposed sine wave drive
Amplitude A = 3 m/s2,
frequency f = 0.05 Hz
Sample time Ts = 0.1 s
• Simulated time = 200s - 400s
Problem specifics

Measured velocity noisy data
(True velocity is smooth sine wave of amp 10, period 20 s)

• 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 accelerometers
Advantages

• Can be modified easily to make tradeoff between drift
performance (convergence) and noise reduction
• Systematic technique for parameter calculations
• No trial and error
Advantages.

Sl No Metric Kalman Filter Modified Filter
1. Drift •Drift is a major problem
(depends inversely on K)
•Needs considerable
characterization.(Offset,
temperature calibration
etc).
•Guaranteed automatic convergence.
•No prior measurement of offset and
characterization required.
•Not sensitive to temperature induced
variable drift etc.
2. Convergence •Non-Zero measurement
and process noise
covariance required else
leads to singularity
•Always converges
•No assumptions on variances required
•Never leads to a singular solution
3. Method •Two distinct phases:
Predict and update.
•Can be implemented in a few single
difference equation or even in
continuum.
Comparison

Comparison.
Note: The right column filter is a super set of a standard Kalman filter
Sl No Metric Kalman Filter Modified Filter
4. Computation •Need separate state
variables for position,
velocity, etc which adds more
computation.
•Highly optimized computation.
•Only single state variable required
5. Gain value
/performance
•In one dimension,
•K = process noise /
measurement noise. dt
• ‘termed as optimal’
•Gains based on systematic design
choices.
•The gains are good though
suboptimal (based on tradeoff)
6. Processor req. •Needs 32 Bit floating point
computation for accuracy
and plenty of MIPS/
computation
•Easily implementable in 16 bit
fixed point processor 40
MIPS/computation is sufficient

• MEMS - Micro electro-mechanical systems
• Simplest MEMS devices possible, consisting of little more than
a cantilever beam with a proof mass (also known as seismic mass).
• Under the influence of external accelerations the proof mass
deflects from its neutral position. This deflection is measured in an
analog or digital manner.
MEMS ACCELEROMETER

MEMS ACCELEROMETER.

• Most commonly, the capacitance between a set of fixed beams
and 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 spring
deformation, 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..

• Most micromechanical accelerometers operate in-plane,
i.e. they are designed to be sensitive only to a direction in the
plane of the die.
• By integrating two devices perpendicularly on a single die a 2-axis
accelerometer can be made
• By adding an additional out-of-plane device 3-axes can be
measured. Such a combination may have much lower
misalignment error than 3 discrete models combined after
packaging.
MEMS ACCELEROMETER...

MEMS GYROSCOPE
• Almost all reported micro machined
gyroscopes use vibrating mechanical
elements (proof-mass) to sense rotation
• They have no rotating parts that require bearings, and hence they
can be easily miniaturized and batch fabricated using
micromachining techniques
• All vibratory gyroscopes are based on the transfer of energy
between two vibration modes of a structure caused by
Coriolis acceleration

• Coriolis acceleration is an apparent acceleration that arises
in a rotating reference frame and is proportional to the rate of
rotation
MEMS GYROSCOPE.

MEMS GYROSCOPE..
• In general, gyroscopes can be classified into
three different categories based on their
performance: inertial grade, tactical - grade, and rate-grade
devices.
• Tuning fork gyroscopes contain a pair of masses that are driven
to oscillate with equal amplitude but in opposite directions.
When rotated, the Coriolis force creates an orthogonal vibration
that can be sensed by a variety of mechanisms.

• The Draper Lab gyro, figure 2, uses comb-type structures to drive
the tuning fork into resonance, and rotation about either in-
plane axis results in the moving masses to lift, a change that can
be detected with capacitive electrodes under the mass.
MEMS GYROSCOPE...

MEMS GYROSCOPE….
• Vibrating-Wheel Gyroscopes have a wheel that is driven to vibrate
about its axis of symmetry, and rotation about either in-plane axis
results in the wheel’ s tilting, a change that can be detected with
capacitive electrodes under the wheel, Figure 3. It is possible to
sense two axes of rotation with a single vibrating wheel.

• Wine Glass Resonator Gyroscopes. A third type of gyro is the wine
glass resonator. Fabricated from fused silica, this device is also
known as a hemispherical resonant gyro.
• Researchers at the University of Michigan have fabricated
resonant-ring gyros in planar form.
• In a wine glass gyro, the resonant ring is driven to resonance and
the positions of the nodal points indicate the rotation angle.
• The input and output modes are nominally degenerate, but due to
imperfect machining some tuning is required.
MEMS GYROSCOPE.....

Thank You
www.controltrix.com

Handheld device motion tracking using MEMS gyros and accelerometer

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