An Improved Active SLAM Algorithm for Multi-Robot Exploration
Viet-Cuong Pham and Jyh-Ching Juang National Cheng Kung University, Taiwan
September 16, 2011
SICE 2011 Tokyo, Japan
Supported by:
1. Introduction
2. Active SLAM problem with multiple robots 3. Proposed approach
General framework
Exploration phase with global optimization strategy
Relocalization phase
Adaptive uncertainty threshold
Limited communication range 4. Simulations and Discussions 5. Conclusions
Outline
Exploration
Robots cover the environment with their sensors
SLAM (Simultaneous Localization and Mapping)
A mobile robot attempts to build a map
At the same time uses this map to deduce its location
Ordinary SLAMs
Only process perceived sensor data
Do not influence the motion of the mobile robot
Path control strategy can have a substantial impact on the quality of the resulting map
This study: blend concepts of SLAM, active path planning, and cooperation among multiple robots
1. Introduction
1. Introduction
Robot
system Cooperative SLAM References Single No Active [9], [10], [11], [17]
Multiple No No [21]
Multiple Yes No [6], [7], [8], [13], [14], [15], [18], [20], [22]
Multiple Yes Passive [2], [3], [16], [19]
Multiple Yes Active [12], this study
Comparison of different exploration methods
The state vector
: pose of the r-th robot at time k : position of the l-th landmark
2. Active SLAM problem with multiple robots
1 2 1 2
( )k T ( )k T ( )k TR( )k T T TL T
x x x x q q q
( ) for 1, 2,
r k r R
x
for 1,2,
l l L
q
Process model:
Measurement model:
2. Active SLAM problem with multiple robots
1 1 1
1
( ( 1), ( )) ( )
( ( 1), ( )) ( )
( ) 0
0
R
R R R R
L
f k k k
f k k k
k
x u w
x u w
x q
q
2 2
, ,
( ) ( )
( ) ( ) ( )
( ) arctan
( )
r l r l
r l r l
r l
r
r l
x k x y k y
k y k y k
k x k x
y v
Objectives:
Cover the whole environment in a minimum amount of time
Guarantee the accuracy of the map Constrained optimization problem
: pose error covariance of the r-th robot α : predefined threshold
exploration time
, 1,2, , trace r r R min
Subject to P
Pr
2. Active SLAM problem with
multiple robots
Two parts:
Path generation: determining a target point for each robot
SLAM operation
Two-phase process
3. Proposed approach
General framework
Frontier-based exploration
Existing method:
Disperse robots at local level
Assume a priori knowledge of the environment
Proposed: Global optimization strategy
Globally disperse robots
Do not assume a priori knowledge of the environment
3. Proposed approach
Exploration phase
Objective function
: utility of information
: utility of localizability (distinguish between target points with different localization quality) : cost of navigation
: weighting factors : penalty coefficient
: assignment matrix
Determine A: integer programming problem
3. Proposed approach
Exploration phase
1 1
1 1 1 1
( , ) ( , )
( , ) ( , ) ( , )
( , ) ( , )
R T I I L L
exploration N N
r t
w U r t w U r t
J r t r t w C r t
r t r t
A
( , ) U r tI
1( , ) UL r t
1( , ) CN r t
1 1
, ,
I L N
w w w
A
Objective: maintain the accuracy of the map
Robot switches to relocalization phase when pose uncertainty becomes large
Revisit previously seen landmarks
Rendezvous with other robots
3. Proposed approach
Relocalization phase
Objective function
: utility of localizability : cost of navigation
: loss due to interruption of exploration task (if other robots involved)
: distance to the nearest exploration point : weighting factors
3. Proposed approach
Relocalization phase
L D
2, 2, , 2
L N Loss D
w w w w
2 2 2 2 2
relocalization L L N N Loss D
J w U w C w L w D
2
UL 2
CN
r-th robot: revisit A or meet s-th robot at C?
D: to assess the effort needed to go back to perform exploration
3. Proposed approach
Relocalization phase
2 2 2 2 2
relocalization L L N N Loss D
J w U w C w L w D
A
Fixed threshold α: robots may get stuck in regions with few or no landmarks
Repeatedly switching between exploration and relocalization phases
3. Proposed approach
Adaptive uncertainty threshold
Temporary increase the uncertainty threshold
Threshold should be reduced asap: avoid large error in the exploration process afterwards.
When to reduce?
Robot pose uncertainty decreases
Landmark density is high
3. Proposed approach
Adaptive uncertainty threshold
Keep robots within communication range?
Robots are allowed to temporary move out of the communication range and rendezvous later
Objective function for choosing rendezvous point
: utility of localizability : cost of navigation
: distance to the nearest exploration point : weighting factors
D
3, 3, 3
L N D
w w w
3
UL 3
CN
3. Proposed approach
Limited communication range
3 3 3 3 3
rendezvous L L N N D
J w U w C w D
Noise covariance matrices
Destination is recomputed whenever a robot reached its current destination or a robot has moved 3 m
Control signals: applied every 0.025 s
Range and bearing measurements: taken every 0.2s
Mean velocity of the robots: 3 m/s
Sensor range: 20 m
No. of runs: 20
4. Simulations & Discussions
2 2
2 0 2
0.3 0
0
0 0 3
velocity
steering
m s
Q
2 2
2 0 2
0.1 0
0
0 0 1
range
bearing
m
R
Case A (proposed): global optimization strategy
4. Simulations & Discussions
Global optimization strategy
Case B: without global optimization strategy
64.6%
4. Simulations & Discussions
Global optimization strategy
4. Simulations & Discussions
Adaptive uncertainty threshold
A snap-shot of an
unfinished exploration mission with fixed
uncertainty threshold
4. Simulations & Discussions
Limited communication range
Case G: robots are allowed to move out of communication, no rendezvous
Case H: robots are allowed to move out of communication and rendezvous later
4. Simulations & Discussions
Limited communication range
An improved active SLAM algorithm for multi-robot exploration is presented
Three important improvements:
A global optimization strategy in the exploration phase
An adaptive strategy: automatically adjust the threshold of the robot pose uncertainty constraints
Rendezvous technique: deal with the limited communication range problem
Improved approach outperforms the original one
5. Conclusions
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References
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