interval analysis for global localization problem …...interval analysis for global localization...
TRANSCRIPT
The Global Localization ContextThe Proposed Method
The Simulator
Interval Analysis for Global Localization Problemusing Range Sensors
Remy GUYONNEAU, Sebastien LAGRANGE, LaurentHARDOUIN and Philippe LUCIDARME.
Laboratoire d’Ingenierie des Systemes Automatises (LISA),University of Angers,
France.
June 13, 2011
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 1
The Global Localization ContextThe Proposed Method
The Simulator
Introduction
F Robot localization is an important issue of mobile robotics.
F Robotics challenge CAROTTE1
F Simultaneous Localization And Mapping (SLAM) and GlobalLocalization problems.
F In this presentation a set membership approach will beconsidered to deal with the global localization problem.
1CArtographie par ROboT d’un TErritoire (Robot Land Mapping) organizedby the french ANR (National Research Agency).
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 2
The Global Localization ContextThe Proposed Method
The Simulator
Outline
1 The Global Localization Context
2 The Proposed MethodThe Static localizationThe Global Localization Algorithm
3 The Simulator
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 3
The Global Localization ContextThe Proposed Method
The Simulator
The RobotThe EnvironmentThe Objective
The Global Localization Context
1 The Global Localization Context
2 The Proposed MethodThe Static localizationThe Global Localization Algorithm
3 The Simulator
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 4
The Global Localization ContextThe Proposed Method
The Simulator
The RobotThe EnvironmentThe Objective
The Robot
The considered robot
We consider a mobile wheeled robot with a LIDARa sensor. Its
pose is defined by p =
xyθ
, with (x , y) its localization and θ
its orientation.
aLight Detection And Ranging
The measurements
The sensor provides a set of nmeasurements:
D =
d0 = (d0x , d0y )...
dn = (dnx , dny )
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 5
The Global Localization ContextThe Proposed Method
The Simulator
The RobotThe EnvironmentThe Objective
The Robot
Robot Obstacle
Figure 1: The robot’s pose.
Robot Obstacle
Figure 2: A measurement di .
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 6
The Global Localization ContextThe Proposed Method
The Simulator
The RobotThe EnvironmentThe Objective
The Environment
The map
The known environment E ∈ R2 is discretized with a resolution δx ,δy and this lead to a grid G composed of n ×m cells (i , j). Ateach cell (i , j) is associated gi ,j ∈ {0, 1}:
gi ,j =
{1 if there is an obstacle in the cell (i , j),
0 else.
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 7
The Global Localization ContextThe Proposed Method
The Simulator
The RobotThe EnvironmentThe Objective
The Objective
Hypotheses
↪→ Bounded error context,
↪→ Outliers are considered,
Figure 3: Measurements from thesensor.
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 8
The Global Localization ContextThe Proposed Method
The Simulator
The RobotThe EnvironmentThe Objective
The Objective
Figure 4: We have a grid map.
Hypotheses
↪→ Bounded error context,
↪→ Outliers are considered,
Figure 5: Measurements from thesensor.
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 8
The Global Localization ContextThe Proposed Method
The Simulator
The RobotThe EnvironmentThe Objective
The Objective
Figure 4: We have a grid map.
Hypotheses
↪→ Bounded error context,
↪→ Outliers are considered,
Figure 5: Measurements from thesensor.
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 8
The Global Localization ContextThe Proposed Method
The Simulator
The RobotThe EnvironmentThe Objective
The Objective
Figure 4: We have a grid map.
Hypotheses
↪→ Bounded error context,
↪→ Outliers are considered,
Figure 6: Initial domain.
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 9
The Global Localization ContextThe Proposed Method
The Simulator
The RobotThe EnvironmentThe Objective
The Objective
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 10
The Global Localization ContextThe Proposed Method
The Simulator
The RobotThe EnvironmentThe Objective
The Objective
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 10
The Global Localization ContextThe Proposed Method
The Simulator
The RobotThe EnvironmentThe Objective
The Objective
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 10
The Global Localization ContextThe Proposed Method
The Simulator
The RobotThe EnvironmentThe Objective
The Objective
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 10
The Global Localization ContextThe Proposed Method
The Simulator
The RobotThe EnvironmentThe Objective
The Objective
The robot is localized
All the measurements fit withthe map.
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 11
The Global Localization ContextThe Proposed Method
The Simulator
The RobotThe EnvironmentThe Objective
The Objective
The robot is localized
Except for one outlier.
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 11
The Global Localization ContextThe Proposed Method
The Simulator
The Static localizationThe Global Localization Algorithm
The Proposed Method
1 The Global Localization Context
2 The Proposed MethodThe Static localizationThe Global Localization Algorithm
3 The Simulator
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 12
The Global Localization ContextThe Proposed Method
The Simulator
The Static localizationThe Global Localization Algorithm
The Static localization
The Context
Let [p] =
[x ][y ][θ]
be an initial domain that encloses the robot’s
pose p =
xyθ
and D =
d0...dn
a set of n measurements.
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 13
The Global Localization ContextThe Proposed Method
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The Static localizationThe Global Localization Algorithm
The Static localization
The Robot-Measurement Distance
||di ||2 = (x − wix )2 + (y − wiy )2.
Robot Obstacle
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 14
The Global Localization ContextThe Proposed Method
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The Static localizationThe Global Localization Algorithm
The Static localization
The Measurement-Measurement Distance
||di − dj ||2 = (wix − wjx )2 + (wiy − wjy )2.
Robot Obstacle
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 15
The Global Localization ContextThe Proposed Method
The Simulator
The Static localizationThe Global Localization Algorithm
The Static localization
The Measurements Coordinates
The coordinates (wix ,wiy ) of an obstacle in the map are defined by:(wix
wiy
)=
(cos(θ) sin(θ)−sin(θ) cos(θ)
)(dixdiy
)+
(xy
)
Robot Obstacle
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 16
The Global Localization ContextThe Proposed Method
The Simulator
The Static localizationThe Global Localization Algorithm
The Static localization
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 17
The Global Localization ContextThe Proposed Method
The Simulator
The Static localizationThe Global Localization Algorithm
The Static localization
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 17
The Global Localization ContextThe Proposed Method
The Simulator
The Static localizationThe Global Localization Algorithm
The Static localization
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 17
The Global Localization ContextThe Proposed Method
The Simulator
The Static localizationThe Global Localization Algorithm
The Static localization
The map constraint.
We define cG the constraintwhich says that themeasurement has to beconsistent with the map.
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 17
The Global Localization ContextThe Proposed Method
The Simulator
The Static localizationThe Global Localization Algorithm
The Static localization
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 17
The Global Localization ContextThe Proposed Method
The Simulator
The Static localizationThe Global Localization Algorithm
The Static localization
The map contractor.
We define CG the contractorof the constraint cG.
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 17
The Global Localization ContextThe Proposed Method
The Simulator
The Static localizationThe Global Localization Algorithm
The Static localization
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 17
The Global Localization ContextThe Proposed Method
The Simulator
The Static localizationThe Global Localization Algorithm
The Static localization
Considered Constraint Satisfaction Problem
V = {x , y , θ,di = (dix , diy )T ,wix ,wiy with i = 1, · · · , n},
D = {[x ] = [−∞,+∞], [y ] = [−∞,+∞], [θ] = [0, 2π],[wix ] = [−∞,+∞], [wiy ] = [−∞,+∞],[dix ] =obtained from the sensor,[diy ] =obtained from the sensor}.
C =
cwix: dix cos(θ) + diy sin(θ) + x
cwiy: −dix sin(θ) + diy cos(θ) + y
cdi : ||di ||2 = (x − wix )2 + (y − wiy )2
cdi,j : ||di − dj ||2 = (wix − wjx )2 + (wiy − wjy )2
cG : to be consistent with the map (using CG)
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 18
The Global Localization ContextThe Proposed Method
The Simulator
The Static localizationThe Global Localization Algorithm
The Global Localization Algorithm
1 The Global Localization Context
2 The Proposed MethodThe Static localizationThe Global Localization Algorithm
3 The Simulator
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 19
The Global Localization ContextThe Proposed Method
The Simulator
The Static localizationThe Global Localization Algorithm
The Global Localization Algorithm
Assumption
We assume u = (ur , ul) the knowledge of the moving of the robot,with ur the speed of the right wheel and ul the speed of the leftwheel.
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The Global Localization ContextThe Proposed Method
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The Static localizationThe Global Localization Algorithm
The Global Localization Algorithm
Prediction Equation
f (pk ,uk) = pk+1 =
xk+1
yk+1
θk+1
=
xk +ukr +ukl
2 cos(θk)
yk +ukr +ukl
2 sin(θk)
θk +ukr−ukl
2
.
Retro-propagation Equation
f −1(pk+1,uk) = pk =
xk+1 −ukr +ukl
2 cos(θk+1 −ukr−ukl
2 )
yk+1 −ukr +ukl
2 sin(θk+1 −ukr−ukl
2 )
θk+1 −ukr−ukl
2
.
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 21
The Global Localization ContextThe Proposed Method
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The Static localizationThe Global Localization Algorithm
The Global Localization Algorithm
Three Constraints
To be consistent with a data set and the map: The staticlocalization.
Retro-propagation : pk−1 = f −1(pk ,uk−1),
Prediction : pk+1 = f (pk ,uk),
with pk−1 ∈ Pk−1,pk ∈ Pk ,pk+1 ∈ Pk+1,uk−1 ∈ [uk−1] anduk ∈ [uk ].
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 22
The Global Localization ContextThe Proposed Method
The Simulator
The Static localizationThe Global Localization Algorithm
The Global Localization Algorithm
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 23
The Global Localization ContextThe Proposed Method
The Simulator
The Static localizationThe Global Localization Algorithm
The Global Localization Algorithm
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 23
The Global Localization ContextThe Proposed Method
The Simulator
The Static localizationThe Global Localization Algorithm
The Global Localization Algorithm
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 23
The Global Localization ContextThe Proposed Method
The Simulator
The Static localizationThe Global Localization Algorithm
The Global Localization Algorithm
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 23
The Global Localization ContextThe Proposed Method
The Simulator
The Static localizationThe Global Localization Algorithm
The Global Localization Algorithm
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 23
The Global Localization ContextThe Proposed Method
The Simulator
The Static localizationThe Global Localization Algorithm
The Global Localization Algorithm
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 23
The Global Localization ContextThe Proposed Method
The Simulator
The Static localizationThe Global Localization Algorithm
The Global Localization Algorithm
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 23
The Global Localization ContextThe Proposed Method
The Simulator
The Static localizationThe Global Localization Algorithm
The Global Localization Algorithm
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 23
The Global Localization ContextThe Proposed Method
The Simulator
The Static localizationThe Global Localization Algorithm
The Global Localization Algorithm
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 23
The Global Localization ContextThe Proposed Method
The Simulator
The Static localizationThe Global Localization Algorithm
The Global Localization Algorithm
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 23
The Global Localization ContextThe Proposed Method
The SimulatorDemonstration
The Simulator
1 The Global Localization Context
2 The Proposed MethodThe Static localizationThe Global Localization Algorithm
3 The Simulator
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 24
The Global Localization ContextThe Proposed Method
The SimulatorDemonstration
Demonstration
Simulation parameters
I A 1000× 1000 cells occupancy grid map (10× 10 meters).
I Each measurement has a bounded error of 10 centimetres anda max range dmax = 3 meters.
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 25
The Global Localization ContextThe Proposed Method
The SimulatorDemonstration
Demonstration
R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 26
The Global Localization ContextThe Proposed Method
The Simulator
Conclusion
F In this presentation we have seen that interval analysis couldbe used to solve the global localization problem.
F This method uses a discrete map so the time processingdepends of the size of the grid.
F The simulation results are promising and this method can beefficient in a real context.
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The Global Localization ContextThe Proposed Method
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ConclusionFuture work
F Experimental tests after the CAROTTE challenge.
F The using of topological maps.
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The Global Localization ContextThe Proposed Method
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ConclusionFuture work
F Experimental tests after the CAROTTE challenge.
F The using of topological maps.
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The Global Localization ContextThe Proposed Method
The Simulator
ConclusionFuture work
F Experimental tests after the CAROTTE challenge.
F The using of topological maps.
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R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 29
The Global Localization ContextThe Proposed Method
The Simulator
ConclusionFuture work
F Experimental tests after the CAROTTE challenge.
F The using of topological maps.
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R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 29
The Global Localization ContextThe Proposed Method
The Simulator
ConclusionFuture work
F Experimental tests after the CAROTTE challenge.
F The using of topological maps.
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R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 29
The Global Localization ContextThe Proposed Method
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Questions
??R. Guyonneau, S. Lagrange, L. Hardouin, P. Lucidarme Interval Analysis for Global Localization Problem using Range Sensors 30