Post on 24-Feb-2016
description
Active SLAM : a FrameworkMy, on-going, PhD Research
Henry Carrillo LindadoAdvised by:
José A. Castellanos
Bio – Academic Background
Name: Henry David Carrillo Lindado. 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: FPI scholarship by the Ministry of Science and Innovation of Spain. 2010-2014.
Contact: Here: 0.59 Cartesium hcarri@unizar.es http://webdiis.unizar.es/~hcarri/pmwiki/pmwiki.php
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So, What is my PhD about? Objective: To build an active SLAM framework. 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)?
What movements should I make in order to keep my metrical error below X mm?
Aim at: Metrical representations. Topological representations. Metrical+Topological representations.
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What have I done?
Metrical
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Preliminaries – SLAM H0: 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.
Preliminaries – Active SLAM (I) Active SLAM => To integrate path planning into
a SLAM process. To explorer more area. Navigate safely. Reduce uncertainty.
Algorithms 1º Alg. [Feder, Leonard](99)
Active perception [Bajacksy](86) Infinite Horizon and MPC [Leung, Dissanayake](06)
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Preliminaries – Active SLAM (II)
Pseudo-code:
Set of trajectories Assign a score to each trajectory
Uncertainty of map+robot Trajectory constraints
Execute the trajectory with the optimum .
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Preliminaries – Active SLAM (II)
Pseudo-code:
Set of trajectories Assign a score to each trajectory
Uncertainty of map+robot Trajectory constraints
Execute the trajectory with the optimum .
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Preliminaries – Active SLAM (II)
Pseudo-code:
Set of trajectories Assign a score to each trajectory
Uncertainty of map+robot Trajectory constraints
Execute the trajectory with the optimum .
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J1 J2 J3 J4 J51 1,5 1,9 0,8 3
Preliminaries – Active SLAM (II)
Pseudo-code:
Set of trajectories Assign a score to each trajectory
Uncertainty of map+robot Trajectory constraints
Execute the trajectory with the optimum .
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J1 J2 J3 J4 J51 1,5 1,9 0,8 3
Uncertainty Criteria for Active SLAM (I) Uncertainty/Inform. Criteria =>
In the TOED, a design (i.e. ), is better than a design, if:
The above does not allow to quantify the improvement, therefore is desirable to:
It permits to quantify the uncertainty in .
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• Theory of Optimal Experiment Design (A-opt, D-opt, E-opt…).
• Information Theory ( Entropy, MI…).
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 (𝜆1 ,…,𝜆𝑘)
Max (E-opt)
trace (Σ )= ∑𝑘=1 ,… , 𝑙
𝜆𝑘det (Σ )= ∏𝑘=1 ,…, 𝑙
𝜆𝑘
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). 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
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 dataset10
1E - Simulated Robot indoor environment (I)
Scenario: Area of 25x25 m 2D EKF-SLAM Sensor: Odometry +
Camera (360º - 3m range)
180 landmarks - DA Known.
Gaussian errors: Odometry + Sensors
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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
1E-Real Robot indoor environment @ DLR
Scenario: Area 60x40 m Sensor: Odometry + Camera
2D EKF-SLAM 576 landmarks – DA known.
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1E-Real Robot indoor environment @ DLR Qualitative results
(a)-(f) A-opt, E-opt, D-opt, determinant, entropy and MI.14
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. H0: D-opt take into account more components than A-opt.
A-opt E-opt D-optA-opt 1 0,9872 0,6003E-opt 0,9872 1 0,5903D-opt 0,6003 0,5903 1
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Second Experiment Second experiment: Active SLAM
What is the effect of the uncertainty criteria in active SLAM?
Active SLAM => Unitary horizon (greedy). Uncertainty criteria => A-opt, D-opt and
Entropy. Effect => MSE y .• Simulated Robot with unitary horizon: MRPT /
C++
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2E-Simulated Robot indoor environment (I)
Scenario: Area of 20x20m and
30x30m 2D EKF-SLAM Sensor: Odometry +
Camera (360º - 3m range)
Gaussian errors: Odometry + sensors.
Path planner: Discrete (A*) and continuous (Attract-Repel).
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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
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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.
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2E – Quantitative Analysis 30x30 m
Evolution of MSE ((a)-(c)) y chi2 ((d)-(f)) ratio. Average of 10 MC simulations.
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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.
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What have I done?
Metrical: an example using D-
opt22
FaMUS: Fast Minimum Uncertainty Search
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• Minimum uncertainty path between A to B in a graph.
• Exhaustive search.
FaMUS: Fast Minimum Uncertainty Search
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• Minimum uncertainty path between A to B in a graph.
• Exhaustive search.
FaMUS: Fast Minimum Uncertainty Search
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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).
FaMUS: Fast Minimum Uncertainty Search
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Examples of paths.
FaMUS: Fast Minimum Uncertainty Search
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Summary of results
• Improvement of a least 50% in timing respect to the state of the art. [Valencia2011]
What have I done?
Topological
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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.
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Topological One solution:
Textons (a.k.a gist)- Undelaying Structure- Probabilistic decision
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What have I done?
TBD
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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.
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Active SLAM : a FrameworkMy, on-going, PhD Research
Thanks!!!hcarri@unizar.es
http://webdiis.unizar.es/~hcarri
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Experimentos Primer experimento : acerca del cálculo
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++
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1E-Robot en ambiente exterior @ VP (I)
Escenario: Área de 350 x 350 m iSAM Sensor: Odometría +
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, entropía y MI.14
1E-Robot en ambiente interior ad-hoc (I)Escenario:
Área 6x4 m 2D EKF-SLAM Sensor: Odometría +
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, entropía y MI.16
2E - Análisis cuantitativo 20x20 m
Evolución del MSE ((a)-(c)) y chi2 ((d)-(f)). Promedio de 10 MC.
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DeterminanteOperación algebraica que transforma una matriz en un escalar. Propiedades (matriz n x n)
Geométrica: Volumen del paralelepípedo definido en el espacio n-dimensional.
Homogéneo de grado n. Si,
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Artículos “Experimental Comparison of Optimum
Criteria for Active SLAM”. Oral presentation in the “III Workshop de Robótica: Robótica Experimental (ROBOT’11)”.
“On the Comparison of Uncertainty Criteria for Active SLAM”. Submitted to ICRA’12.
“Planning Minimum Uncertainty Paths Over Pose/Feature Graphs Constructed Via SLAM” . Submitted to ICRA’12.
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On the Comparison of UncertaintyCriteria for Active SLAM
Thanks!!!hcarri@unizar.es
http://webdiis.unizar.es/~hcarri
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FaMUS: Fast Minimum Uncertainty Search
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