Tracking Solutions for Mobile Robots: Evaluating Positional Tracking

using Dual-axis Rotating Laser Sweeps

Sebastian P. Kleinschmidt, Christian S. Wieghardt and Bernardo Wagner

Real Time Systems Group, Institute of Systems Engineering, Leibniz Universit

at Hannover,

Appelstraße 9A, 30167 Hannover, Germany

Keywords:

Tracking Technologies, Marker Tracking, Dual-axis Rotating Laser Sweeps.

Abstract:

This paper provides a comprehensive introduction into state of the art marker-based tracking methods. There-

fore, optical, magnetic, acoustic and inertial tracking are described and evaluated. All presented approaches

are compared regarding accuracy, resolution, tracking volume, measurement rate and outdoor and indoor suit-

ability. Additionally, typical technical limitations are mentioned for each system according to their functional

principle.

As a technology with increasing potential for mobile robotics, we evaluate the achievable accuracy for pose

tracking using dual-axis rotating laser sweeps as used in modern tracking systems for virtual reality applica-

tions.

1 INTRODUCTION

In many applications, the pose of an object, a robot or

an instrument needs to be determined as accurate as

possible. Examples of such applications are medical

engineering, augmented reality and mobile robotics.

A detailed overview of tracking systems in medical

applications is presented in (Birkfellner et al., 2008).

In general, there are two basic solutions for determin-

ing and tracking the pose of an object: Marker- and

non marker-based systems. Due to higher accuracy,

marker-based tracking systems have been established

as the standard solution for pose measurements which

can be used as ground truth for many research areas

to evaluate the performance of developed algorithms.

This paper gives a general overview of tracking sys-

tems, which can be used in robotic applications.

This paper is organized as follows: The ﬁrst sec-

tion introduces evaluation criteria which can be used

to compare state of the art marker-based tracking sys-

tems. Then, the functional principles of different sys-

tems as optical, magnetic, acoustic and inertial sys-

tems are described. Subsequently, a comparison of

the approaches is presented. The results are given in

a comprehensive table. The paper ends with an eval-

uation of a tracking system based on dual-axis rotat-

ing laser sweeps. Experiments are performed using

a trackable handheld device as well as a Pioneer 2

robot.

2 EVALUATION CRITERIA

All tracking systems considered in this paper will be

evaluated based on the criteria presented in this sec-

tion. If possible, we will quantify the results by speci-

ﬁcations of commercial tracking systems or scientiﬁc

publications.

Accuracy: According to ISO 5725, accuracy consists

of trueness and precision. Trueness describes how

close the mean of a set of measurements results to

the true value, whereas precision describes the degree

of scattering of the set of measurements. In tracking

applications, trueness and precision may vary if the

observed object is static or moving. Based on this

fact, to evaluate tracking systems, it is necessary to

differentiate between static accuracy and dynamic ac-

curacy:

Static Accuracy: Static accuracy describes the accu-

racy which can be achieved for a non-moving object.

Dynamic Accuracy: Analogue to the static accuracy,

the dynamic accuracy is used for moving objects.

Resolution: The resolution of a tracking system is the

smallest yet to distinguish difference in position and

orientation which can be measured by the system.

Tracking Volume: The space in which a tracking

system tracks objects, is called tracking volume. This

tracking volume is described by geometric primitives,

for which tracking is provided within deﬁned accu-

racy boundaries. The achievable accuracy may vary

within this volume.

Kleinschmidt, S., Wieghardt, C. and Wagner, B.

Tracking Solutions for Mobile Robots: Evaluating Positional Tracking using Dual-axis Rotating Laser Sweeps.

DOI: 10.5220/0006473201550164

In Proceedings of the 14th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2017) - Volume 1, pages 155-164

ISBN: 978-989-758-263-9

155

Measurement Rate: The measurement rate deﬁnes

how many pose updates can be generated in a deﬁned

time period.

Indoor and Outdoor Suitability: Based on the func-

tion principle of the used tracking system, the system

can be affected by external factors such as direct sun-

light. Therefore, not all systems are equally suited for

outdoor applications and need a controlled environ-

ment.

3 OPTICAL SYSTEMS

Traditional optical tracking systems consist of one or

more cameras which are placed rigidly in the envi-

ronment. The tracking volume is deﬁned by the re-

sulting overlapping ﬁeld of view (fov) of the cameras.

To track the position of a marker, the marker has to

be visible in at least two cameras with a direct line-

of-sight. Except are tracking approaches using pre-

deﬁned pattern such as ﬁducial marker which can be

tracked by a single camera (see Section 3.1).

The accuracy of an optical system is mainly deter-

mined by the resolution of the used cameras, the fov

given by the used lenses, the distance to the measured

markers and the distance between the cameras in case

of using multiple cameras.

The measurement rate is limited by the framerate

of the cameras and can be further limited by the pro-

cessing time which is needed to identify the maker or

pattern structure. In case of using multiple cameras,

the cameras need to be time synchronized. To sim-

plify the identiﬁcation of the marker position in the

camera images, typical markers are coated with a re-

ﬂective material which is illuminated by light sources

arranged around the camera lenses (LEDs in most ap-

plications). To further facilitate the marker identiﬁ-

cation and prevent the inﬂuence of ambient light, the

light sources often emit light in the infrared spectrum

(e.g. 850 nm) which is ﬁltered by an optical band-pass

ﬁlter in front of the camera lenses.

Besides passive concepts, there are also ac-

tive markers which are mostly battery powered and

equipped with a light source (e.g. LEDs) inside the

marker enclosure. There are also optical tracking sys-

tems which work without cameras such as laser track-

ing systems. In this kind of systems, the cameras are

replaced by rotating planes of coherent lasers light

which are detected using an array of photosensors.

Laser based systems are described at the end of this

section.

(a) Concentric Cir-

cles

(b) Intersense (c) ARToolkit

(d) ARTag. (e) RUNE-43. (f) RUNE-129.

Figure 1: Examples of common ﬁducial markers (Bergam-

asco et al., 2011).

3.1 Single View Systems

The most basic setup for an optical tracking system is

a single camera setup. Because tracking is not pos-

sible using triangulation with a spherical marker be-

ing visible in only one camera, it is necessary to use

marker with predeﬁned pattern as ﬁducial marker.

Besides typical spherical markers, it is common

for simple applications to use ﬁducial markers as

augmented reality tags or other predeﬁned patterns.

These markers are placed in the camera’s fov as a

point of reference. The resulting transformation be-

tween the pose of the marker and the camera can then

be computed using conventional algorithms that solve

the perspective-n-point problem. Typical applications

for the usage of ﬁducial marker are augmented real-

ity applications in mobile applications where virtual

models are rendered into the camera image based on

the computed transformation between the camera and

the AR-Tag. Examples of ﬁducial markers are shown

in Figure 1.

The accuracy of tracking a Metaio marker using

a single camera has been evaluated in (Pentenrieder

et al., 2006) using a simulated ground truth. The

accuracy of Metaio marker detected by a simulated

640 ×480 (15 fps) camera has been evaluated from

different distances and from different rotation angles.

The accuracy of optical tracking with an AR-

ToolKit ﬁducial marker has been evaluated in (Abawi

et al., 2004) using a camera with a resolution of

640 ×480 (15 fps). The systematic error was given

by 2 cm in a distance of 20 cm and increases at higher

distances.

The tracking volume for ﬁducial maker tracking is

limited by the fov and the resolution of the used cam-

era. The setup for a single camera tracking is sim-

ICINCO 2017 - 14th International Conference on Informatics in Control, Automation and Robotics

156

P(x,y,z)

(x,y)

Figure 2: The basic setup of a stereo tracking system. The

resulting tracking volume is marked dark gray.

ple because no time synchronization between differ-

ent cameras needs to be performed and there is only

an intrinsic calibration of one camera necessary. It

is possible to determine the 6-dof transformation of a

marker inside the camera’s fov.

3.2 Stereo View Systems

Stereo-based tracking systems consist of two cameras

which are placed in a rigid geometric relation to each

other, and therefore have to be extrinsically and in-

trinsically calibrated. Figure 2 shows the basic setup

of a stereo tracking system.

To triangulate the distance of a marker, both cam-

eras need to be time synchronized. The depth of a

marker Z given its disparity d can then be computed

as follows (Szeliski, 2010):

Z = f

. (1)

The theoretical depth resolution of a stereo camera

system has been evaluated in (Mikko Kyt, 2011) and

can be computed for the overlapping fov of both cam-

eras:

dZ =

f b

d p

. (2)

The theoretical depth resolution of a stereo system dZ

depends on the focal length f , the baseline between

both cameras b and the disparity accuracy d p

. For a

constant image resolution, d p

increases with a grow-

ing fov wherefore the depth resolution impair.

While a small baseline b minimizes the regions

of the image, where partial occlusions can occur, the

depth uncertainty grows, because of a small triangu-

lation angle. In contrast, a large baseline b increases

the chance of an object only to be visible in one image

but also increases the depth accuracy. Commercial

stereo systems reach an accuracy of about 0.35 mm

in a tracking volume up to approx. 1.6 m

(Andrew

D. Wiles and Frantz, 2004).

Because the tracking volume is limited to the over-

lapping area of both cameras, the resulting tracking

volume is smaller than the tracking volume which

could be achieved with a single view system.

3.3 Multi-view Systems

In multi-view systems (also known as multi-view

stereo), the marker must be visible in at least two cam-

eras at the same time to perform triangulation. While

depth estimation is already possible with two cam-

eras, matching more images can be used to increase

the tracking volume and make the system more ro-

bust against occlusions. One major factor for gaining

high accuracy is to track objects with two cameras at

perpendicular line of sights and small distances to the

objects. Therefore, stereo view systems have a limited

tracking volume with high accuracy. Whereas multi-

view systems can easily deploy additional cameras in

the tracking volume to increase such conditions, not

for a signiﬁcant higher accuracy, but for a larger high

accurate tracking volume.

3.4 Laser Systems

Laser tracking systems are optical systems which

work without the usage of cameras (in contrast to the

optical approaches presented before). Instead of us-

ing passive or active markers which are detected in a

camera image, the markers are replaced with an array

of photosensors in a known geometric arrangement

which are illuminated by two or more rotating planes

of coherent lasers light. Therefore, the concept is also

named dual-axis rotating laser sweeps, because every

emitter is rotating two different laser planes. The po-

sition of the sensor array relative to the emitter is com-

puted by sampling the position of the laser plane and

the signal from the photosensors (Birkfellner et al.,

2008).

While the outdoor suitability of laser-based track-

ing systems is determined by the wavelength and the

power of the emitting light source, the possible track-

ing volume is mainly determined by the emitting an-

gles of the laser planes which are rotated. Besides,

the maximal distance between tracked device and the

emitting base station is limited by the power of the

emitting light source. The static resolution, which is

achieved by a commercial laser tracking system, is

given with 0.1 mm at a distance of 1 m (laserBird 2

by Ascension Technology Corporation working at a

measurement rate of 250 Hz (Ascension Technology

Corporation, 2000).

While laser tracking systems are not often used in

medical applications (Birkfellner et al., 2008), they

are interesting for head tracking in virtual reality ap-

plications based on the possible high frame rate and

Tracking Solutions for Mobile Robots: Evaluating Positional Tracking using Dual-axis Rotating Laser Sweeps

157

3-Axis

Magnetic

Source

Field Coupling

Position and Orientation

Measurements

Driving

Circuits

Computer

Amplifying

Circuits

3-Axis

Magnetic

Sensor

Figure 3: Magnetic coupling (based on ﬁgure presented in

(Raab et al., 1979)).

low latency (which is necessary to avoid simulator

sickness). Laser-based systems have become a highly

available consumer product due to the usage in the

HTC Vive virtual reality headset. Whereas the HTC

Vive includes two controllers in addition to the head-

set, the system can be extended by stand alone track-

able devices called HTC Trackers, which provide 6-

dof tracking information. When this paper was writ-

ten, the HTC Tracker were not yet available for pur-

chase.

4 MAGNETIC SYSTEMS

Magnetic tracking systems consist of multiple

magnetic emitters and one or more sensors whose

position and orientation are tracked. In most systems,

the source has three orthogonal coils which generate

individual perpendicular magnetic ﬁelds and induce

currents in the three orthogonal coils of the sensor

(Raab et al., 1979). The amplitudes of the nine

measured currents result in the position of the sensor,

a comparison delivers the orientation. Small changes

of the source position and orientation are determined

and the previous measurements are updated. There

are also alternative methods that use just two coils

(Paperno et al., 2001) or a magnet (Hu et al., 2007) as

a source. The basic structure of a magnetic tracking

system is presented in Figure 3.

There are altering current (AC) and direct current

(DC) based magnetic tracking systems. In AC sys-

tems, a signal sequence on a high carrier frequency

wave is transmitted. The signal induces eddy cur-

rents in conductive materials nearby and therefore

also small local electromagnetic ﬁelds which inter-

fere with the measurements. DC-based magnetic sys-

tems generate pulsed constant magnetic ﬁelds. That

prevents disturbances by conductive materials since

eddy currents vanish fast enough. Whereas, constant

magnetic ﬁelds such as the Earth’s ﬁelds or caused by

ferromagnetic materials can vary the measurements.

Hence, the trueness of the magnetic tracking strongly

depends on its environment.

Since the induced ﬁeld penetrates all sorts of ma-

terials, the tracking does not depend on a direct line-

of-sight and are therefore not affected by occlusions.

The method is also independent of lightning condi-

tion, thus is not restricted to indoor utilization.

Commercial magnetic tracking systems achieve

a static precision of 0.76 mm RMS and 0.15

◦

resp.

RMS at a distance of 762 mm (FASTRACK by Pol-

hemus Inc. (Polhemus, 2017a)). The system has a

measurement rate of 120 Hz and a latency of 4 ms.

The resolution is given by 0.0058 mm and 0.0026

◦

at a distance of 304.8 mm and rapidly decreases with

the displacement between source and sensor. At a dis-

tance of 3048 mm only a resolution of 40.64 mm and

2.96

◦

resp. can be achieved. The range is limited

to 10 feet but can be extended to 30 feet. There are

also wireless magnetic tracking systems available e.g.

(PATRIOT WIRELESS by Polhemus Inc. (Polhemus,

2017b)). They support a higher range, but suffer a

loss in accuracy.

5 ACOUSTIC SYSTEMS

Acoustic tracking systems use the duration of ultra-

sonic waves to determine the position of the marker.

For this purpose, the object is equipped with an ul-

trasonic transmitter as a marker while receivers are

placed statically on deﬁned locations in the environ-

ment. The position of a transmitter can then be deter-

mined by triangulating the time of ﬂight of the ultra-

sonic waves.

Based on the limited propagation speed of ultra-

sonic waves in air (c≈ 343

at 20

◦

C) the maximal

update rate f is limited according to Equation 3. Be-

cause the propagation speed depends on the environ-

mental conditions like temperature and pressure, the

measurement of the time of ﬂight needs to be fused

with other sensors measuring these inﬂuencing fac-

tors to determine the correct distance. Furthermore,

the time of ﬂight can be affected by obstacles between

the transmitter and the receiver.

f =

(3)

The propagation speed c for different gases can be

computed according to Equation 4.

c =

κ ·p

√

κ ·R ·T , (4)

with the adiabatic exponent κ, the pressure of the gas

p, and the density of the gas ρ and R being the general

gas constant.

ICINCO 2017 - 14th International Conference on Informatics in Control, Automation and Robotics

158

The work presented in (Priyantha et al., 2000) de-

scribes a system called Cricked whose setup is in-

verse to the description above: The emitter are placed

static in an indoor environment and the receivers are

kept mobile on a robot for position tracking. The sys-

tem achieves a location granularity of 4x4 square feet

(Priyantha et al., 2000).

(Ward et al., 1997) presents a system called Active

Bats which operates in a volume of 1100 m

using 256

ultrasonic receivers. The trueness of Active Bats is

given with 9 cm for 95 % of the measurements with an

update rate of 25 Hz (Hightower and Borriello, 2001)

(Ward et al., 1997).

Compared to other tracking solutions, the price of

an ultrasonic based tracking system is low (the price

of each device used for the Cricked system costs less

than 10 USD (Priyantha et al., 2000)). The propa-

gation speed limits the update rate of systems based

on ultrasonic time of ﬂight measurements. Ultrasonic

based systems are inaccurate compared to other track-

ing systems, can be disturbed by reﬂecting ultrasonic

signals and are therefore not often used in state of the

art applications.

6 INERTIAL SYSTEMS

Inertial navigation systems (INSs) use inertial mea-

surement units (IMUs) as markers with no external

tracking system to track the position of an object start-

ing from a known initial position and orientation with

a known initial velocity. These initial information are

then combined with the output of the IMU to compute

the position, velocity and attitude of the object (No-

vAtel, 2014). An IMU typically consists of a three-

axis gyroscope and a three-axis accelerometer. Fur-

thermore, there are also hybrid IMUs (magnetic, an-

gular rate and gravity - MARG) available which in-

clude an additional three-axis magnetometer. INSs

are divided into two different categories (Noriega-

Manez, 2007) (Woodman, 2007):

• Stable Platform Systems (also known as Gimbal-

Mounted or Mechanized Systems)

• Strap-Down Systems

Stable Platform Systems are mounted on a platform

using gimbals to isolate the IMU from any external

rotational motion (Woodman, 2007). The gyroscopes

of the IMU are then used to measure occurring rota-

tions to keep the platform’s rotation static regarding

a global frame of reference using servo motors. The

orientation of the system can then be determined

by reading the servo encoders. The position of

the system is computed by double integrating the

Orientation

Servo

Feedback

Initial Position

Initial Velocity

Global

Accel

Velocity

∫

Accelerometer

signals

Correct for

gravity

Position

Figure 4: Stable platform inertial navigation algorithm

(based on ﬁgure presented in (Woodman, 2007)).

Orientation

Rate-gyroscope

signal

Accelerometer

signal

Position

Initial Position

Initial Velocity

Project

accelerations

onto global

axes

Correct for

gravity

Global

Accel

Velocity

∫

Initial

Orientation

Figure 5: Strapdown inertial navigation algorithm (based on

ﬁgure presented in (Woodman, 2007)).

acceleration which has to be corrected regarding

gravity before integration. The basic structure of a

stable platform inertial navigation algorithm is shown

in Figure 4.

Strap-Down Systems are mounted directly onto the

object with no additional mechanic structures and are

therefore smaller than stable platform systems. In

contrast to stable platform systems, strap-down sys-

tems can be rotated regarding the global frame and the

accelerometer needs to be transformed into the global

frame to correct the gravity. The position of the sys-

tem can then be computed by double integrating the

accelerometer signal (see Figure 5).

Signals from an IMU can typically be processed at

a high measurement rate (e.g. 200 Hz) (NovAtel,

2014). Because the signals are measured directly

at the object, there is no line-of-sight between the

marker and an external device necessary.

If the bias error of the accelerometer is not

removed, the error will be integrated twice as part

of the mechanization process which will lead to a

quadratic error in position computation (NovAtel,

2014). The same applies for the double integration of

measurement noise and an error-prone compensation

of gravity. Because the integration of the accelerom-

eter signals is error-prone, the resulting position

is strongly affected by drift. The average error in

position for a Xsens Mtx IMU was given with 150 m

after 60 s of operation (Woodman, 2007). For drift

reduction, the IMU signal often gets merged with

additional sensor signals as an absolute positioning

system (e.g. GPS for outdoor applications or optical

systems for indoor applications, see Section 3).

A full introduction to inertial navigation systems

(INSs) with a trial on error sources can be found in

(Woodman, 2007) (NovAtel, 2014).

Tracking Solutions for Mobile Robots: Evaluating Positional Tracking using Dual-axis Rotating Laser Sweeps

159

7 EVALUATION

Because a comprehensive evaluation of all presented

tracking systems would exceed the scope of this pa-

per, this section will focus on laser-based tracking

as presented in Section 3.4. More precisely, posi-

tional tracking using dual-axis rotating laser sweeps

will be evaluated, which recently gains importance for

the robotic community due to virtual reality end con-

sumer products such as the HTC Lighthouse track-

ing system, which drastically reduces the necessary

investment costs. As a result, laser based systems

become a widely available alternative to expensive

multi-view camera systems. Consequently, the appli-

cability of tracking robots using an HTC Lighthouse

tracking system will be evaluated. The mathematical

foundation of tracking using dual-axis rotating laser

sweeps is presented in detail in (Islam et al., 2016).

An outline of the underlying mathematics will be pre-

sented in the following section.

7.1 Architecture

Each vertical and horizontal swipe ends with an in-

dividual synchronization pulse indicating the starting

position of the speciﬁc laser plane. The time between

the individual synchronization pulse and the moment

when the light hits a photodiode is measured and can

be used to determine the horizontal and vertical an-

gles ϕ

and θ

of the n-th photodiode according to

Equation 5 and 6:

h,sync

−t

h,n

total

·2π (5)

v,sync

−t

v,n

total

·2π, (6)

with t

h,n

and t

v,n

, the points in time when the asso-

ciated laser plane passes the photodiode, t

h,sync

and

v,sync

when the corresponding synchronization signals

trigger and t

total

, the total time one laser plane takes

for a complete revolution.

The pose of a rigid body with three rigid points

at deﬁned relative angles and distances as shown in

Figure 6 can be computed as follows: The points A,

B and C can be described in spherical coordinates by

the following vectors x

, x

and x



, ϕ

, θ



(7)



, ϕ

, θ



(8)



, ϕ

, θ



. (9)

Whereas ϕ

and θ

of every point can be computed

according to Equation 5, the distances r

needs to be

computed by solving a system of non-linear equations

ᵩ

Figure 6: Illustration of the sensor triangle

(cf. (Islam et al., 2016)).

which can be set by applying the law of cosines trian-

gle:

+ r

−2 ·r

·r

·cos(α

) −AB

= 0 (10)

+ r

−2 ·r

·r

·cos(α

) −BC

= 0 (11)

+ r

−2 ·r

·r

·cos(α

) −AC

= 0. (12)

The distances AB, BC and AC of the rigid body are

constant and are assumed to be known. To com-

plete the set of Equations, cos(α

), cos(α

) and

cos(α

) need to be computed using the dot product

according to Equation 13:

·r

·cos(α

) = x

+ y

+ z

. (13)

With respect to the vectors given in Equation 7,

the cartesian coordinates can be computed using the

spherical vectors as follows:

= r

·sin(θ

) ·cos(ϕ

) (14)

= r

·sin(θ

) ·sin(ϕ

) (15)

= r

·cos(θ

). (16)

After inserting Equation 14 to 16 in Equation 13,

cos(α

), cos(α

) and cos(α

) can be computed

according to:

cos(α

) = sin(θ

) ·cos(ϕ

) ·sin(θ

) ·cos(ϕ

) (17)

+ sin(θ

) ·sin(ϕ

) ·sin(θ

) ·sin(ϕ

)

+ cos(θ

) ·cos(θ

)

cos(α

) = sin(θ

) ·cos(ϕ

) ·sin(θ

) ·cos(ϕ

) (18)

+ sin(θ

) ·sin(ϕ

) ·sin(θ

) ·sin(ϕ

)

+ cos(θ

) ·cos(θ

)

cos(α

) = sin(θ

) ·cos(ϕ

) ·sin(θ

) ·cos(ϕ

) (19)

+ sin(θ

) ·sin(ϕ

) ·sin(θ

) ·sin(ϕ

)

+ cos(θ

) ·cos(θ

Finally, Equations 10 to 12 can be solved using New-

ton’s root ﬁnding method as presented in detail in (Is-

lam et al., 2016). In the following section, the HTC

ICINCO 2017 - 14th International Conference on Informatics in Control, Automation and Robotics

160

56°

Prime 13

Lighthouse

emitter

Lighthouse

emitter

(a) Resulting tracking area of the Optitrack Prime 13

setup.

110°

(b) Resulting tracking area of the HTC Lighthouse emit-

ter.

Figure 7: Camera setup for the multi-view and the dual-axis

rotating laser sweeps system.

Lighthouse system will be evaluated regarding track-

ing volume, accuracy, and applicability for mobile

robots.

7.2 Experimental Setup

To evaluate the possible accuracy of the HTC Light-

house system, an HTC Vive controller is equipped

with an optically trackable rigid body. The rigid body

is tracked by four Optitrack Prime 13 cameras. The

cameras have a horizontal fov of 56

◦

and a vertical

fov of 46

◦

. The laser planes of the HTC Vive light-

house emitter have a vertical and horizontal fov of

110 degrees. Figure 7 illustrates the camera placing

including the opening angle of the different tracking

solutions in a top-down view.

The setup for tracking the HTC Vive controller is

presented in Figure 8. A rigid body consisting of six

infrared marker is attached to the HTC Vive controller

to validate the tracked trajectory’s accuracy. In a sec-

ond experiment, the controller is ﬁxed on the Pioneer

2 robot to measure the robot’s movement.

(a) Rigid setup of an HTC

Vive controller and an opti-

cally trackable rigid body.

(b) Pioneer 2 Robot with at-

tached trackable device ac-

croding to Figure 8(a).

Figure 8: Tracked controller device and robot platform as

used for evaluation.

7.3 Calibration

The tracking information of the HTC Vive is extracted

using the Valve OpenVR library which merges the

pose estimation based on the rotating laser sweeps

with additional measurements of an inertial measure-

ment unit.

The homogenous transformations X between the

rigid body and the controller and Z between the in-

frared marker coordinate system and the dual-axis

laser sweep coordinate system (see Figure 9) can be

computed by solving the following equation:

X = ZB



0 1



0 1





0 1



0 1



(20)

The rotational and translational part in Equation 20

can be rearranged in the linear system:



⊗R

−I

9×3

3×9

⊗t

−R









vec(R

)

vec(R

)









9×1



(21)

Filling the position and orientation data from the

measurement systems into A

(HTC Vive Lighthouse)

and B

(Optitrack), Equation 21 can be solved in

the least-square sense. Notice, that the controller

has to undergo at least two independent general mo-

tions with nonparallel axes to retain a unique solu-

tion. Calibration was performed on 1000 measured

poses within a sphere diameter of 70.46 mm. The

overall mean pose error was 0.892 mm and 0.423

◦

With X and Z known, the following trajectories could

be transformed into the same coordinate system and

their position and rotation errors are calculated.

Tracking Solutions for Mobile Robots: Evaluating Positional Tracking using Dual-axis Rotating Laser Sweeps

161

Prime 13

Lighthouse

emitter

HTC

controller

marker

rigid

body

Figure 9: Geometric relation between the tracking Z and

the rigid body X coordinate systems. A

: Time varying

measurement data.

7.4 Indoor and Outdoor Suitability

As an end consumer product for entertainment appli-

cations, the HTC Lighthouse is developed for indoor

usage. Based on the expected interference due to di-

rect sunlight, the photosensor signals will be strongly

affected by noise. Additionally, a clear detection of

the passing laser sweeps will probably not be possi-

ble in the presence of sunlight. Therefore, the system

is not suited for outdoor applications.

7.5 Measurement Rate

The laser planes of the HTC Lighthouse rotate at

3600 r pm. Thus, a full rotation takes 16.66 ms. One

laser sweep is completed in a half rotation and there-

fore takes 8.333 ms. The possible measurement rate

for considering both sweeps of one emitter results in

60 Hz. Updating the pose every sweep, the update

rate increases to 120 Hz. Because the sensor fusion

algorithm implemented in the OpenVR library also

uses an additional IMU for pose estimation, the re-

sulting update rate is higher after sensor fusion.

7.6 Tracking Volumes

We determine the trackable volume by manually mov-

ing the tracked device within the measurement se-

tups along the trajectory shown in Figure 10. The

trajectory is grid-like to receive a good coverage of

the volume. Since the illustration in Figure 10 only

shows the received pose data from the measurement

systems, gaps are indicating uncovered areas. As ex-

pected by the theoretical tracking area presented in

Figure 7, the object could be tracked more robust and

inside a larger volume using the HTC lighthouse sys-

tem. Whereas the rigid body needs to be visible in

at least two camera images to be tracked, the posi-

tion of the controller can be computed only visible

for one Lighthouse emitter. In contrast, the optical

-1

-2

(a) Optitrack Prime 13.

-1

-2

(b) HTC Lighthouse.

Figure 10: Measured trajectories of the different setups.

-1

-2

(a) Optitrack Prime 13:

= 10.22 m

-1

-2

(b) HTC Lighthouse:

= 27.02 m

Figure 11: Convex tracking volume of the different setups.

system is more robust against occlusions supporting

multiple points of view.

Figure 11 illustrates the tracking volume of the

Optitrack Prime 13 cameras and the HTC Lighthouse

systems. To get a measurable value to compare both

systems, the convex volumes around the trajectories

were calculated. Thereby we assume that the space

within the trajectory-grid is measurable as well.

Comparing both volumes, we see that the HTC

Lighthouse system is covering almost three times as

much volume as the Optitrack system. That ratio is no

constant value for all possible setups but underlines

the effect for setups with limited space and cameras.

7.7 Accuracy

To determine the static and dynamic accuracy, the

tracked device has been rigidly mounted on a Pioneer

2 robot. The resulting setup is shown in Figure 8. It

must be taken into consideration that the quality of

the calibration of Section 7.3 affects the dynamic and

static trueness.

Static Accuracy: To determine the static accuracy,

the robot has been placed statically on different posi-

tions inside the tracking volume near the center. The

trueness and precision have then been computed, us-

ing the tracking information of the Optitrack Prime 13

setup as ground truth. The static accuracy is given in

Table 1.

Dynamic Accuracy: The dynamic accuracy has been

computed controlling the robot manually on the tra-

jectories shown in Figure 12. As for the static accu-

racy, the Optitrack Prime 13 measurements are uses

as ground truth.

Table 1 shows the precision and trueness of the

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(a) Circle trajectory.

(b) Square trajectory.

Figure 12: Experimental trajectories.

reconstructed trajectories tracked by the Optitrack

Prime 13 setup and the HTC Lighthouse.

Table 1: Static and dynamic accuracy

Position

trueness

[mm]

Position

precision

[mm]

Orientation

trueness[

◦

]

Orientation

precision[

◦

]

Static 1.699 0.361 0.353 0.008

Dynamic 1.615 0.433 0.291 0.046

Results: With a position trueness of 1.615 mm

(static) and 1.699 mm (dynamic), the results are simi-

lar to the results given in (Burdea and Coiffet, 2003),

which declare an RMS of 1.0 mm at a distance of

1.0 m for the similar Laserbild 2 system. Consider-

ing the larger average distance between the emitter

and the tracking device in our setup, the measured ac-

curacy also increases as expected. The dynamic and

static position trueness are of a comparable magni-

tude. This can be reasoned by the relatively low speed

of the robot compared to the measurement rate of the

system.

8 CONCLUSION

In the ﬁrst part of this paper, optical, acoustic, mag-

netic and inertial systems are compared regarding

their principle of function. A summarizing compar-

ison is given in Table 2.

The usage of the different tracking technologies

strongly depends on the application which the sys-

tem is needed for. Besides their line-of-sight limita-

tion, optical tracking systems are proofed to be robust

and to have a high accuracy. That is why stereo and

multi-camera systems are typically used for commer-

cial motion capture systems and are the standard in

clinical applications (Birkfellner et al., 2008). Based

on the widespread of mono cameras in handheld de-

vices as smartphones, ﬁducial markers are currently

state of the art for AR-applications. To improve the

accuracy of these systems further, the results of ﬁdu-

cial marker tracking are often combined using sensor

fusion techniques with IMU data which are also state

of the art in smartphone applications.

Magnetic tracking systems use AC or DC ﬁeld

coupling between source and sensor to determine the

transformation between them. Therefore, no line-of-

sight is required. As a restriction, magnetic systems

are susceptible to conductive and ferromagnetic mate-

rials. The resulting magnetic ﬁeld distortions worsen

the trueness. A high resolution and precision can be

obtained, but decreases rapidly with the distance.

Acoustic systems based on the duration of ultra-

sonic waves are too inaccurate to be used for accurate

motion tracking. They are used in applications which

do not require a high accuracy as in basic indoor nav-

igation.

Inertial Systems are infrequently used as stand

alone tracking solutions based on the occurring drift.

Due to their low price microelectromechanical IMUs

are often used as additional sensors.

Laser-based optical systems using rotating laser

planes systems do have advantages, especially for vir-

tual reality applications because of the high measure-

ment rate and the low latency time (which is necessary

to avoid motion sickness) and the possibility to realize

position and orientation tracking on the same printed

circuit board. Therefore, no additional time synchro-

nization effort is necessary compared to combined de-

vices for orientation and position tracking, such as ex-

ternal multi-view systems. In contrast to other optical

systems, the usage of laser tracking based systems is

less ﬂexible, based on the higher marker complexity.

Also, post processing is necessary to compute the po-

sition and the orientation based on the photodiode sig-

nals.

In the second part of this paper, it has been shown

experimentally, that pose tracking using dual-axis ro-

tating laser sweeps is a tracking solution which can

cover a large tracking volume only using a small

number of emitters. The experimentally evaluated

static and dynamic accuracy is lower than the accu-

racy which can be achieved by commercial multi-

camera setups. Nevertheless, the possible accuracy

of the HTC Lighthouse system can be considered to

be sufﬁcient for many robotic applications.

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