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10th IEEE MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION 1
Instituto de
Sistemas e
Robótica
Instituto Superior Técnico – Instituto de Sistemas e RobóticaAv. Rovisco Pais, 1 – 1049-001 Lisboa - Portugal
A Probabilistic Approach For The Localisation of Mobile
Robots in Topological Maps
Alberto Vale Maria Isabel [email protected] [email protected]
10th IEEE MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION 2
Instituto de
Sistemas e
Robótica
Objective
Robot Navigation in Outdoors Environment
• Highly non-structured environments
• Large amount of available information
• Physical area with large dimensions
10th IEEE MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION 3
Instituto de
Sistemas e
Robótica
Problem Relevance
• Safety concerns are leading to an increase in the use of robots. Mainly in outdoors environments where a communication channel might not be available and the robot may have to operate autonomously rather than being remotely operated by a central station
• Outdoors environments mean large and unstructured physical area, which can change in time and where scarcea priori information is usuallyavailable
10th IEEE MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION 4
Instituto de
Sistemas e
Robótica
Navigation Uncertainty
Uncertainty
Impossible to work with
T
T+1
T+3
T+2
Uncertainty
Uncertainty
Uncertainty
Mobile platform navigation along
time
…
10th IEEE MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION 5
Instituto de
Sistemas e
Robótica
Navigation Uncertainty Bounding
Uncertainty
Environment Model
+Sensor Model
Probabilistic Approach
...T T+1 T+2
Uncertainty Uncertainty
Probabilistic Approach
Probabilistic Approach
...
10th IEEE MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION 6
Instituto de
Sistemas e
Robótica
Navigation Block Diagram
Environment Model
Defines a set of states as an environment model using Markov Models
LocalizaçãoLocalizationProbabilistic approach to evaluate the localization on the environment model
Navigation Defines an optimized trajectory to the goal based on the environment model
Path Execution
Guides the mobile robot through the trajectory with obstacle avoidance
10th IEEE MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION 7
Instituto de
Sistemas e
Robótica
qt {s1,s2,s3,s4,s5,s6,s7}
robot state in
time instant t
set of states of the topological map
A set of properties
defines each state si (ex:
color, pattern, geometry, reflectance, temperature, height, etc)
s2
s3
s6
s5
s7
s1s4
Topological Map
, q2 = s4
t=2
, q3 = s5
t=3
q4 = s3
t=4
, q5 = s6
t=5
q1 = s1
t=1
Environment Model
sum of Gaussians
L
lililtil RoNk
1
),,(
10th IEEE MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION 8
Instituto de
Sistemas e
Robótica
Markov Models (to support robot navigation)
q1 q2 q3 qt
o1 o2 o3 ot
...
qt is the robot state in time instant t, qt {s1,s2, ... ,si, ... ,sN }
ot is the observation in time instant t
QT ={q1,q2,...,qT} is a sequence of states from t=1 to t=T
OT ={o1,o2,...,oT} is a sequence of observations from t=1 to t=T
states of the topological map
10th IEEE MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION 9
Instituto de
Sistemas e
Robótica
• Initial State Distribution
• State Transition Probability Distribution
• Observation Probability Distribution
)sP(q i1i
Set of parameters of the model
)sq|sP(qa itjtij 1
)sq|P(o)(ob ittti
a priori information
dependent of distances between states
10th IEEE MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION 10
Instituto de
Sistemas e
Robótica
Localization
How to identify the state qt (or sequence of states) based on
observations obtained until time instant T ?
)o,...,o,o|sP(qmaxargq̂ T21itq
tt
)sq|o,...,P(o)sq,o,...,P(o
)o,...,o,P(o
)sq|o,...,P(o)sq,o,...,P(o
)o,...,o,P(o
)sq,o,...,o,P(o
)o,...,o,o|sP(q
itT1titt1
T21
itT1titt1
T21
itT21
T21it
Information from the past of instant t Information from the future of instant t
10th IEEE MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION 11
Instituto de
Sistemas e
Robótica
0 1 2 … t-1 t t+1 … T time
t t
)sq|o,...,P(o)sq,o,...,P(o
)o,...,o,o|sP(q
itT1titt1
T21it
Information from the past of instant t Information from the future of instant t
Forward-Backward (FB) algorithm
0 t T
N
jttjijt
tj
N
iijtt
jobai
obaij
111
11
1
)()()(
)()()(
Nii
ob
sqoPsqPi
T
ii
ii
1,1)(
)(
)|()()(
1
1111
10th IEEE MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION 12
Instituto de
Sistemas e
Robótica
FB algorithm revisited
0 1 2 … t ... T1+1 time
t
T1
t
T1
2
1
12
21
)(
,)()( 1
TT
Tt
Tt
Tt
Tt
i
Ttjj
t
T2
T2
T1
… T2 time
More observations
= tT2
10th IEEE MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION 13
Instituto de
Sistemas e
Robótica
FB algorithm revisited
… (k-1)T kT t (k+1)T … time
observationsT
)sq|o,...,P(o)sq,o,...,P(o
)o,...,o,o,o,...,o,o|sP(q
itTkT1tittkT
1)T(k1kTkT1-kT21it
kT t kT+1
t (i)kT+T t (i)
kT+T
N
j
TkTttjij
TkTt
tj
N
iij
TkTt
TkTkT
jobai
obaij
111
11
1
)()()(
)()()(
Nii
ob
sqoPsqP
i
TkTTkT
kTiTkT
i
ikTkTikT
TkTkT
1,1)(
)(
)|()(
)(
1
111
1
10th IEEE MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION 14
Instituto de
Sistemas e
Robótica
Simulation Results
Experimental results of Robot Localization with 6 states
(s1, s2, s3, s4, s5, s6)
Each state is identified with 3 different attributes
(example)
Attri
bute
1
(col
ors
- RG
B)
Attri
bute
2
(geo
met
ry)
At
tribu
te 3
(tem
pera
ture
)
...
s1
s2
s3
s4
s5
s6
P1 P2 P3 P4
P5
P6
P7
P8
P9
P10
P11
P12
P13
P14 P15 P16 P17
P18
P19
P20
P21
P22
v1 v2 v3 v4 v5
v1 v2 v3 v4 v5
v1 v2 v3 v4 v5
v1 v2 v3 v4 v5
v1 v2 v3 v4 v5
10th IEEE MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION 15
Instituto de
Sistemas e
Robótica
Simulation Results
Localization probability as result of a path execution
)o,...,o,o|sP(q T21it
Pj - via points
10th IEEE MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION 16
Instituto de
Sistemas e
Robótica
Log of Prob. Localization (new paths)
Observation variance 12Observation variance 2
2 = 412Observation variance 1
2 = 2512
10th IEEE MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION 17
Instituto de
Sistemas e
Robótica
Future Development
• Development of new techniques to adjust the model
parameters aij (state transition probability distribution)
• Adjust the parameters kil , uil and Ril of the environment model
according to attributes
• Identify new attributes (if necessary) which adds more
information to each state
• Identify and remove useless attributes
10th IEEE MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION 18
Instituto de
Sistemas e
Robótica
Future Development
As a challenging application, this will be applied in the Rescue Project.
The outdoor navigation will be applied on the wheeled robot using all the sensors information from the team.
This project will endow a team of two outdoors robots with cooperative navigation capabilities in search and rescue-like operation under large-scale catastrophe scenarios.
