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MOBILE ROBOT NAVIGATION USING MONTE CARLO
LOCALIZATION
Amina Waqar
NUCES-FAST [email protected]
ABSTRACT
This paper presents an algorithm for the mobile navigation of a
robot using MonteCarlo. Previously, people did a lot of work for
the tracking of mobile robot.Previously people used grid-based
approach that used high resolution 3D grids torepresent the state
space. Whereas, this method is computationally quite
efficient.Using Monte Carlo Localization we apply the sampling
approach to divide thestate space into samples. We can increase the
number of samples where required.Monte Carlo Localization is easy
to implement. Several results proved that MonteCarlo yields more
accurate results. And also, it is computationally very
efficient.
Keywords: Kalman Filter, Markov Localization, Monte Carlo
Localization.
1 INTRODUCTION
Throughout the last decade, sensor-basedlocalization has been
recognized as a key problem inmobile robotics. In Localization, a
mobile robotestimates its position in a global co-ordinate
frame.There are two types of localizations: GlobalLocalization and
position tracking. In globallocalization, a robot does not know its
original position whereas in position tracking the robotknows its
original position.Global Localization isalso known as hijacked
robot problem (Engelson1994)in which the robot has to determine its
positionfrom scratch.Many of the previous researches wereon
tracking but now many people are working onboth types of
localizations.In this paper we shallrepresent the robots belief by
probability densityover the region in its range. The range is
determinedby the range in which the sensors will be able towork
effectively.[1]
Figure 1 .Tracking using Kalman Filter
2 PREVIOUS WORK
Previously people have done a lot of workon tracking using
Kalman filter which is a form ofPhase Locked Loop (PLL) and is less
efficient ,because of it , it can be used as tracking.
Fig.1 shows working of Kalman filter. Theblack boxes show the
original position , green stars
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show the estimated position and red crosses show themodified
position by taking averages of both.
3 MARKOV LOCALIZATION
Markov localization caters the problem ofstate estimation from
sensor values. Markovlocalization is a probabilistic algorithm:
Instead ofmaintaining a single hypothesis as to where in theworld a
robot might be, Markov localizationmaintains a probability
distribution over the space ofall such hypotheses. The
probabilistic representationallows it to weigh these different
hypotheses in amathematically sound way.
Before we delve into mathematical detail,let us illustrate the
basic concepts with a simpleexample. Consider the environment
depicted in Fig2. For the sake of simplicity, let us assume that
the
space of robot positions is one-dimensional, that is,the robot
can only move horizontally (it may notrotate). Now suppose the
robot is placed somewherein this environment, but it is not told
its location.Markov localization represents this state
ofuncertainty by a uniform distribution over allpositions, as shown
by the graph in the first diagramin Fig 2. Now let us assume the
robot queries itssensors and finds out that it is next to a
door.
Markov localization modifies the belief byraising the
probability for locates next to doors, andlowering it anywhere
else. Consider that the resulting belief is multi-modal, reflecting
the fact that the
available information is insufficient for globallocalization.
Notice also that places not next to adoor still possess non-zero
probability. This isbecause sensor readings have noise, and a
singlesight of a door is typically insufficient to exclude
thepossibility of not being next to a door.
Now let us assume the robot moves a meterforward. Markov
localization incorporates thisinformation by shifting the belief
distributionaccordingly, as visualized in the third diagram in
Fig2.
To account for the inherent noise in robotmotion, which
inevitably leads to a loss of
information, the new belief is smoother (and lesscertain) than
the previous one. Finally, let us assumethe robot senses a second
time, and again it findsitself next to a door.
Now this observation is multiplied into thecurrent (non-uniform)
belief, which leads to the finalbelief shown at the last diagram in
Fig 2. At thispoint in time, most of the probability is
centeredaround a single location. The robot is now quitecertain
about its position.[6]
Bel (l)=P(l|l,a)Bel(l)dl (1)
[3]
Bel is the belief of the robot that wasuniform distribution
initially. To update a beliefthere must an action a done by the
robot. The beliefat position l, Bel(l) is updated using the
previous belief at position l, Bel(l).Then we convolve theboth the
beliefs to get the new belief which guidesthe robot where to
go.
4 MONTE CARLO LOCALIZATION
In the Monte Carlo localization wediscretize the space into
random samples. Since it isusing global localization, it can
represent intomultimodal distributions .Due to this reason,
lessmemory is required and is computationally efficient.Grid-based
approaches were also used but they werecomputationally cumbersome.
Grid-basedapproaches required more memory also because theywere
using 3-D figures.[4]
In our experiment we have modelled therobot with four sensors on
each side. Each of it emitsa signal which is reflected back as 1 if
there is a walland 0 if there is door or any empty space. The
rangein our cases is five units ( 0-4).As it moves along thepath
from door to wall the signals will convert from0s to 1s.Fig.3
explains the above simulation.Fig.3(a) represents first belief of
the robot after anaction. Fig.3(b) is an updated PDF based
theprevious PDF. Fig3.(c) shows the convolution ofboth the PDFs
where the door actually is and thatway the robot should
move.[5]
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Figure 3 : Monte Carlo Simulation
5 CONCLUSION
In this paper we have concluded that MonteCarlo Localization is
an easy to implement andrequires less memory and is
computationallyefficient. Less memory is attributed to the fact
thatbelief is updated in the memory location rather thanoccupying
more and more memory locations.Thisrecursive algorithm is far more
effective thanKalman filter which was a form of Phase LockedLoop
(PLL) and was less efficient computationallyand was not as precise.
Hence Kalman filter was
only used for tracking purposes.
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