슬라이드 1

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Transcript 슬라이드 1

Vision-based SLAM Enhanced by
Particle Swarm Optimization
on the Euclidean Group
Vision seminar : Dec. 30. 2009
Young Ki BAIK
Computer Vision Lab.
ComputerVisionLab
Seoul National University
Outline
Introduction
Related works
Problem statement
Proposed algorithm
PSO-based visual SLAM
Single camera SLAM using ABC algorithm
Demonstration
Conclusion
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Seoul National University
What is SLAM?
SLAM : Simultaneous Localization And Mapping
ComputerVisionLab
Seoul National University
Why visual SLAM?
To acquire observation data
Use many different type of sensor
Laser rangefinders, Sonar sensors
Too expensive : about 2000$
Scanning system : complex mechanics
Camera
Low price : about 30$
Acquire large and meaningful information
from one shot measure
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Seoul National University
How to solve SLAM problem?
SLAM problem
Solved by filtering approaches
Extended Kalman Filter (EKF)
has scalability problem of the map
Rao-Blackwellised Particle Filter
(RBPF)
handles nonlinear and non-Gaussian
reduces computation cost by decomposing sampling space
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Seoul National University
Previous works
EKF-based visual SLAM
Andrew Davison (1998)
Stereo camera + odometry
Andrew Davison (2002)
Single camera without odometry
RBPF-based visual SLAM
Robert Sim (2005)
Stereo camera + odometry
Mark Pupilli (2005)
Single camera without odometry
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Seoul National University
RBPF-SLAM
State equation
(Process noise)
(User input or odometry)
(Nonlinear stochastic difference equation)
Measurement equation
(Measurement noise)
(Camera projection function)
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Seoul National University
Problem of RBPF-SLAM
How to choose importance function?
?
t
Odometry
Naive motion model
Constant position
Xt+1=Xt+N
Angle
Change
+
Distance
Change
Left
Encoder
Distance
t+1
Right
Encoder
Distance
Constant velocity
Xt+1=Xt+∇t(Vt+N)
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Seoul National University
Problem of RBPF-SLAM
Sampling by transition model
Landmark
Particle
Robot
t
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Problem of RBPF-SLAM
Sampling by transition model
t
t+1
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Seoul National University
Problem of RBPF-SLAM
Sampling by transition model
t
t+1
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Seoul National University
Problem of RBPF-SLAM
Sampling by transition model
t+1
(Gaussian)
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Seoul National University
Problem of RBPF-SLAM
Sampling by transition model
t+1
ComputerVisionLab
Seoul National University
Problem of RBPF-SLAM
How to choose importance function?
Hand-held camera case
?
t
t+1
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Seoul National University
RBPF-SLAM
Sampling by transition model
t
t+1
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Problem of RBPF-SLAM
Particle impoverishment
Mismatch between proposal and likelihood distribution.
Likelihood
Proposal
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Optimal Importance Function (OIF)
For better proposal distribution
Use observation for proposal distribution
Optimal importance function approach
(Doucet et al., 2000)
- Observation incorporated proposal
- Linearize the optimal importance function
- Used in FastSLAM 2.0 (Montemerlo et al.)
The state of the art !!
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Seoul National University
Optimal Importance Function (OIF)
Sampling by optimal importance function
OIF
t
t+1
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Seoul National University
Problem of OIF-based SLAM
Linearization Error
Smooth camera motion
Abrupt camera motion
Linearization Error
: Real camera state
: Estimated camera state by linearization
: Predicted camera state by a motion model
ComputerVisionLab
Seoul National University
Problem statement
OIF-based visual SLAM
State of the art
Weak to abrupt camera motion
Novel visual SLAM
robust to abrupt camera motion
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Target
Proposed SLAM system
6-DOF SLAM
Hand-held camera
Single or stereo camera
No odometry
RBPF-based SLAM
Robust to sudden changes
Real-time system
ComputerVisionLab
Seoul National University
Our contribution
We propose …
Novel particle filtering framework
combined with geometric PSO
Based on special Euclidean group SE (3)
Reformulating original PSO in consideration of SE (3)
Applying Quantum particles
to more actively explore the problem space
Robust to abrupt camera motion!!
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Seoul National University
Special Euclidean group SE (3)
Conventional
State
6-D vector
by local coordinates
Geometric
as a Lie group SE(3)
State Equation
Ignores geometry of the underlying space
Considers geometry of the curved space!
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Special Euclidean group SE (3)
6D vector  Euclidean group SE(3)
Lie group  Group + Differentiable manifold
Lie algebra  Tangent space at the identity (se(3))
Origin
Exp Log
se(3)
Identity
SE(3)
Exp: se(3)  SE(3)
Log: SE(3)  se(3)
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Special Euclidean group SE (3)
6D vector  Euclidean group SE(3)
Sampling on Tangent space at the identity (se(3))
Reasonable to consider the geometry of motion
Sampling
se(3)
Exp
SE(3)
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Main idea
We use optimization method for better proposal distribution…
Particle Swarm Optimization
Propagate particles
using motion prior
Prior
PSO Moves
Particles
with high
likelihood
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Seoul National University
Particle Swarm Optimization
Developed in evolutionary computation community
Sampling-based optimization method
Uses the relationship between particles
PSO
OIF
Interaction
Linearization
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Seoul National University
Particle Swarm Optimization
Particle from motion prior
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Particle Swarm Optimization
Initialization
(current optimum)
(individual best)
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Seoul National University
Particle Swarm Optimization
Particle from motion prior
(current optimum)
(individual best)
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Seoul National University
Particle Swarm Optimization
Particle from motion prior
(current optimum)
(individual best)
(Inertia)
(Coefficient)
(Random)
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Particle Swarm Optimization
Velocity updating
(current optimum)
(individual best)
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Particle Swarm Optimization
Moving
(current optimum)
(individual best)
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Particle Swarm Optimization
Global and local best updating
(current optimum)
(individual best)
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Particle Swarm Optimization
For all Particles
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Geometric Particle Swarm Optimization
 
Tangent space at
X iold
log Xi Xiold
old
 
old
log Xi Pgb
old
 
log Xi Pibi
Manifold
v i
X iold
v iold
Pgb
exp Xi
old
X
i
new
Pibi
Random perturbation &
coefficient multiplication
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Seoul National University
Experiments
System environment
CPU : Intel Core-2 Quad 2.4 GHz process
Real-time with C++ implementation
Synthetic sequence
Real sequence
Virtual stereo camera
Quantitative analysis
Bumblebee stereo camera
(BB-HICOL-60)
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Demonstration
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Demonstration
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Artificial Bee Colony
Additional work !!
Visual Odometry
Determining the position and orientation of a robot
by analyzing the associated camera images …
David Nister (2004)
Monocular or binocular camera
Yang Cheng et al. (2008)
Stereo camera
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Artificial Bee Colony
Additional work !!
Propagate particles
via visual odometry
Propagate particles
using motion prior
PSO Moves
PSO Moves
Particles
with high
likelihood
Artificial Bee Colony
ComputerVisionLab
Seoul National University
Conclusion
Novel visual SLAM is presented !!
RBPF based on the special Euclidean group SE (3)
Geometric Particle Swarm Optimization
Robust to abrupt camera motion
Real-time system
Novel monocular SLAM will be presented !!
Geometric Artificial Bee Colony
Combined proposal ( VO + Naive motion model )
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Q
&
A
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