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A Landmark-Bounded Method for
Large-Scale Underground Mine Mapping
N. James Lavigne∗
LTI Systems
Toronto, ON M5R 2Y9 Canada
njlavigne@ltisys.com
Joshua A. Marshall
Mining Systems Laboratory
The Robert M. Buchan Department of Mining
Queen’s University
Kingston, ON K7L 3N6 Canada
joshua.marshall@mine.queensu.ca
Abstract
A practical localization technology for underground drift networks—like those
excavated in the practice of underground mining—has yet to become commer-
cially available. This paper focuses on the problem of mapping GPS-deprived
underground environments with the eventual goal of using these maps for nav-
igation. Recent industry-directed work in the creation of a landmark-bounded
occupancy grid mapping tool that combines odometry, scanning laser data,
and sporadically placed passive RFID tags is described. Unlike other works,
the suggested approach takes the philosophy that precise localization of the
actual landmark locations is not necessary, rather that landmarks serve as a
global means for partitioning the map. Successful field experiments were con-
ducted in two underground environments, with the results of those used to
conduct a basic analysis of the described method.
∗Corresponding author. This work was performed while N. J. Lavigne was with the Department of
Mechanical and Aerospace Engineering, Carleton University, Ottawa, ON K1S 5B6 Canada.
1 Introduction
To find and extract new mineral wealth, today’s mining industry is being forced to operate
in increasingly severe conditions. The ability to deploy robotically enhanced machines into
deeper, hotter, and more dangerous mines will, in the future, be essential. One fundamental
challenge in mining has long been that of global localization for mining vehicles. In recent
years, the advent of satellite-based global positioning systems (GPS) has largely solved this
problem for surface mines, and has revolutionized the industry by enabling improved safety
and productivity in many areas. Unfortunately, in underground mines, where satellite com-
munications are unavailable, no comparable system exists to take the place of GPS. Modern
automated underground vehicle systems do require localization abilities, but to date this has
necessitated only local navigation; e.g., along a single route (?).
Because of this, one current approach is to place many uniquely-identifiable radio frequency
identification (RFID) tags or, more recently, wireless IEEE 802.1X devices throughout the
mine for vehicle tracking. This method requires that wireless devices (e.g., tags, tag readers,
or transmitters) be strategically placed at known locations throughout the mine. Mobile
equipment can then only be roughly monitored by registering sensed wireless devices with
a central database of known device locations by way of an underground communications
network. However, these technologies lack many of the important properties of the satellite-
based GPS available on surface. Obviously, this approach requires not only the expensive
installation, but also manual localization of fixed infrastructure. Most notably, only occa-
sional position information can be provided—only whenever the vehicle happens to be near
a wireless device. This information is inevitably of poor accuracy and does not inherently
include information about the vehicle’s direction of travel.
Outside of mining, some have tried to explore the use of radio or Wi-Fi signal strength, as
received from multiple wireless access points, to estimate a vehicle’s position; e.g., see (?;?)
and references therein. However, despite the emergence of a few industry products, even the
most recent research suggests that this can be a very difficult problem to solve to any useful
accuracy in non “free-space” environments. Three or more overlapping yet independent
access point signals are usually required for triangulation, which is not very practical for
underground mines. However, the main problem is that of “severe multipath and shadowing
conditions, non-line-of-sight (NLOS) propagation, and interference from other devices” (?,
p. 689). Relatively recent underground experiments concluded the same; specifically, that
the accuracy obtainable from Wi-Fi-based localization in an underground mine is likely at
its absolute best 5–15 m and, as such, “could [only] serve as a low-level proximity indicator
or secondary measure for equipment position estimation” (?, p. 229). However, all of this is
not to say that advances in this approach will not be made in the future.
1.1 Map-Based Approach
One proposed method for solving the highlighted underground navigation problem takes a
two-step approach (?): 1) create a sufficiently accurate, expandable, and consistent met-
ric map of the underground mine environment; and, 2) use relative measurements from a
specially-equipped vehicle’s onboard sensors in order to localize itself within the map.
In this paper, we focus only on the 2D mapping problem. Our motivation is to bring ideas
from the mobile robotics literature into mainstream application in mining with the eventual
goal of using these maps for underground navigation. Others have also explored related
problems, with different objectives. For example, (?) pursued 3D mapping of abandoned
underground mines by using multiple laser rangefinders. With mapping in mind, (?) studied
scan registration with application to underground mine environments. Unfortunately, apart
from a few relevant examples (?;?), much of the academic literature focuses on small-scale
indoor environments; e.g., see (?).
Underground mines usually consist of horizontal levels that are connected by vertical shafts
and/or spiral ramps. Figure ?? shows one level at the CANMET Experimental Mine in
Val-d’Or, Qu´ebec, where we conducted experiments. One of the challenges is that large
mines usually comprise thousands of metres of tunnels or drifts. Here, the practicality of
laboratory-scale methods is in question. Several issues arise, two of which are studied in
this paper by way of experiments. These are the consistency and computational problems in
large-scale mapping. In this paper, by consistency we mean that there is a 1:1 relationship
between map points and real-world points and that, when viewed locally, the map represents
a good1metric approximation of the real-world area.
To this end, the method described in this paper employs a minimal infrastructure of installed
landmarks. We have used EPC Class 1, Generation 2 RFID tags (?), but this is interchange-
able with other technologies that provide unique signatures. Of particular interest is that
we do this without explicit knowledge of the number or location of landmarks, but with only
the practical assumptions that they each possess a unique identifying feature (with RFID
these are tag serial numbers) and are stationary once installed.
We contend that by treating RFID tags not as real objects but as virtual sources of sparse
global information—and thus not becoming preoccupied with their exact physical location,
unlike in much of the published literature—it is possible to do simultaneous localization and
mapping (SLAM) in environments containing landmarks without any prior knowledge of the
environment features or the RFID landmarks.
Several studies on robot navigation have used an approach based on RFID landmarks at
known locations (?;?;?). A popular approach is to build a topological graph of beacons,
and navigate through the graph using the RFID beacons as “stepping stones” to reach
some desired goal. (?) developed a method of localizing RFID tags by learning a sensor
model from measurements. It was shown that the use of RFID information in the map
allows for very efficient localization. Their approach, however, requires a preexisting map
1Some error will always be present, but the maps must be useful for metric localization purposes.
Figure 1: CAD drawing of an underground level at the CANMET Experimental Mine.
of the environment. (?;?) have similar methods for localizing the tags given an existing
map. Others (?) have taken the approach of using dispersed tags as landmarks as an aid in
producing consistent metric maps, though this has only been demonstrated in comparatively
small laboratory environments.
All this is not to say that natural landmarks might not also be quite suitable. The work of
(?) is an excellent example of this, where a method for detecting passageway intersections
is presented that is based on the use of Voronoi diagrams. However, in this paper, we
view the use of artificial landmarks as appealing from a practical perspective in that they
are absolutely robust. The use of artificial landmarks is also of limited burden in mining,
especially if they are of minimal cost (e.g., RFID) and explicit knowledge of their location
need not be known beforehand.
1.2 Baseline Work
The ideas developed in this paper arise from preliminary experiments by the authors (?;?)
and fundamentally on the well-known work of (?;?) and other related works (?;?) for
enforcing consistency of a map by recognizing similar scans taken by range sensing devices
and by performing a global optimization over a “closed loop” set of vehicle pose estimates.
The authors implemented this in an offline SLAM approach with the goal of producing
maps of sufficient quality to be used later in vehicle localization efforts. Figure ?? shows
a typical progression of mapping results from such experiments (?, pp. 658–659). In this
case, the mapping vehicle traversed a nearly rectangular (roughly 80 ×60 m) underground
tunnel environment twice. Figure ?? shows the map resulting from odometry measurements
alone (here, two wheel encoders). The distance travelled is realistic, but the encoders do
a poor job of estimating orientation. Figure ?? demonstrates the use of consecutive range
scan matching. This generates better orientation estimates but has trouble in long, straight
tunnels with few features from which to reliably distinguish longitudinal motion. Combining
the two sensors by way of a filter obviously allows for a better outcome, as shown in Figure
??, but the accumulation of error is still significant enough that the resulting map is clearly
not consistent. The work described in (?) built upon this by introducing RFID landmarks
as a means of automating the map-building process, while the underlying method remained
unchanged. While that work marked our initial use of RFID, it did not attempt to address
the underlying scaling issues identified in the earlier work, as is the purpose of the method
described in this paper.
As in (?), by recognizing that there are duplicate points in this map that correspond to single
points in the real world, one is able to match non-consectuive scans so that a least-squares
process is able to produce a set of globally-aligned pose estimates that is consistent, as is
shown in Figure ??. One significant problem with this, however, is that it is not practically
scalable to very large scale environments such as those encountered in underground mining.
(a) Map from odometry. (b) Map from scan matching.
(c) Map after combining odometry and
scan matching.
(d) Map after global alignment.
Figure 2: Occupancy grid maps of a roughly 80 ×60 m underground tunnel loop (con-
crete floor) generated by different methods by using a Pioneer 3DX mobile robot and SICK
LMS200 scanning laser rangefinder (?, pp. 658–659).
The closed-loop pose estimation problem relies on matrix operations that increase in size
with the number of links n, making it at least an O(n2.376) problem2. Localization will
similarly become increasingly costly as the map size increases.
1.3 Objectives
The principal contribution of this paper is the presentation and (field) evaluation of a
landmark-bounded method for occupancy grid mapping of large-scale underground drift
networks. The method was designed to meet the following objectives:
2Assumes the Coppersmith-Winograd algorithm is used for inversion (?). This is the ideal case; the
O(n2.807) Strassen algorithm is more commonly used in practice.
1. The method should scale to very large underground passageway environments (e.g.,
on the order of kilometres);
2. The method should be tolerant of changes in the environment or expansion of the
drift network over time as new drifts are constructed and old ones modified or closed;
specifically, modifying a small part of the environment should not necessitate re-
mapping the entire environment;
3. No prior knowledge of the environment should be needed, aside from the requirement
that it lie (approximately) in two-dimensional plane (e.g., a mine level); manual
surveying should not be required and the building of maps should not necessitate
human intervention; and,
4. The resulting maps should provide a natural basis for efficient localization (but local-
ization is beyond the scope of this paper).
From a commercial perspective, the use of relatively low-cost devices is also important.
2 Landmark-Bounded Method
This section details the algorithms necessary for implementation of the landmark-bounded
method. The underlying graph structure of an environment is introduced, and is used to
decompose the mapping problem into smaller sub-problems based on local reference frames.
The sub-problems are then solved by more conventional means, and the section concludes
with a description of how to reassemble the sub-problem solutions into a global solution. A
simple block diagram of the process described in this section is provided in Figure ??.
The first step is to collect data about the environment. For this, we employ a 2D scanning
laser rangefinder3and collect simultaneous odometry data (e.g., from wheel encoders). The
32D scanning laser rangefinders are now standard on modern commercially-available automated mining
Local map
loop closure
RFID beacon
location + range
Edge
assembly
Odometry +
scan matching
Landmarks
∆qodom
∆qsm
∆q
(b,E)
∆Θ
Vehicle
sensors
Pose estimation
Map assembly
edge
maps
assembled
map
Figure 3: Overall block diagram the method described in Section ??.
data must be sufficiently “rich” in the sense that it covers the desired area to be mapped,
possibly multiple times. The data is then processed offline, as described next.
2.1 Pose Estimation
Let qk= (xk, yk, θk)∈R2×S1denote the pose of the mapping vehicle at time step k. In our
experiments, we utilized a time step of T= 0.1 s when collecting data. If one assumes that
the vehicle cannot slip laterally, then a suitable kinematic model for the vehicle’s motion is
qk+1 =qk+T
cos θk0
sin θk0
0 1
vk
ωk
,(1)
vehicle systems (?).
where vkis the vehicle’s speed and ωkits angular rate. For mapping, the objective is to
estimate qkwith covariance Pk. Note that the estimated rates, when obtained from wheel
odometry alone, can contain a significant amount of noise, thus corrupting the pose estimates.
Since (??) is nonlinear, one can propagate the the uncertainty associated with qkby way of
an augmented unscented transformation (?), for example.
To improve on the results obtainable from wheel odometry, one can fuse the odometry
estimate with independent pose estimates obtained by matching rangefinder scans from one
step to the next. This is widely known as scan matching, of which there are many algorithm
variants. For the results presented in this paper we used a polar scan matching algorithm
(?). The basic premise yields a relative measurement ∆qk,k+1 in the frame of qk, which
satisfies
qk+1 =qk+
cos θk−sin θk0
sin θkcos θk0
0 0 1
∆qk,k+1 .(2)
The operation (??) is also nonlinear so, again, an augmented unscented transformation is
used propagate uncertainty through the model.
These independent estimates are then fused by using a simple Kalman filter, where the
odometry estimates provide the a priori estimate and the scan matching output serves as
the a posteriori estimate, such that
∆qk,k+1 = ∆qodom
k,k+1 +Kk∆qsm
k,k+1 −∆qodom
k,k+1 ,(3)
where Kkis the usual Kalman gain (e.g., see (?) or any other text about Kalman filtering),
which also allows for the propagation of the estimate covariance
∆Pk,k+1 = (I−Kk) ∆Podom
k,k+1 .(4)
q1q2q3
q11
q20
q21
Figure 4: Illustration of closed-loop pose estimation. Additional non-consecutive links are
shown as dashed lines, found by distance and angle criteria.
The superscripts refer to odometry and scan matching.
During the mapping process it is possible that the vehicle passes through the same area
of the mine more than once. In order to stitch these data together in a consistent way, a
technique for closing the loop is necessary. Unlike the open-loop methods described so far,
where only measurements between consecutive timesteps kand k+ 1 are considered, the
closed-loop method can also include relative measurements (e.g., matched scans) between
non-consecutive time steps. Figure ?? shows a schematic example with two paths.
Given a set of these measurements, or links, a method similar to that of (?) is applied to
generate yet another set of pose estimates. New non-consecutive links from pose qiare added
by searching for other poses qj, where j6=i±1, lying within a threshold radius ∆rmax and
heading ∆θmax. To reduce the number of links, mininum thresholds are also applied. For
successful measurements, a weighted least-squares method is applied to generate a new set
of poses based on the existing and new measurements. This basic method is detailed in (?),
albeit for a slightly different setup.
2.2 Landmark Model
The results presented here are based on the use of RFID for landmarks, although the general
method is applicable to other distinct features (e.g., Wi-Fi access points, natural features).
The practical benefit of RFID is that robustly unique landmarks can be easily and cheaply
added to an environment wherever they are useful. Used this way they provide a sparse4kind
of information: unreliable measurements indicating only whether a given tag is nearby or
not. The measurements are unreliable in that a tag may not respond to a reader even when
it is nearby, leading to an unpredictable fraction of false negative readings, and complicating
matters is the fact that “nearby” is not well-defined either. Indeed, the intended application
of the EPC standard for passive RFID: inventory (?) has very different requirements than
that of a navigation system intended for mobile robots.
We conducted several experiments aimed at characterizing the readability properties of some
common tags so that a realistic model of the interaction between tags and reader could be
developed (the hardware is described in Section ??). The read probability for different
distances and directions of relative motion were computed empirically. Published studies
(?), as well as our own laboratory experiments, indicate that the interaction between a tag
and reader is complicated at best. Explicitly modeling the interaction between tag and
reader is an arduous process, and experience shows that in uncontrolled environments it is of
little use anyway since the interaction is strongly affected by the surrounding environmental
characteristics. Some of our experiments on RFID detectability are briefly described in
Appendix ??.
However, in our method we are interested only in where an RFID beacon is detectable and
we have little interest in where the physical tag is actually located. This allows us to use a
very simple sensor model. We make the assumption that a beacon can be detected with a
constant probability everywhere within a certain range of the beacon “center”, and with a
4In the work presented here, RFID tags are always placed well beyond the range of other tags.
Require: Raw observations Rof beacon IDs read at each time step k
Ensure: A set of beacon estimates {ˆ
b}
First, locate “clouds” of RFID measurements isolated by a fixed-width buffer of non-
measurements
for each RFID cloud with index range kmin →kmax do
# Locate the index at the center
c= median(kmin, kmin + 1, kmin + 2, . . . , kmax )
# Store the global coordinates of the center
(x, y)=(qx,c,qy,c)
# Estimate beacon range
r=1
2||(qx,kmax ,qy,kmax )−(qx,kmin ,qy,kmin )||
# Store the beacon ID (raw measurement)
N=Rc
end for
Figure 5: Estimating RFID beacon location and range from observed data.
zero probability outside it. Since each tag’s readability is affected by its surroundings, we
must individually estimate each beacon’s detectable range from measurements. A beacon
estimate ˆ
b= (x, y, r, N ) can then be represented in a map using four coordinates: its
globally-unique identification number N, the (x, y) location of its center, and its effective
detectable range r. Clouds of RFID measurements with constant ID number Nare observed
whenever the reader-equipped vehicle passes a stationary beacon. Each cloud reduces to a
beacon estimate ˆ
b: the median index of the cloud is designated as the beacon center, and
the detectable range ris estimated from the spatial spread of the measurements in the cloud.
The simple process of producing these beacon estimates is outlined in Figure ??. The beacon
centers are then used to define the “break points” for partitioning the collected data and
identifying the associated graph edges, as described below.
2.3 Graph Structure
The scaling issue introduced in Section ?? is a major obstacle if the goal is truly large-scale
mapping. However, with the addition of unique landmarks (e.g. RFID beacons), there exists
an underlying graph structure to the environment: the RFID beacons form nodes in the graph
and the traversable paths between them are the graph edges. We denote nodes by biand
edges by Eij, where iand jare node indices. Since the nodes represent real, fixed points
in the real world, not only is the graph topology significant, but also the relative distances
between the nodes in the plane. This is known in the literature as an undirected planar
straight-line graph (?), a subtype of metric graphs which are embedded in the Euclidean
plane.
For mapping, the main significance of the graph structure is that it provides a natural and
well-defined way of breaking the problem of mapping a large environment into pieces (?).
Furthermore, since the beacons can (presumably) be placed anywhere in the environment,
it is possible to choose the size of the pieces as to be appropriate for any particular task.
Given that the problem can be decomposed in this way into a number of small sub-problems,
the task is then to solve each of the sub-problems (mapping a small area), and assemble the
solutions of these sub-problems to solve the original one.
The goal is to break the problem into pieces as described above, so two things are required:
1. A reference frame is needed for each sub-map; and
2. The position and orientation (i.e., pose) of each of these frames must be known with
respect to each other, in a global frame.
Knowing that the environment has a metric graph structure, as introduced above, both
requirements can be met by using local coordinate frames attached to the graph. Each edge
naturally defines its own coordinate frame. One of the two beacons defining the edge is
arbitrarily chosen as the origin (by convention, the lower-numbered tag is chosen), and a
straight line from that beacon to the other defines the frame’s x-axis, with the y-axis defined
using the familiar right-hand rule. This frame is termed the edge frame and is used as the
base reference frame for all pose estimation and mapping.
Pose estimation in the edge frame follows the same procedure as it would in any reference
frame. For each path (data sequence) in the edge, an open-loop set of pose estimates is first
constructed using the laser-corrected approach introduced in Section ??. Each path is allowed
to begin at the origin of some arbitrary frame, with the first pose (x0, y0, θ0) = (0,0,0). This
is illustrated for an example case with two paths in Figure ??. The laser-corrected odometry
measurements are saved as the set of weak links to be used in the closed-loop estimation
process. The set of poses is then searched for pose pairs meeting distance and angular
thresholds, and scan matching measurements are made between them. These measurements
are then added to the problem as strong links, and the resulting set of combined strong
and weak links are then solved using the least-squares pose estimation process of (?) for
the most likely set of poses. This process is iterated, with new strong links added and old
ones removed at each iteration until convergence on an optimal set of closed-loop poses, as
illustrated in Figure ??.
The pose set is then transferred into the edge frame. Since the first pose qstart is necessarily
located at the origin, this transformation can be interpreted as a simple rotation of the
entire pose set about the origin until the last pose in the set, qend , is also coincident with
the x-axis. This forces both RFID beacons of the edge to be in place: one is at the origin of
the coordinate frame and the other is some distance away on the x-axis.
2.4 Edge Assembly
Once the graph edges have been constructed, the next step is to assemble the edges into a
metric graph. This involves determining the relative orientations of the edge frames.
Consider a pair of connected edges Eij and Ejk and a continuous data path (i.e., one collected
by driving from beacon i, then to j, then to k) as illustrated in Figure ??. Since the path
is continuous, the last pose in edge Eij (call it qlast
ij ) and the first in edge Ejk (qfirst
jk ) are
consecutive poses in the same path, but they are expressed in different frames. Let the
X
Y
(a) Initial open-loop pose estimates for two paths between two
landmarks, showing strong links found using distance and angu-
lar criteria.
X
Y
(b) Consistent closed-loop estimates of the two pose sets.
X
Y
(c) The closed-loop pose estimates, rotated into the edge frame.
Figure 6: The pose estimation process in an edge containing two paths.
∆Θij,jk
β
α
δ
Path w.r.t. Eij
bibj
bk
Path w.r.t. Ej k
Figure 7: Relative angular measurements between edges.
relative orientation between edges Eij and Ejk be ∆Θij,jk . Let the orientation component
(θ-component) of qlast
ij be αand the θ-component of qfirst
jk be β. Since qlast
ij and qfirst
jk are
continuous poses, their difference in orientation δshould be near zero. Obtain a measurement
of δby taking a scan matching measurement between qlast
ij and qfirst
jk , and again picking out
the θ-component. By inspection of Figure ??, the desired quantity ∆Θij,jk is
∆¯
Θij,jk =β+δ−α. (5)
The solution is now to formulate the edge placement as a constrained optimization problem.
The “best” placement of the edges can be defined in a least-squares sense, where the objective
is to minimize the sum of the squared differences between orientation differences in the graph
∆Θ and their measured values ∆¯
Θ. The objective function wto be minimized is defined is
w=X∆Θij,jk −∆¯
Θij,jk 2,(6)
where the summation is over all the measurements ∆ ¯
Θij,jk . To ensure a consistent solution,
the minimization must be constrained so that each edge retains its computed edge length.
Denoting the length of edge Eij as Lij , the constraints are
||Xj−Xi|| =Lij ,(7)
where Xidenotes the (x, y) location of beacon biin the plane. There is one constraint
equation of the form (??) for each edge in the graph. The problem is then defined: the
measurements ∆ ¯
Θij,jk are obtained from the process described above, the edge lengths Lij
are known as a byproduct of the edge-frame pose estimation, the orientation differences
∆Θij,jk are computed by simple trigonometry from the node location estimates Xi= [ xi
yi] as
∆Θij,jk = Θj k −Θij
= arctan yk−yj
xk−xj−arctan yj−yi
xj−xi,(8)
and the node locations Xiare free variables. This problem may then be solved using one of
many constrained nonlinear optimization methods. For the results shown in this paper, we
used the interior point method of (?).
Finally, if one wishes to assemble these edges into a single map (e.g., for visualization pur-
poses), a map-stitching routine is outlined in Appendix ??. However, in future we intend to
use only the edge maps for underground localization purposes.
3 Experimental Apparatus
This section describes the environments and hardware used for testing of the algorithms
developed in Section ??. Computer-based simulation was also used as a method for algorithm
evaluation, but specifics about the created MATLAB simulator itself are not included in this
paper for brevity’s sake (see also Section ??).
Laser
rangefinders
IMU
Embedded
computer
Power
converters
RFID
reader
Figure 8: Inside view of the custom hardware enclosure showing sensors.
3.1 Hardware and Software
A custom sensor platform was designed and built to enable hardware experiments in a variety
of environments. The sensor platform was developed around the custom enclosure shown in
Figure ?? to be portable to different vehicles and support the following sensors:
1. Two SICK LMS 111 scanning laser rangefinders: a “primary” rearward-facing laser
scanning in a plane parallel to the ground, and an “auxiliary” laser scanning in a
plane perpendicular to the direction of travel; of these, only the primary was used;
2. Two US Digital A2 absolute optical encoders, mounted in one of two possible config-
urations on the vehicle; and,
3. An Alien ALR-9650 RFID reader, mounted with the antenna facing upward.
A custom realtime data acquisition system (DAQ) named RTLog was developed to collect the
data from the various sensors. RTLog was designed using a client/server model, where the
RTLog server runs on an embedded board inside the sensor enclosure (shown in Figure ??)
and the client runs on an operator’s vehicle-mounted laptop. The system was implemented in
Python and C and uses the Linux kernel’s CONFIG_PREEMPT_RT extension to provide sensor
measurements at precisely-timed intervals of T= 0.1 s.
3.2 Field Test Environments
Results from field testing in two appreciably-different underground environments are pre-
sented in this paper. In each environment a different vehicle base was used, as described
below, but the employed hardware and software described in Section ?? was the same.
3.2.1 CU Tunnel Network
All buildings at Carleton University (CU) are connected by way of a network of underground
service tunnels5—in total, there are approximately five kilometres of tunnels. An electric
service vehicle was configured for data collection in this environment. The vehicle is based
on the Taylor-Dunn model SS-534 service vehicle shown in Figure ??, and allows data to
be collected while driving at speeds up to 20 km/h (similar to underground mine haulage
vehicles). The SS-534 is a three-wheeled vehicle, with two rear drive wheels and a single
wheel in front for steering (?). The sensor box was mounted facing backwards and two US
Digital A2 encoders were installed to measure wheel rotations and steering angle.
3.2.2 CANMET Experimental Mine
The CANMET Experimental Mine is an underground research facility operated by Natural
Resources Canada in Val-d’Or, Qu´ebec6. This facility features a multilevel underground
gold mine, out of production since 1991, that is now used exclusively for research. The mine
contains 2400 m of drifts in five levels, two of which were selected (referred to as the “70 m
level”—see also Figure ??—and “130 m level”) for testing based on their size and the ability
to drive in closed loops. Figure ?? shows some representative areas of this environment.
5See also the “tunnels” layer at http://www.carleton.ca/campus/.
6See also http://www.nrcan.gc.ca/smm-mms/tect-tech/ser-ser/val-val-eng.htm.
Figure 9: Customized Taylor-Dunn SS-534 electric vehicle.
(a) A long, straight tunnel section. (b) A typical intersection of tunnels.
Figure 10: Representative areas at the CANMET Experimental Mine in Val-d’Or, QC.
Figure 11: Customized utility trailer used for mine testing in Val-d’Or, QC.
A customized utility trailer was employed for mine testing and is shown in Figure ??. The
sensor platform described in Section ?? was mounted together with deep cycle batteries for
power and two US Digital A2 encoders to measure wheel rotations.
4 Results and Analysis
This section presents the results of our experiments carried out first in simulation, then in
the CU tunnels and at the CANMET Experimental Mine (see Section ??). Here we focus
on the experimental outcomes and on analysis of the landmark-bounded method in terms of
its advantages and experimentally observed shortcomings.
4.1 Algorithm Validation
Prior to field testing, a simulator was developed in MATLAB for algorithm validation. The
complete sensor suite was simulated with additive noise, including odometry, laser scanners,
and RFID devices. Simulated zero-mean Gaussian noise was added to the odometry and laser
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(a) Map resulting from noise-free input data.
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(b) Map resulting from input data with simulated
Gaussian noise (six RFID beacons).
Figure 12: Landmark-bounded method results by using simulated data in a modeled loop (all
dimensions in metres). Maps were constructed from simulated input data with and without
added noise.
measurements, each using a constant covariance deemed realistic by analysis of real sensor
measurements. Measurement noise was simulated for RFID measurements as a fraction
of randomly-distributed false negative readings. In addition to facilitating debugging, the
simulator allowed for comparison of results with “ground truth”, something that was not
available7in both the CU tunnels and at the CANMET Experimental Mine.
By using simulated data both with and without added noise, map results produced using
the landmark-bounded method were compared. Local edge maps were assembled using the
map-stitching routine outlined in Appendix ??.
Figure ?? shows the stitched map made from the noise-free input data. The estimated graph
structure is shown as an overlay on the map. The result is a near-perfect representation of the
environment, a promising sign that the new method works as intended. In contrast, Figure
?? shows the map made using the noisy input data. One noticeable feature of this map are
7The lack of ground truth data speaks to the challenging scenario that exists in underground navigation.
One possible alternative, which we have not yet explored due to the work it entails, would be to manu-
ally survey-in the vehicle’s position at selected locations during the mapping process to estimate mapping
accuracy with respect to an external reference frame. We may do this on a small scale in future work.
the slight “kinks” visible in the tunnel walls near some of the beacons. This phenomenon
results from an accumulation of orientation error in the edge maps (as expected) which may
not even be visible over the length of the edge but becomes apparent near the graph nodes.
Here, the pose estimation process has produced edges bent slightly inward around the loop
caused by imperfect measurements. When the loop is forced to be closed by the graph
topology, the kinks are evident as the gradual accumulation of error is suddenly corrected
at the graph nodes, always appearing at the map “break points”. Since this error correction
results from the closed-loop nature of this graph, kinks never occur in graphs without cycles.
4.2 Landmark Spacing and Error
Another study conducted in simulation was about the effect of landmark density on the
resulting map. Twenty-two beacons were placed throughout the simulator environment,
and a data run was collected by driving the simulator vehicle once around the loop. The
landmark-bounded method was used to create a map using the noisy data, then a subset
of the beacons were ignored (effectively removing them) and the environment re-mapped.
This process was repeated until only two beacons, the minimum required for the landmark-
bounded method remained. The results are shown in Figure ??.
As Figure ?? illustrates, the density of beacons impacts the resulting map. With an in-
creasing number of beacons, the kinks described above disappear. By understanding that
kinks result from the sudden correction of the map error which builds up gradually along
the length of the edges, this is expected. Given that the same distance was driven in each
case (the same data run was used), the error accumulated over the whole run is the same.
This means that there is no less error in the case of many edges in Figure ?? than in the case
of one (Figure ??), but instead the same amount of overall error is distributed throughout
many map kinks instead of one. Though the total sum of error remains constant with any
number of beacons, the sum of the squared error decreases as it is spread evenly throughout
−20 0 20 40 60 80
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(a) 22 Beacons.
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(b) 12 Beacons.
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(c) 8 Beacons.
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(d) 5 Beacons.
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(e) 3 Beacons.
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(f) 2 Beacons.
Figure 13: Maps made using noisy simulated data with varying numbers of RFID beacons.
Map quality generally increases with increasing density of beacons, at the cost of increased
complexity in the graph estimation process (all dimensions in metres).
the map. By this measure, it can be concluded that using more landmarks does produce
better results.
Additionally, as the number of edges increases, the time required to compute the vehicle
poses decreases and the time required to solve the graph estimation problem (Section ??)
increases. This is discussed further in Section ??.
As seen in Figure ??, the amount of accumulated pose error in each edge map increases
with the size of the edges. This is a predictable effect because each edge map is effectively
open-loop. This adds a constraint on the placement of beacons: the maximum edge size is
bounded by the amount of accumulated error that is deemed acceptable so that the edge
map remains locally consistent. This, in turn, is dependent on the sensors used, vehicle, and
environmental conditions.
4.3 CU Tunnel Network
A number of data runs were collected using the electric vehicle in the Carleton University
undergound tunnel network. A set of 19 of the data runs covering the entire tunnel network
was selected, and the landmark-bounded method was used to create a map. For this large
environment, no maps from other methods are available as they are not able to handle the
large scale. RFID tags were installed on the tunnel ceilings at approximately even intervals
and were not localized before mapping. Straight tunnel sections were chosen for the tag
locations instead of intersections in order to restrict the orientation of the mapping vehicle
at those points, as a way of mitigating scan matching error. Because our laser rangefinder
provides less than a 360◦view of the vehicle’s surroundings, the uncertainty in scan matching
measurements increases with increasing angular difference ∆θas fewer point pairs can be
matched between scans. With 41 RFID beacons installed in the tunnel network, the resulting
graph as shown in Figure ?? has 41 nodes and 42 edges, and contains two nested loops.
−500 −400 −300 −200 −100 0 100 200
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1
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23
24
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26
27
28
29
30
31
32
33
34
3536
37 38
39
40
41
42
Figure 14: Graph structure of the Carleton University underground tunnel network, con-
taining 42 edges. Graph was constructed from a set of 19 data runs covering the network
(all dimensions in metres).
Again, the edge maps were stitched together as a visualization of the resulting map and
shown in Figure ??. The quad loop area introduced in Figure ?? can be recognized as the
small rectangular loop near the lower left hand corner of the map. Figure ?? shows a few of
the edges in the network with greater detail.
Consider the three-way intersection at the center in Figure ?? (shown in detail in Figure
??). Notice that the stitched map is not consistent. This occurs here because, in the real
environment, one of the edges contains a significantly inclined tunnel section (that in the
lower right of Figure ??), which distorts the odometry measurements in that edge. Figure
−400 −300 −200 −100 0 100
−100
0
100
200
300
400
Figure 15: Assembled map of the Carleton University underground tunnel network. The map
was constructed from a set of 19 data runs covering the network, with the corresponding
graph shown separately in Figure ?? (all dimensions in metres).
−10 0 10 20 30 40 50 60 70 80
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(a) Edge 4.
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(b) Edge 27.
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−50 −40 −30 −20 −10 0 10 20 30
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0 20 40 60 80 100
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40
(f) Edge 33.
Figure 16: A few of the 42 edge maps covering the Carleton University underground tunnel
network in their respective frames. Edge numbers correspond to those shown on the graph
in Figure ?? (all dimensions in metres).
?? shows an intersection containing significant overlap between edges in an area where the
real environment floor is level. Here, the map is consistent. Changes in tunnel inclination
where there is no overlap between edges simply result in a distorted distance scale (since
odometry measures the length of path travelled), but the map remains consistent.
At its root, this failure is due to the fact that the current formulation of the landmark-
bounded method makes the assumption that the environment lies in a two-dimensional plane,
while the real test environment does not. This is not a shortcoming if only the edge maps are
employed for subsequent localization purposes. In most cases this does not result in much
trouble: significant tunnel inclines are handled gracefully in many areas where the change
in inclination happens entirely within an edge. At certain points, however, where there is
no choice of beacon locations allowing the sudden change in inclination to occur within a
single edge (e.g., at a three-way intersection), the result is often inconsistency about a single
point in the map. This problem may not be resolvable without relaxing the two-dimensional
assumption, a significant undertaking. However, its effects can be minimized with careful
placement of landmarks: the three nodes shown in Figure ?? could, for example, be moved
closer to the intersection in order to reduce the area subject to inconsistency.
4.4 CANMET Experimental Mine
The trailer platform shown in Figure ?? together with a Mine Mule vehicle was used to
collect a number of data runs from the 70 m and 130 m levels of the CANMET Experimental
Mine described in Section ??. RFID tags were again mounted on the mine tunnel ceiling
at approximately equal intervals and were not manually localized. Straight tunnel sections
were again chosen instead of intersections for the same reason mentioned in Section ??. For
each level, a set of runs covering the full environment was chosen and used to construct a
map using the landmark-bounded method. Three data runs were used to map the 70 m
level, and two for the 130 m level. For brevity’s sake, in this paper we show only the results
−160 −150 −140 −130 −120 −110 −100 −90 −80 −70 −60
20
30
40
50
60
70
80
(a) A rapid change in elevation causes distorted odometry mea-
surements in one of the overlapping edges, violating the two-
dimensional assumption.
−40 −30 −20 −10 0 10 20 30 40 50
290
300
310
320
330
340
350
360
(b) A flat-ground case where the two-dimensional assumption is
valid, resulting in a consistent map.
Figure 17: Two examples of overlapping edge maps in the CU underground tunnel network.
The inconsistent case occurs as a result of a violation of the two-dimensional assumption at
a point of overlapping edges (all dimensions in metres).
from the 70 m level since this level is much larger and includes a long loop. A schematic of
this level is shown in Figure ??.
Again, the edge maps were stitched together for visualization, with the resulting global map
shown in Figures ?? with the graph structure overlaid. A few edges from this level are shown
in detail in Figure ??. Worth mentioning is that, due to an uneven ground surface, odometry
measurements are significantly worse in this case than in the CU tunnel network.
4.5 Scaling to Large Pose Sets
The ability to scale to very large environments is an important property of the landmark-
bounded method. Tests in the CU underground network and the CANMET Experimental
Mine have demonstrated the ability of this method to handle environments beyond the
limitations of standard approaches. By using some simple assumptions, it is possible to do
some rudimentary analysis of the scaling properties of the landmark-bounded method, as
compared to a Lu & Milios-style estimation of all poses at once as in the earlier methods.
Given a set of input data with ntimesteps, the two methods can be compared in the time
taken to complete the task of generating a set of closed-loop pose estimates. Assume (cf.
Section ??) that the time required to estimate nposes is proportional to n2.376 , written as
O(n2.376). The time required for a Lu & Milios-style method is then simply
TL&M(n) = O(n2.376 ).(9)
In the landmark-bounded method, poses are computed by multiple smaller sub-problems
whose solutions are then reassembled. Assume that a problem containing nposes is divided
0 50 100 150 200 250 300
−150
−100
−50
0
50
100
Figure 18: Assembled map of the CANMET Experimental Mines 70 m level, with the graph
structure overlaid. Inconsistency is evident at some intersections, again due to violation of
the two-dimensional assumption. A manually-surveyed map of the same area is shown in
Figure ?? (all dimensions in metres).
0 20 40 60 80 100
−10
0
10
(a) Edge 5.
−10 0 10 20 30 40 50 60 70 80 90
−10
0
10
(b) Edge 7.
−10 0 10 20 30 40 50 60
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−5
0
5
10
15
(c) Edge 13.
Figure 19: A few edge maps from the CANMET Experimental Mine’s 70 m level (all dimen-
sions in metres).
into kequally-sized sub-problems, each containing n
kposes. Each sub-problem is of order
On
k2.376
=1
k2.376 On2.376.
If these sub-problems are solved serially, then the total time taken for the landmark-bounded
method is ktimes the sub-problem time
TLBM,s(n) = k1
k2.376 On2.376
=1
k1.376 On2.376.(10)
Since the sub-problems are independent, it is also possible to solve them in parallel. Assuming
the resources are present for a parallel solution, the parallel solution time for the landmark-
bounded method is the same as that for a single sub-problem:
TLBM,p(n) = 1
k2.376 On2.376.(11)
From (??), the landmark-bounded method is faster than a simple Lu & Milios-style method
by a constant factor depending on the number of independent sub-problems k. Define
the speedup as the number of times faster that the landmark-bounded method can solve
a problem of order nthan the simpler method can. For the parallelized landmark-bounded
method, the speedup, from (??), is k2.376 , and for the serialized version, from (??), is k1.376.
The speedup, tabulated for a few values of kin Table ??, is certainly significant.
However, the landmark-bounded method also requires the solution of the graph estimation
problem (section ??) in addition to the solution of each edge. In this analysis it has been
assumed that this problem (of order k, the number of independent sub-problems) is much
Table 1: Landmark-bounded method speedup with the number of edges k.
kSerial LBM Parallel LBM
2 2.6 5.2
5 9.2 45.8
10 23.8 237.7
20 61.7 1233.8
smaller than the edge problems (each of order n
k) and has been neglected. This is a reason-
able assumption for open chains, but for closed ones (i.e., the graph contains cycles), the
time required to solve the graph estimation problem is itself significant. Since it is non-
deterministic, the analysis of the time required by the graph estimation process is beyond
the scope of this paper.
5 Conclusion
The contributions of this applied research include the design, implementation, and field
testing of a technique for large-scale underground mine mapping. RFID beacons were used
as unique landmarks in order to meet both consistency and computational requirements,
although these are interchangeable with other uniquely identifiable features. The objectives
were largely met with the development of the landmark-bounded method, which is based on
assigning a natural graph structure to an underground network containing stationary RFID
beacons. Validation of the proposed method was done by using both simulated data and field
experiments in a two distinct underground environments. These environments were of a large
enough scale as to present significant computational obstacles to standard approaches and,
importantly, included a real underground mine. In each case the landmark-bounded method
was able to practically produce a useful result while the simpler conventional method was
not. The resulting maps generate a type of atlas: a set of local maps (edges) together with
an estimate of the graph configuration, defining how these fit together. This format leads
to not only scalable 2D mapping but also the potential for efficient map-based localization
techniques that take advantage of it.
One issue with the method in its current form is the inconsistency seen in stiched maps in
certain cases when edges overlap at locations of changing elevation. However, relaxing the
assumption that the environment lies in a 2D plane and reformulating the problem is beyond
the scope of this paper. To do so would surely involve additional sensors (e.g., an inertial
measurement unit) for elevation estimation. At odds with this is our objective of creating a
low-cost solution that might eventually find widespread use in mining. Also, in future, we
intend to use only the edge maps for underground localization purposes.
The proposed landmark-bounded method also has additional benefits, not already men-
tioned. For example, the method’s graph framework allows for maps to be easily modified
and extended once built—i.e., re-mapping of the entire environment is not necessary. More-
over, the ability to easily merge graphs means that it is not necessary to collect data in a
single run, which is very practical in dynamic and growing underground mining operations.
Acknowledgments
The authors wish to thank Unal Artan, Lewis Li, and Joseph Bakambu at MDA Space
Missions (Brampton, ON), James MacLean (formerly at MDA, now at Google), as well
as Stefan Radacina Rusu and David Grove at Carleton University (Ottawa, ON) for their
technical support. Thanks also to Pierre Lalibert´e, Phillipe De la Sablonni`ere, and Denis
Gagnon at the CANMET Experimenal Mine (Val-d’Or, QC) for field experiments assistance.
This research was supported in part by MDA Space Missions and by the Natural Sciences
and Engineering Research Council of Canada (NSERC) under project CRDPJ 382256-09.
References
Artan, U., Lavigne, N. J., and Marshall, J. A. (2009). Globally consistent mapping of large-
scale passageway environments. In Proceedings of the 22nd IEEE Canadian Conference
on Electrical and Computer Engineering, pages 656–659, St. John’s, NL.
Bakambu, J. N. and Polotski, V. (2007). Autonomous system for navigation and surveying
in underground mines. Journal of Field Robotics, 24:829–847.
Bosse, M., Newman, P., Leonard, J., and Teller, S. (2004). Simultaneous localization and map
building in large-scale cyclic environments using the Atlas framework. The International
Journal of Robotics Research, 23(12):1113–1139.
Byrd, R. H., Hribar, M. E., and Nocedal, J. (1998). An interior point algorithm for large
scale nonlinear programming. SIAM Journal on Optimization, 9(4):877–900.
Coppersmith, D. and Winograd, S. (1990). Matrix multiplication via arithmetic progressions.
Journal of Symbolic Computation, 9(3):251–280.
Diosi, A. and Kleeman, L. (2007). Fast laser scan matching using polar coordinates. Inter-
national Journal of Robotics Research, 26:1125–1153.
EPCglobal Inc. (2010). EPCglobal Tag Data Standards Version 1.4. Retrieved from http:
//www.epcglobalinc.org/standards/tds/tds_1_4-standard-20080611.pdf.
H¨ahnel, D., Burgard, W., Fox, D., Fishkin, K., and Philipose, M. (2004). Mapping and
localization with RFID technology. In Proceedings of the 2004 IEEE International Con-
ference on Robotics and Automation, volume 1, pages 1015–1020.
Howard, A., Siddiqui, S., and Sukhatme, G. S. (2003). An experimental study of localization
using wireless Ethernet. In Proceedings of the 4th International Conference on Field and
Service Robotics, pages 201–206.
Joho, D., Plagemann, C., and Burgard, W. (2009). Modeling RFID signal strength and tag
detection for localization and mapping. In Proceedings of the 2009 IEEE International
Conference on Robotics and Automation, pages 1213–1218, Piscataway, NJ, USA. IEEE
Press.
Julier, S. J. and Uhlmann, J. K. (2004). Unscented filtering and nonlinear estimating.
Proceedings of the IEEE, 92:401–422.
Kleiner, A., Prediger, J., and Nebel, B. (2006). RFID technology-based exploration and
SLAM for search and rescue. In Proceedings of the 2006 IEEE/RSJ International Con-
ference on Intelligent Robots and Systems, pages 4054–4059.
Kubitz, O., Berger, M., Perlick, M., and Dumoulin, R. (1997). Application of radio frequency
identification devices to support navigation of autonomous mobile robots. In 1997 IEEE
47th Vehicular Technology Conference, volume 1, pages 126–130.
K¨ummerle, R., Steder, B., Dornhege, C., Kleiner, A., Grisetti, G., and Burgard, W. (2011).
Large scale graph-based slam using aerial images as prior information. Autonomous
Robots, 30:25–39. 10.1007/s10514-010-9204-1.
Kushki, A., Plataniotis, K. N., and Venetsanopoulos, A. N. (2007). Kernel-based positioning
in wireless local area networks. IEEE Transactions on Mobile Computing, 6(6):689–705.
Lavigne, N. J., Marshall, J. A., and Artan, U. (2010). Towards underground mine drift
mapping with RFID. In Proceedings of the 23rd IEEE Canadian Conference on Electrical
and Computer Engineering, pages 1–6, Calgary, AB.
Liao, I.-E. and Kao, K.-F. (2008). Enhncing the accuracy of WLAN-based location determi-
nation system using predicted orientation information. Information Sciences, 178:1049–
1068.
Lu, F. and Milios, E. (1997). Globally consistent range scan alignment for environment
mapping. Autonomous Robots, 4(4):333–349.
Magnusson, M., Lilienthal, A., and Duckett, T. (2007). Scan registration for autonomous
mining vehicles using 3D-NDT. Journal of Field Robotics, 24(10):803–827.
Marshall, J. A. (2010). Navigating the advances in underground navigation. CIM Magazine,
5(4):20–21.
Marshall, J. A., Barfoot, T. D., and Larsson, J. (2008). Autonomous underground tramming
for center-articulated vehicles. Journal of Field Robotics, 25(6–7):400–421.
Milella, A., Vanadia, P., Cicirelli, G., and Distante, A. (2007). RFID-based environment
mapping for autonomous mobile robot applications. In 2007 IEEE/ASME International
Conference on Advanced Intelligent Mechatronics, pages 1–6.
Olson, E., Leonard, J., and Teller, S. (2006). Fast iterative alignment of pose graphs with
poor initial estimates. In Robotics and Automation, 2006. Proceedings of the IEEE
International Conference on, pages 2262–2269.
Preparata, F. P. and Shamos, M. I. (1985). Computational Geometry: An Introduction.
Springer-Verlag, New York.
Ralston, J. C., Hargrave, C. O., and Hainsworth, D. W. (2005). Localisation of mobile
underground mining equipment using wireless Ethernet. In Proceedings of the 2005
Industry Applications Conference, volume 1, pages 225–230. IEEE.
Schneegans, S., Vorst, P., and Zell, A. (2007). Using RFID snapshots for mobile robot
self-localization. In European Conference on Mobile Robots, pages 241–246.
Silver, D., Ferguson, D., Morris, A., and Thayer, S. (2006). Topological exploration of
subterranean environments. Journal of Field Robotics, 23:395–415.
Stengel, R. F. (1994). Optimal Control and Esimation. Dover Publications, Inc., New York.
Thrun, S., H¨ahnel, D., Ferguson, D., Montemerlo, M., Burgard, W., Baker, C., Omohundro,
Z., Thayer, S., and Whittaker, W. (2003). A system for volumetric robotic mapping
of abandoned mines. In Proceedings of the IEEE International Conference on Robotics
and Automation, pages 4270–4275.
Tsukiyama, T. (2005). World map based on RFID tags for indoor mobile robots. In Casasent,
D. P., Hall, E. L., and R¨oning, J., editors, Intelligent Robots and Computer Vision
XXIII: Algorithms, Techniques, and Active Vision, volume 6006, pages 600–613. SPIE.
Zhang, X. Z., Rad, A. B., Wong, Y. K., Huang, G. Q., Ip, Y. L., and Chow, K. M. (2007). A
comparitive study of three mapping methodologies. Journal of Intelligent and Robotic
Systems, 49(4):385–395.
Zhou, J. and Shi, J. (2009). RFID localization algorithms and applications—a review. Jour-
nal of Intelligent Manufacturing, 20(6):695–707.
A Map Assembly
Once the data structure introduced in Section ?? is complete with pose sets and maps, and
the graph structure is known, the map is considered complete. However, in some cases it is
useful to visualize the full environment an a single map. Since each edge has an associated
map, and the relative positions of the edges are known, it is possible to construct one. The
method is straightforward, but has been included here in Figure ?? for completeness.
Require: A graph structure G, containing maps and beacon locations
Ensure: A global environment map M
# Initialize a large occupancy grid Mwith “unknown” probability values in each cell
M=
.
.
.
. . . 0.5. . .
.
.
.
# Place each edge map in the global map
for each edge Eij do
# Locate the coordinates of beacons iand jdefining the edge
Xi= [ xi
yi]
Xj=xj
yj
# Compute the displacement and rotation of the edge map Mij
rij =Xi
θij = arctan yj−yi
xj−xi
Rij =cos (−θij )−sin (−θij )
sin (−θij ) cos (−θij )
# Update the probability value in each cell
for each cell in the edge map Mij with coordinates (xlocal, ylocal)do
# Compute the corresponding global coordinates
xglobal
yglobal =R−1
ij xlocal
ylocal +rij
# Update the probability of the global map cell with the cell value from the edge map
M(xglobal, yglobal ) = probability update(Mij (xlocal, ylocal))
end for
end for
Figure 20: Process used for stitching edge maps of Ginto a single global map M.
B RFID Detectability
Some simple experiments were conducted to characterize the “detectability” properties of
some common tags, so that a realistic model of the interaction between tags and reader
could be developed. The experiments aimed to test the detectability of the tags as they were
moved laterally at a fixed distance, and also with varying distance. The experimental setup
is illustrated in Figure ??. The Alien ALR-9650 reader was oriented so that the antenna of
the reader was facing a cinder block wall. The distance between the reader and the wall was
denoted h, the point on the wall directly opposite the reader was defined as point “0”, and
distances rwere measured and marked horizontally in increments of 10 cm.
h
r
RFID tag
RFID reader
Figure 21: Schematic diagram of the first RFID experiment used to characterize the inter-
action between tag and reader.
A tag was attached to the wall at point 0 and a series of data measurements from the reader
was recorded. After each run, rwas increased in 10 cm increments and the process was
repeated, holding hconstant. Later, the effect of hwas investigated by varying it in 10 cm
increments while holding rconstant. This data collection procedure was done for two tag
models (Alien 9654, Alien 964X), each in two orientations (parallel or perpendicular to the
direction of movement). In these runs, RFID measurements were recorded at a frequency
of 25 Hz8and were approximately 35 seconds long, resulting in about 875 measurements
per run. For each run, each of the approximately 875 data points was counted as either a
“measurement” or a “non-measurement”, indicating whether the tag was correctly detected.
For each run this was reduced to a read probability, the fraction of the total number of
attempted measurements where a response from the tag was successfully received. After this
was done, the read probabilities were plotted as functions of rand hfor each tag orientation.
Plots of varying rare shown in Figures ?? and ?? for both tags, and a plot showing the
results of varying his shown in Figure ??.
From Figures ?? and ??, it is apparent that for both tags there is a large, approximately
constant read probability at small r(call it the saturated read probability,Pmax), which
generally drops off with increasing r. Both tags have slightly different detectability properties
in the parallel and perpendicular directions. It is apparent that the 9654 tag is the most
readable (measured by the area under the plots), but less predictably so than the 964X.
The 9654 is a strangely shaped tag with a much larger antenna area than the 964X, and so
one can speculate that external factors affecting the tags’ detectability (discussed below) are
more pronounced in the larger tag.
From Figure ?? it is apparent that the read probability behaves in a similar way as his varied.
There is an approximately constant read probability out to some maximum range, where
the probability drops off sharply. In this plot there are additional factors influencing the
detectability in apparently similarly unpredictable ways as is evident in Figure ??. Consider
also some of the external factors which may influence the detectability.
RF Harmonics: Harmonics occurring in the radio interrogation signal may have a signifi-
cant impact on the tag detectability. The hypothesis is that there should be maxima
in the detection probability where the distance between the tag and reader is an
8Other experiments (not described here) found the read probability to be invariant of the sampling
frequency.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Horizontal distance [m]
Detection probability
Detection plot for Alien 9654
parallel
perpendicular
(a) Alien 9654.
0 0.5 1 1.5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Horizontal distance [m]
Detection probability
Detection plot for Alien 964X
parallel
perpendicular
(b) Alien 964X.
Figure 22: Read probability plots for two tags, varying rwith h= 139 cm.
0 1 2 3 4 5 6
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Distance [m]
Detection probability
Detection plot for Alien 9654
Figure 23: Read probability for Alien 9654, varying hwith r= 0 cm.
integral multiple of the RF wavelength. That is, there should be a maximum where
√r2+h2=nλ, (12)
where λis the wavelength of the reader’s interrogation signal and nis an integer node
number. The EPC C1G2 RFID standard has a median frequency of 915 MHz (?),
which translates to a wavelength λof 0.327 m. This suggests a step-like beacon model
with higher-probability “fringes” on the outside may be appropriate, where the fringe
locations can be calculated by equation (??).
Aside from a few outlying measurements, most of the previously unexplainable spikes
in probability outside of the constant-probability range can be explained by this. For
example, in Figure ?? with h= 1.39 m, we should expect high detection probability
for nodes 5 and 6 at 1.3 m and 1.8 m, and both of these are seen in the plot for the
9654, but the 965X is too far out of range at that point. There are also other features
which cannot be explained by this, and what is seen in the results is undoubtedly a
combination of several effects.
Nearby objects: Since constructive and destructive RF interference was shown to be a
significant factor in the tag detectability, it is reasonable to assume that there are other
significant sources of interference also. A number of large steel objects nearby during
the course of the experiments likely had an effect on the results, though the extent
of this in the experiment is not known. This provides another piece of insight: since
each installed tag will be uniquely and unpredictably affected by its surroundings, any
beacon model used will not be able to fully account for tag behaviour. This raises
the question of whether a detailed beacon model is worth developing and using at all,
when it will perform equally as badly in the real world as the most simple model.
Materials: Similarly to the previous point, nearby materials, and especially that on which
the RFID tag is mounted, have a significant impact on the detectability of the tags.
It is found that the tags are usually completely unreadable when attached to “hard”
surface materials such as metal, concrete, and rock, and are generally readable when
attached to “softer” surfaces such as wood, drywall, plastic, and glass.
