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Pose tracking of magnetic objects

Niklas Wahlstrom

Department of Information Technology, Uppsala University, Sweden

February 2, 2018

niklas.wahlstrom@it.uu.se VASCO workshop

Magnetometer measurement models

1. Common use: Magnetometer provides orientationinformation.

Assume that the magnetometer (almost) only measures thelocal (earth) magnetic field.

2. My use: Magnetometer(s) to provide position andorientation information.

I Magnetic mapping: Build a map of the (indoor) magneticfield.

I Magnetic tracking: Measure the position and orientation of aknown magnetic source.

1 / 17 niklas.wahlstrom@it.uu.se VASCO workshop

Magnetometer measurement models

1. Common use: Magnetometer provides orientationinformation.

Assume that the magnetometer (almost) only measures thelocal (earth) magnetic field.

2. My use: Magnetometer(s) to provide position andorientation information.

I Magnetic mapping: Build a map of the (indoor) magneticfield.

I Magnetic tracking: Measure the position and orientation of aknown magnetic source.

1 / 17 niklas.wahlstrom@it.uu.se VASCO workshop

Magnetometer measurement models

1. Common use: Magnetometer provides orientationinformation.

Assume that the magnetometer (almost) only measures thelocal (earth) magnetic field.

2. My use: Magnetometer(s) to provide position andorientation information.

I Magnetic mapping: Build a map of the (indoor) magneticfield.

I Magnetic tracking: Measure the position and orientation of aknown magnetic source.

1 / 17 niklas.wahlstrom@it.uu.se VASCO workshop

Magnetic mapping

Build a map of the indoor magnetic field. This map can be usedfor localization.

We have used Bayesian models (Gaussian processes) to model suchfields with good results

2 / 17 niklas.wahlstrom@it.uu.se VASCO workshop

Magnetometer measurement models

1. Common use: Magnetometer provides orientationinformation.

Assume that the magnetometer (almost) only measures thelocal (earth) magnetic field.

2. My use: Magnetometer(s) to provide position andorientation information.

I Magnetic mapping: Build a map of the (indoor) magneticfield.

I Magnetic tracking: Measure the position and orientation of aknown magnetic source.

3 / 17 niklas.wahlstrom@it.uu.se VASCO workshop

Sensor setup

We use a sensor network with four three-axis magnetometers todetermine the position and orientation of a magnet.

4 / 17 niklas.wahlstrom@it.uu.se VASCO workshop

Magnetic tracking

Advantages

I Cheap sensors

I Small sensors

I Low energy consumption

I No weather dependency

I Passive unit, requires nobatteries

5 / 17 niklas.wahlstrom@it.uu.se VASCO workshop

Magnetic tracking

Advantages

I Cheap sensors

I Small sensors

I Low energy consumption

I No weather dependency

I Passive unit, requires nobatteries

5 / 17 niklas.wahlstrom@it.uu.se VASCO workshop

Magnetic tracking

Advantages

I Cheap sensors

I Small sensors

I Low energy consumption

I No weather dependency

I Passive unit, requires nobatteries

5 / 17 niklas.wahlstrom@it.uu.se VASCO workshop

Magnetic tracking

Advantages

I Cheap sensors

I Small sensors

I Low energy consumption

I No weather dependency

I Passive unit, requires nobatteries

5 / 17 niklas.wahlstrom@it.uu.se VASCO workshop

Magnetic tracking

Advantages

I Cheap sensors

I Small sensors

I Low energy consumption

I No weather dependency

I Passive unit, requires nobatteries

5 / 17 niklas.wahlstrom@it.uu.se VASCO workshop

Mathematical model - dipole field

The magnetic field can be described with a dipole field.

J(r′)

mr

B(r)

B(r) =µ0

4π‖r‖5(3r · rT − ‖r‖2I3

)︸ ︷︷ ︸

=C(r)

m

m ,1

2

∫r′ × J(r′)d3r′

6 / 17 niklas.wahlstrom@it.uu.se VASCO workshop

Sensor model - single dipole

The measurements can be described with a state-space model

xk+1 = Fkxk +Gkwk, wk ∼ N (0, Q),

yk,j = hj(xk) + ek, ek ∼ N (0, R)

Point target sensor model (one dipole)

hj(xk) = C(rk − θj)mk, xk = [rTk vTk mT

k ωTk ]

T

C(r) =µ0

4π‖r‖5 (3rrT − ‖r‖2I3),

Measurement from a sensor network ofmagnetometers positioned at {θj}Jj=1.

Degrees of freedom

I 3D position

I 2D orientation

7 / 17 niklas.wahlstrom@it.uu.se VASCO workshop

Experiment 1

0.2

0.1-0.1

-0.2

-0.05

y-coordinate [m]

0

Trajectory

0

-0.1

0.05

x-coordinate [m]

0.1

z-co

ordi

nate

[m]

0 -0.1

0.15

0.2

0.1

0.25

-0.20.2

0.3

Trajectory

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2y-coordinate [m]

-0.1

-0.05

0

0.05

z-co

ordi

nate

[m]

0.1

0.15

0.2

0.25

0.3

Theaccuracy is

8 / 17 niklas.wahlstrom@it.uu.se VASCO workshop

Experiment 2 - setup

9 / 17 niklas.wahlstrom@it.uu.se VASCO workshop

Experiment 2 - results - position

20 25 30 35 40 45 50

−0.2

−0.1

0

0.1

0.2

0.3

Time [s]

Posi

tion

[m]

Black: Ground truth position. Color: Estimated position

10 / 17 niklas.wahlstrom@it.uu.se VASCO workshop

Experiment - results - orientation

20 25 30 35 40 45 50−200

−100

0

100

Time [s]

Ori

enta

tion

[deg

ree]

Black: Ground truth orientation. Color: Estimated orientation

11 / 17 niklas.wahlstrom@it.uu.se VASCO workshop

Application 1: 3D painting book

12 / 17 niklas.wahlstrom@it.uu.se VASCO workshop

Application 2: Digital water colors

13 / 17 niklas.wahlstrom@it.uu.se VASCO workshop

Application 3: Digital table hockey

14 / 17 niklas.wahlstrom@it.uu.se VASCO workshop

Application 4: Digital pathology

15 / 17 niklas.wahlstrom@it.uu.se VASCO workshop

Stylaero AB

I In February 2017 acompany was startedaround this technology

I In total seven people areinvolved in the companyon part-time.

I Collaborations with bothgaming companies andindustrial partners.

16 / 17 niklas.wahlstrom@it.uu.se VASCO workshop

Thank you!

17 / 17 niklas.wahlstrom@it.uu.se VASCO workshop