Efficient GPU-based Construction of Occupancy Grids Using

EfficientGPU-basedConstruction

of OGs

Motivation

OccupancyGridsBayesian Model

Sensor Model

From rangeinformation to2D gridPrevious Work

GPU Imple-mentationGeneral AlgorithmArchitecture

Dirac model

Gaussian model

ResultsEvaluationAlgorithms

Evaluation

Fusion results

Summary andperspectives

Efficient GPU-based Construction ofOccupancy Grids Using several Laser

Range-finders

M. Yguel1 O. Aycard2 C. Laugier3

1Institut National Polytechnique de GrenobleProBayes S.A.

2University of Joseph Fourier

3Institut National de Recherche en Informatique et Automatique

International Conference on Intelligent Robots andSystems, 2006

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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results


Outline

1 Motivation

2 Occupancy GridsBayesian ModelSensor Model

3 From range information to 2D gridPrevious Work

4 GPU ImplementationGeneral Algorithm ArchitectureDirac modelGaussian model

5 Results EvaluationAlgorithmsEvaluationFusion results

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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results


Environment modelling

Enforce vehicle safety by• percieving the whole robot

surroundings,• being robust to false

measurements,• having precise map,• providing real-time map.

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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results


Occupancy Grids (OGs)

DefinitionAn OG is a stochastic tessellatedrepresentation of spatial informa-tion that maintains probabilistic es-timates of the occupancy state ofeach cell in a lattice [1].

Features:• no assumption about

environment geometry,• simple fusion process,• occultation information,• each cell is independent.

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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results





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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results





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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results





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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results





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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results


OGs drawback

Grids have image-like structures:• huge amount of data

e.g. 100mx100m grid with cell side of 5cm→ 4M cells

• enlarging the field of view→ increases the amount of data

• increasing precision→ increases the amount of data

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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results


OGs drawback

Grids have image-like structures:• huge amount of data

e.g. 100mx100m grid with cell side of 5cm→ 4M cells

• enlarging the field of view→ increases the amount of data

• increasing precision→ increases the amount of data

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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results


The Graphical Hardwares

Graphical processor units (GPUs):

• dedicated to work with images,• high level of parallelism,• easy to program with shading languages,• cheap.

Objective:accurate implementation of OG fusion with the GPU

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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results


The Graphical Hardwares

Graphical processor units (GPUs):

• dedicated to work with images,• high level of parallelism,• easy to program with shading languages,• cheap.

Objective:accurate implementation of OG fusion with the GPU

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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results


Outline

1 Motivation





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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results


OG Bayesian Model

• Variables:•−→Z = (Z1, . . . , Zn) a vector of n random variables,

• Ox,y ∈ O ≡ {occ, emp}. Ox,y is the state of the cell(x , y),

• joint probability distribution:

P(Ox ,y ,−→Z ) = P(Ox ,y )

n∏i=1

P(Zi |Ox ,y )

• inference:let −→z = (z1, . . . , zn) a vector of sensor measurements:

p(ox ,y |−→z ) =

p(ox ,y )∏n

i=1 p(zi |ox ,y )

p(occ)∏n

i=1 p(zi |occ) + p(emp)∏n

i=1 p(zi |emp)

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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results


OG Bayesian Model


• Ox,y ∈ O ≡ {occ, emp}. Ox,y is the state ofthe cell (x , y),

• joint probability distribution:

P( Ox ,y ,−→Z ) = P( Ox ,y )

n∏i=1

P(Zi | Ox ,y )

• inference:let −→z = (z1, . . . , zn) a vector of sensor measurements:

p( ox ,y |−→z ) =

p( ox,y )∏n

i=1 p(zi | ox,y )

p(occ)∏n


i=1 p(zi |emp)

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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results


OG Bayesian Model


• ∈ O ≡ {occ, emp}. is the state of the cell (x , y),

• joint probability distribution:• inference:

let −→z = (z1, . . . , zn) a vector of sensor measurements:

p(ox ,y |−→z ) =

p(ox ,y )∏n

i=1 p(zi |ox ,y )

p(occ)∏n


i=1 p(zi |emp)

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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results


Outline

1 Motivation





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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results


Sensor Model

Values of sensor model characteristics for a beam:

position ρ dependent z dependentif z << ρ −− ×

if z around ρ × ×of z >> ρ −− ×

where:1 ρ is the cell range,2 z the measured range,3 gaussian sensor uncertainty,

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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results


Sensor Model

Values of sensor model characteristics for a beam:

position ρ dependent z dependentif z << ρ −− −−

if z around ρ × ×of z >> ρ −− −−

where:1 ρ is the cell range,2 z the measured range,3 gaussian sensor uncertainty,4 very weak occupancy a priori : world almost empty.

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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results


1D Occupancy Function

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 20 40 60 80 100 120

Occ

upan

cy p

roba

bilit

ies.

Cell indices.

(a)

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

-25 -20 -15 -10 -5 0 5 10 15 20 25X cell indices. 0 50

100 150

200 250

300

Y cell indices.

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

Occupancy probabilities.

(b)

Extension from 1D to 2D OG. (a) 1D OG (b) 2D OG of asensor beam.The sensor is positioned in (0,0).

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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results


Laser Beam and Grid Geometry

(x,y)

drho

dx

dthetarho

Omega

Figure: Polar and Cartesian grids parameters.

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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results


Outline

1 Motivation





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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results


Moirage problem with Bresenham algorithm

Figure: Grid based slam (from Dirk Hähnel home page).

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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results



Bresenham algorithm (standard plot) superposition problem

Bresenham algorithm (log plot) exact algorithm

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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results





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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results





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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results





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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results





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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results


Outline

1 Motivation





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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results


General Algorithm Architecture

FUSION

NEW GRID

Geometric transform Geometric transform

precalculated

sensor model

precalculated

sensor model

inferencePREVIOUS GRID

p(z|occ) p(z|emp)

Sensor model selection Sensor model selection

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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results


General Algorithm Architecture

FUSION

NEW GRID

Geometric transform Geometric transform

precalculated

sensor model

precalculated

sensor model

inferencePREVIOUS GRID

p(z|occ) p(z|emp)

Sensor model selection Sensor model selection

GPU STEPS

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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results


Outline

1 Motivation





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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results


Polygons geometric primitives

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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results


Result with Dirac model

Figure: Occupancy grid generated by the GPU, polygon mode

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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results


Outline

1 Motivation





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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results


Texture Mipmaps

Angle beam in abscissa and ρ in ordinate at different scales

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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results


Result with gaussian model

Figure: Occupancy grid generated by the GPU.

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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results


Outline

1 Motivation





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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results


Exact Algorithm: Map Overlay

A B

D C

A B

CD

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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results


Algorithms for sick sensors with Dirac model

1 exact,2 Bresenham,3 adaptative sampling,4 GPU (polygon mode)

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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results


Outline

1 Motivation





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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results


results

Method Avg. Error Max. Error avg. timeexact 0 0 1.23s (CPU)line drawing 0.98 25.84 0.22s (CPU)sampling 0.11 1.2 1.02s (CPU)

GPU 0.15 1.80.049s on MS0.0019s onboard

Table: Comparison of change of coordinate system methods (MS:master storage).

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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results


Outline

1 Motivation





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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results


fusion results

-vo x11 cycabFusion.aviFusion of four SICK laser range-finders surrounding a vehicle.

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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results


Summary

1 correct sampling is necessary,2 graphical hardwares for sensor geometry,3 graphical hardwares for multiple sensor fusion and grid

handling,4 on board: fusion of 50 sensors is possible in real-time.

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of OGs

Motivation


Sensor Model



Dirac model

Gaussian model


Evaluation

Fusion results


Perspectives

Handling with GPU:1 angle uncertainty,2 sensor position uncertainty,3 scan matching.

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of OGs

Alberto Elfes.Occupancy grids: a probabilistic framework for robotperception and navigation.PhD thesis, Carnegie Mellon University, 1989.

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Documents

Efficient GPU-based Construction of Occupancy Grids Using