Active SLAM : a Framework My, on-going, PhD Research Henry
Carrillo Lindado Advised by: Jos A. Castellanos
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Bio Academic Background Name: Name: Henry David Carrillo
Lindado. Hometown Hometown : Barranquilla Colombia. Academic: PhD
in Computer Science and System Engineering (2010 -2014) University
of Zaragoza - Spain M.Sc. in Computer Science and System
Engineering M.Sc. in Electronics Engineering B.Eng. in Electronics
Engineering Funding: Funding: FPI scholarship by the Ministry of
Science and Innovation of Spain. 2010-2014. Contact: Here: 0.59
Cartesium [email protected]
http://webdiis.unizar.es/~hcarri/pmwiki/pmwiki.php 1
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So, What is my PhD about? Objective: Objective: To build an
active SLAM framework. Why? Why? : Where should I go in order to
improve my localization and map representation? If I go from A to
B, will I be lost (e.g. Unable to localize)? X What movements
should I make in order to keep my metrical error below X mm? Aim
at: Metrical representations. Topological representations.
Metrical+Topological representations. 2
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What have I done? Metrical 3
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Preliminaries SLAM H 0 : H 0 : A model of the operative
environment is an essential requirement for an autonomous mobile
robot. Three basic tasks: Where am I? What does the world look
like? Where do I go? SLAM => Joint of two tasks. SLAM => Does
not define the path-trajectory of the robot. Integrated approach
=> On the way to autonomy. 4 Exploration and Mapping with Mobile
Robots. Cyrill Stachniss. 2006.
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Preliminaries Active SLAM (I) Active SLAM => To integrate
path planning into a SLAM process. To explorer more area. Navigate
safely. Reduce uncertainty. Algorithms 1 Alg. [Feder, Leonard](99)
Active perception [Bajacksy](86) Infinite Horizon and MPC [Leung,
Dissanayake](06) 5
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Preliminaries Active SLAM (II) 6
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Preliminaries Active SLAM (II) 6J1J2J3J4J5 11,51,90,83
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Uncertainty Criteria for Active SLAM (I) 7 Theory of Optimal
Experiment Design (A-opt, D-opt, E-opt). Information Theory (
Entropy, MI).
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Uncertainty Criteria for Active SLAM (II) Some possible
uncertainty criteria for active SLAM are: Previous works ([Sim and
Roy, 2005], [Mihaylova and De Schutter, 2003]) report A-opt as the
best criterion and that D-opt gives null values. A-opt, widely
used: [Kollar2008] [MartinezCantin2008] [Meger2008]
[Dissanayake2006]. Although D-opt is commonly used in the TOED
because it is optimal. 8 Determinant (D-opt) Trace (A-opt) Max
(E-opt)
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Uncertainty Criteria for Active SLAM (III) It is indeed
possible to use D-opt in the Active SLAM context: The structure of
the problem needs to be taken into account (i.e. The covariance
matrix varies with time). ll mm. It is not informative to compare
the determinant of a matrix l x l with a m x m. det(l x l) is
homogeneous of grade l. The computation of the determinant of a
highly correlated matrix (e.g. SLAM) is prone to round-off errors.
Processing in the logarithm space D-opt for a l x l covariance
matrix: Stem from [Kiefer, 1974] : 9
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First experiment First experiment: on the computation Is it
possible to compute D-opt from a robot doing SLAM? Execute a SLAM
algorithm (e.g. EKF-SLAM, iSAM). Compute in each step: A-opt,
E-opt, D-opt, Determinant, entropy and mutual Information.
Simulated Robot indoor environment : MRPT/C++ Real Robot indoor
environment : Pioneer 3 DX - Ad-hoc Real Robot indoor environment :
DLR dataset Real Robot outdoor environment : Victoria Park dataset
10
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1E - Simulated Robot indoor environment (I) Scenario: Area of
25x25 m 2D EKF-SLAM Sensor: Odometry + Camera (360 - 3m range) 180
landmarks - DA Known. Gaussian errors: Odometry + Sensors 11
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1E-Simulated Robot indoor environment (II) Qualitative results
(a)-(f) A-opt, E-opt, D-opt, determinant, entropy and MI. 12
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1E-Real Robot indoor environment @ DLR Scenario: Area 60x40 m
Sensor: Odometry + Camera 2D EKF-SLAM 576 landmarks DA known.
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First experiment Quantitative analysis Average correlation
between the uncertainty criteria: Variance: A-E (0,0002) / A-D
(0,0540) / D-E (0,0481). A-opt y E-opt => High correlation.
E-opt is guided by a single eigenvalue. A-opt y D-opt => Medium
correlation. H 0 : D-opt take into account more components than
A-opt. A-optE-optD-opt A-opt10,98720,6003 E-opt0,987210,5903
D-opt0,60030,59031 15
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Second Experiment Simulated Robot with unitary horizon: MRPT /
C++ 16
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2E-Simulated Robot indoor environment (I) Scenario: Area of
20x20m and 30x30m 2D EKF-SLAM Sensor: Odometry + Camera (360 - 3m
range) Gaussian errors: Odometry + sensors. Path planner: Discrete
(A*) and continuous (Attract-Repel). 17
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2E-Simulated Robot indoor environment (II) Resulting paths for
each uncertainty criterion: (a) D-opt, (b) A-opt y (c) Entropy.
Each colour represents an executed path. 20 x 20 m map. Qualitative
analysis 18
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2E-Simulated Robot indoor environment (III) Resulting
trajectories for 10000 steps active SLAM simulation. (a). Initial
trajectory. (b) A-opt. (c). D-opt. Qualitative analysis. 19
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2E Quantitative Analysis 30x30 m Evolution of MSE ((a)-(c)) y
chi2 ((d)-(f)) ratio. Average of 10 MC simulations. 20
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Take home message D-opt is the optimum criterion to measure
uncertainty according to the TOED (i.e. better than A-opt (Trace)).
It is possible to obtain useful information regarding the
uncertainty of a SLAM process with D-opt. D-opt shows better
performance than A-opt in our simulated experiments of active SLAM.
To compute D-opt in the context of a SLAM process => use the
formulation presented here. 21
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What have I done? Metrical: an example using D-opt 22
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FaMUS: Fast Minimum Uncertainty Search 17 AB Minimum
uncertainty path between A to B in a graph. Exhaustive search.
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FaMUS: Fast Minimum Uncertainty Search 17 AB Minimum
uncertainty path between A to B in a graph. Exhaustive search.
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FaMUS: Fast Minimum Uncertainty Search 24 minimum uncertainty
path shortest path Experiment: Are the minimum uncertainty path and
the shortest path necessarily equal? Select two points A and B, and
compare the final uncertainty. 1000 times x 4 datasets. (Biccoca,
Intel, New colleges and Manhattan).
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FaMUS: Fast Minimum Uncertainty Search 25 Examples of
paths.
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FaMUS: Fast Minimum Uncertainty Search 26 Summary of results
50% Improvement of a least 50% in timing respect to the state of
the art. [Valencia2011]
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What have I done? Topological 27
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Topological Guiding question: Where should I go in order to
improve my topological map? Challenges: well-posed and egocentric
images. Execute a SLAM algorithm (e.g. EKF-SLAM, iSAM). Compute in
each step: A-opt, E-opt, D-opt, Determinant, entropy and mutual
Information. 28
TBD Which are the confidence intervals in the active
predictions? When do I stop the active behaviour? Find a
relationship between uncertainty and metrical error. Use other
constraints other than uncertainty. Speed up the decision process.
Real experiments. 31
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Active SLAM : a Framework My, on-going, PhD Research Thanks!!!
[email protected] http://webdiis.unizar.es/~hcarri 32
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Experimentos Primer experimento : acerca del clculo Segundo
experimento : SLAM activo Robot simulado ambiente interior : MRPT /
C++ Robot real ambiente interior : Pioneer 3 DX - Ad-hoc Robot real
ambiente interior : DLR dataset Robot real ambiente exterior :
Victoria Park dataset Robot simulado con horizonte unitario : MRPT
/ C++ 7
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1E-Robot en ambiente exterior @ VP (I) Escenario: rea de 350 x
350 m iSAM Sensor: Odometra + Laser 150 landmarks DA conocida.
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1E-Robot en ambiente exterior @ VP (II) Resultados cualitativos
(a)-(f) A-opt, E-opt, D-opt, determinante, entropa y MI. 14
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1E-Robot en ambiente interior ad-hoc (I) Escenario: rea 6x4 m
2D EKF-SLAM Sensor: Odometra + Kinect 5 landmarks DA conocida
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1E-Robot en ambiente interior ad-hoc (II) Resultados
cualitativos (a)-(f) A-opt, E-opt, D-opt, determinante, entropa y
MI. 16
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2E - Anlisis cuantitativo 20x20 m Evolucin del MSE ((a)-(c)) y
chi2 ((d)-(f)). Promedio de 10 MC. 18
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Determinante 15
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Artculos Experimental Comparison of Optimum Criteria for Active
SLAM. Oral presentation in the III Workshop de Robtica: Robtica
Experimental (ROBOT11). On the Comparison of Uncertainty Criteria
for Active SLAM. Submitted to ICRA12. Planning Minimum Uncertainty
Paths Over Pose/Feature Graphs Constructed Via SLAM. Submitted to
ICRA12. 18
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On the Comparison of Uncertainty Criteria for Active SLAM
Thanks!!! [email protected] http://webdiis.unizar.es/~hcarri 19
