S95 Arial, Bld, YW8, 37 points, 105% line spacing

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An Improved Quaternion-Based Filtering Algorithm
for Real-Time Tracking of Human Limb Segment
Motions using Sourceless Sensors
Eric Bachmann, Xiaoping Yun, Robert McGhee,
Michael Zyda bachmann_at_cs.nps.navy.mil
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Outline

• Introduction
• Filter Algorithm Improvements
• Improved Sensors
• Wireless Tracking
• 3D Positioning

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Inertial / Magnetic Body Tracking

• Body posture can be ascertained by attaching
  inertial / magnetic sensors to human limbs
• Based on the passive measurement of physical
  quantities directly related to motion and
  attitude. (Sourceless)
• Each segment is oriented independently
• Segments are positioned relative to each other by
  adding rotated limb-translation vectors
• Position data for a single reference point is
  needed to place the avatar within a virtual
  environment.

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Goal

• Wireless full body tracking system based on
  inertial/magnetic orientation sensing
• MARG sensors are used to determine posture
• Position of one point on the body tracked using a
  simple optical or ultrasonic tracking system
  (DGPS outdoors)

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Source Based Tracking

• Sourced tracking systems require maintenance of a
  link between a tracked rigid body and one or
  more fixed stations via a transmitted source
• Interference, noise, or occlusion may cause the
  link to be distorted or broken
• Distance over which the link can be maintained is
  often limited
• Update rate and accuracy may be limited by the
  physical characteristics of the source

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Orientation Using Angular Rate

• Orientations of individual segments can be
  determined by integrating angular rates
• The angular rates p, q, and r may be used to find
  the time derivative of an orientation quaternion
• This derivative is given by
• where the quaternion q relates the body-fixed
  reference frame to the earth fixed frame
• Drift and bias in the angular rate sensors will
  limit the period of time over which q can be
  accurately estimated

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Orientation Using Gravity And Magnetic Field

• Orientations of individual segments can be
  determined by sensing
• the gravity vector
• the local magnetic field vector
• There is a rotation which relates the vectors
  sensed in a body based reference frame to their
  known values in an earth-fixed reference frame
• The rotation can be expressed using a unit
  quaternion
• The rotation or orientation represented by the
  quaternion is the orientation of the limb segment

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Magnetic Angular Rate Gravity (MARG) Sensors

• 3-DOF MARG sensors have nine-axes
• Three-axis rate sensor
• Three-axis accelerometer
• Three-axis magnetometer
• Three-axis accelerometer senses the three
  components of the gravity vector in body
  coordinates
• Sensed accelerations must be averaged over time
• Three-axis magnetometer senses three components
  of the magnetic field vector in body coordinates
• Rate sensor data gives velocity of rotation
• Quickens response by providing short-term
  orientation estimates

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A Complementary Quaternion Attitude Filter-
Block Diagram

• The quaternion-based complementary estimation
  filter estimates attitude
• Combining of filter inputs is treated as a
  parameter optimization problem
• Error minimization is accomplished by adjusting
  the derivative of the estimated orientation
  quaternion, q-hat
• Tracks through all orientations without
  singularities
• Continuously corrects for drift

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A Complementary Quaternion Attitude Filter-
Actual Measurement Vector

• Accelerometer readings return an approximation to
  the local vertical
• Represented by the pure unit quaternion
• Magnetometers provide an approximation to the
  local magnetic field vector
• Represented by the pure unit quaternion
• Combining the vector parts of h and b produces a
  6 x 1 measurement vector

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A Complementary Quaternion Attitude Filter-
Computed Measurement Vector

• Gravity in an earth-fixed reference frame is
  always down
• It can be expressed as the down unit quaternion
• The direction of the local magnetic field vector
  can be expressed as a pure unit quaternion
• These may be expressed in body coordinates using
  the estimated q as a rotation operator
• Combining the vector parts of h-hat and b-hat
  produces a 6 x 1 computed measurement vector

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Gauss-Newton Iteration

• Gauss-Newton iteration is a least squares
  estimation method based upon the minimization of
  a criteria function which expresses the
  difference between the actual measurement vector
  and computed measurement vector.
• The correction step is given by
• where the elements of the X-matrix represent the
  partial derivatives of the computed measurement
  vector with respect the components of the
  estimated orientation quaternion
• X-matrix must be non-singular and invertible

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Reduced Order Estimation

• Restriction of q to unit length eliminated
  singularity problems and
• simplifies the calculation of the X-matrix
  elements by allowing use
• of the conjugate of q
• Due to the constrained length of a unit
  quaternion, its components are
• not independent variables
• This fact combined with the orthogonal quaternion
  theorem reduced the order of the estimation
  problem
• Calculation of ?q requires only a 3 x 3 matrix
  inversion

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Reformulation of the Criterion Function

• Use of a incremental rotation quaternion allows
  ?q to be expressed as
• with the result that X-Matrix can be constructed
  using just the elements of the
• computed measurement vector
• Magnitude reduction in the effort needed to
  compute the X-matrix

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Incremental Rotation Quaterion Theorem

• The Incremental Rotation Quaterion Theorem
  offers singularity-free way to represent
  three-dimensional rotations using
  three-dimensional vectors.
• Given a rigid body with an orientation
  represented by a unit quaternion, q, then any
  rotation of this body in the range p about any rotation axis results in a new
  orientation unit quaternion, p, given by
• where the incremental rotation quaternion, r, is
  a unique unit real quaternion.

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MARG Sensor Improvements

• MARG-0-1
• Rate and Magnetometer drift issues became
  evident, requiring repeated calibrations.
• Drift due to temperature affects from power
  supply regulator
• Magnetometer was influenced by any magnetic or
  ferrous metals
• MARG-0-2
• Drift problems were reduced by
• Moving power regulator off main board
• Improved rate sensor electronics
• Manual magnetometer calibrator
• Adjustable magnetometer offsets
• Periodic calibrations still required

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Second Generation MARG Sensor Units

• MARG-1-0 R D
• Second generation sensors have been delivered.
• Reduced form factor
• Capacitive coupling
• Superior drift characteristics
• Accurate tracking with reduced gain values
• Buffer stage reduces noise feedback and provides
  low impedance signal to analog to digital
  converter
• Getting closer to removing calibration
  limitations to system design.

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Third Generation MARG Sensor Units

• MARG-2-0 RD
• Third generation sensor design stage nearing
  completion
• Miniaturized components flat form factor
• Onboard microprocessor and A to D converter
• digital output
• Continuous digital set/reset of magnetometers
• Automatic temperature compensation
• Eliminate need for repeated calibrations
• Incorporation of onboard microprocessor will make
  possible filter implementation on the sensor
  itself
• Tether cable will have 5 wires instead of 14
  wires
• Illustration shows MARG2-0 major components in
  the MARG-0-0/1/2 enclosure box

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Untethering the User

• Tethered systems increase user encumbrance and
  cancel the
• advantages that a sourceless tracking system has
  to offer
• Incorporation of a wireless technologies into the
  body tracking system will eliminate this problem
• Indoor range is expected to be 200 300ft
• Wearable computer will process sensor signals and
  submit to a fixed
• workstation via wireless LAN
• Wireless demonstration system is working
• Working on sensor to wearable computer interface

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Positioning System Integration

• Practical spread spectrum RF positioning systems
  are three to five
• years away.
• Currently examining the use of ultrasonic or
  optical tracking in the
• near term
• Initial discussions made with UC Santa Barbara to
  cooperatively construct a simple two camera
  optical tracking system
• Examining off-the-shelf ultrasonic positioning
  devices
• Expected accuracy on the order of 3 cm

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Summary

• Inertial / magnetic (MARG) body tracking avoids
  the shortcomings associated with current
  technologies.
• It is capable of providing wide area tracking of
  multiple users for networked synthetic
  environment applications
• Nine-axes sensor data is processed by a
  quaternion attitude filter
• Avatar posture is determined using only
  orientation data
• Posture is accurately tracked with minimal lag
• The technology is practical, robust and easy to
  use
• - Working prototype system
• - Major software and hardware improvement
  underway
• - Sensors for full body-suit ordered

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Sponsors

• U. S. Army Research Office (ARO)
• U. S. Navy Modeling and Simulation Management
  Office (N6M)
• Naval Postgraduate School

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References

• E. R. Bachmann, R. B. McGhee, X. Yun and M. J.
  Zyda, Inertial and Magnetic Posture Tracking
  for Inserting Humans into Networked Virtual
  Environments, ACM Symposium on Virtual Reality
  Software and Technology (VRST), November 2001,
  Banff Canada.
• J. L. Marins, X. Yun, E. R. Bachmann, R. B.
  McGhee, and M. J. Zyda, An Extended Kalman
  Filter for Quaternion-Based Orientation
  Estimation Using MARG Sensors, IEEE/RSJ
  International Conference on Intelligent Robots
  and Systems, October 2001, Maui, Hawaii.
• E. R. Bachmann, R. B. McGhee, X. Yun and M. J.
  Zyda, Real-Time Tracking and Display of Human
  Limb Segment Motions Using Sourceless Sensors and
  a Quaternion-Based Filtering Algorithm - Part II
  Implementation and Calibration, submitted to
  Presence Teleoperators and Virtual Environments.
  
• R. B. McGhee, E. R. Bachmann, X. Yun and M. J.
  Zyda, Real-Time Tracking and Display of Human
  Limb Segment Motions Using Sourceless Sensors and
  a Quaternion-Based Filtering Algorithm - Part I
  Threory, submitted to Presence Teleoperators
  and Virtual Environments.
• E. R. Bachmann, I. Duman, U. Usta, R. B. McGhee,
  X. Yun, and M. J. Zyda, "Orientation tracking for
  Humans and Robots Using Inertial Sensors,"
  International Symposium on Computational
  Intelligence in Robotics Automation (CIRA 99),
  Monterey, CA, November 1999, pp.187-194.

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Background - Quaternions

• Quaternions are an extension of complex numbers
• Define a four dimensional volume using three
  imaginary parts and one real
• Four dimensional vector with an associated
  quaternion product
• Represent an orientation using an arbitrary axis
  and a rotation about that axis
• The rotation of a vector, p, by a quaternion, q,
  is defined as
• Quaternions can be used to describe any
  orientation without singularities
• Trigonometric functions are not required

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Background - MARG Sensor

• 10.1 x 5.5 x 2.5 cm
• Output range 0 - 5 vdc
• Power 12 vdc, 50 ma
• Crossbow Accelerometers
• Tokin Rate Sensors
• Honeywell Magnetometers
• Incorporates set/reset circuit for magnetometers
• Manually adjustable magnetometer null points

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Background - Derivation of the X matrix

• From the product rule of differential calculus
• thus
• The general form for each column is

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EXPERIMENTAL RESULTS- Weighted Least Squares
Test the stability of the orientation estimate
under exposure to strong magnetic fields using
various magnetometer weighting factors
Estimated Orientation During Exposure To
Magnetic Source p 1.0, k 4.0
Estimated Orientation During Exposure To
Magnetic Source p 0.25, k 4.0
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Background- Dynamic Response and Accuracy

• Sensors cycled through various rotation angles
• Sensor moved and positioned using a precision
  rotary tilt table

Roll Angle vs. Time45 Degree Roll Excursions at
10 deg/sec.
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Background - Static Stability

• Stability of orientation measurement monitored
  for extended periods

One Hour Static Test Nine-axes Enabledk 1.0
One Hour Static Test No Rate Sensorsk 1.0
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Background - Static Convergence

• Test convergence of the filter following the
  introduction of transient orientation errors

Criterion Error vs. TimeFollowing30 Degree
Transient Errork 1.0
Criterion Error vs. TimeFollowing30 Degree
Transient Errork 4.0