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Particle Filters In Robotics or: How the World Became To Be One Big Bayes NetworkPowerPoint Presentation

Particle Filters In Robotics or: How the World Became To Be One Big Bayes Network

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Particle Filters In Robotics or: How the World Became To Be One Big Bayes Network Sebastian Thrun Carnegie Mellon University University of Pittsburgh This Talk Robotics Research Today Particle Filters In Robotics 4 Open Problems Robotics Yesterday Robotics Today Robotics Tomorrow?

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### Particle Filters In Roboticsor: How the World Became To Be One Big Bayes Network

Sebastian Thrun

Carnegie Mellon University

University of Pittsburgh

Robotics @ CMU, 1997

with W. Burgard, A.B. Cremers, D. Fox, D. Hähnel, G. Lakemeyer, D. Schulz, W. Steiner

Robotics @ CMU, 1998

with M. Beetz, M. Bennewitz, W. Burgard, A.B. Cremers, F. Dellaert, D. Fox,

D. Hähnel, C. Rosenberg, N. Roy, J. Schulte, D. Schulz

The Localization Problem

fast-moving

ambiguous

identity

non-statio-

nary

many objects

static

few objects

one object

uniquely

identifiable

local

(tracking)

global

kidnapped

- Objects
- Robots
- Other Agents

Probabilistic Localization

- “Bayes filter”
- HMMs
- DBNs
- POMDPs
- Kalman filters
- Particle filters
- Condensation
- etc

m

map

z1

z3

z3

z2

observations

. . .

x1

x1

x1

x2

x2

x2

x3

xt

robot poses

robot poses

u3

u3

u3

u3

ut

ut

ut

u2

u2

u2

u2

controls

controls

map m

laser data

What is the Right Representation?

Multi-hypothesis

Kalman filter

[Weckesser et al. 98], [Jensfelt et al. 99]

[Schiele et al. 94], [Weiß et al. 94], [Borenstein 96],

[Gutmann et al. 96, 98], [Arras 98]

Particles

[Kanazawa et al 95] [de Freitas 98]

[Isard/Blake 98] [Doucet 98]

Histograms

(metric, topological)

[Nourbakhsh et al. 95], [Simmons et al. 95], [Kaelbling et al. 96],

[Burgard et al. 96], [Konolige et al. 99]

Monte Carlo Localization (MCL)

With: Wolfram Burgard, Dieter Fox, Frank Dellaert

Particle Filter in High Dimensions

fast-moving

ambiguous

identity

non-statio-

nary

many objects/features

static

few objects

one object

uniquely

identifiable

local

(tracking)

global

kidnapped

Learning Mapsaka Simultaneous Localization and Mapping (SLAM)

70 m

The SLAM Problem with known data association

Kalman Filter Mapping: O(N2)

EKS-SLAM for Underwater MappingCourtesy of Stefan Williams and Hugh Durrant-Whyte, Univ of Sydney

Insight: Conditional Independence

Factorization first developed by Murphy & Russell, 1999

1

Landmark 1

z1

z3

observations

. . .

x1

x2

x3

xt

Robot poses

u3

ut

u2

controls

z2

zt

2

Landmark 2

Rao-Blackwellized Particle Filters

…

robot poses

landmark n=1

landmark n=N

landmark n=2

…

landmark n=1

landmark n=N

landmark n=2

[Murphy 99, Montemerlo 02]

FastSLAM - O(MN)

O(M)

Constant time per particle

O(M)

Constant time per particle

O(MN)

Linear time per particle

- Update robot particles based on control ut
- Incorporate observation zt into Kalman filters
- Resample particle set

M = Number of particles

N = Number of map features

Ben Wegbreit’s Log-Trick

n 4 ?

T

F

new particle

n 2 ?

F

T

n 3 ?

T

F

[i]

[i]

m3,S3

n 4 ?

k 4 ?

T

T

F

F

old particle

k 2 ?

n 2 ?

k 6 ?

n 6 ?

T

T

F

F

T

T

F

F

k 1 ?

n 1 ?

k 3 ?

n 3 ?

k 1 ?

n 5 ?

k 3 ?

n 7 ?

T

T

F

F

T

T

F

F

T

T

F

F

T

T

F

F

[i]

[i]

[i]

[i]

[i]

[i]

[i]

[i]

[i]

[i]

[i]

[i]

[i]

[i]

[i]

[i]

[i]

[i]

[i]

[i]

[i]

[i]

[i]

[i]

[i]

[i]

[i]

[i]

[i]

[i]

m1,S1

m1,S1

m2,S2

m2,S2

m3,S3

m3,S3

m4,S4

m4,S4

m5,S5

m5,S5

m6,S6

m6,S6

m7,S7

m7,S7

m8,S8

m8,S8

FastSLAM - O(M logN)

O(M)

Constant time per particle

O(MlogN)

Log time per particle

O(M logN)

Log time per particle

- Update robot particles based on control ut
- Incorporate observation zt into Kalman filters
- Resample particle set

M = Number of particles

N = Number of map features

Advantage of Structured PF Solution

FastSLAM: O(MlogN)

Moore’s Theorem: logN 30

M: discussed later

+ global uncertainty, multi-modal

+ non-linear systems

+ sampling over data associations

Kalman: O(N2)

500 features

Indoor Mapping

- Map: point estimators (no uncertainty)
- Lazy

Tracking Moving Features

With: Michael Montemerlo

Map-Based People Tracking

With: Michael Montemerlo

Autonomous People Following

With: Michael Montemerlo

Advantage of Structured PF Solution

+ global uncertainty, multi-modal

+ non-linear systems

+ sampling over data associations

Kalman: O(N2)

FastSLAM: O(MlogN)

500 features

Moore’s Theorem: logN 30

M: discussed now!

Worst-Case Environment ?

…

…

N landmarks

robot path

…

…

Kalman filters: Maps (relative information) converges for linear-Gaussian case

Relative Map Error (Simulation)

Kalman Filter

Kalman Filter

250 particles

250 particles

100 particles

100 particles

2 particles

error

steps

Summary Results

O(N2)

O(logN)

- O(N2) O(MN) O(M logN) O(logN)

- Scalable(?) solution to data association problem

Robotics

Research Today

Robotics

Research Today

Particle Filters

In Robotics

4 Open Problems

Example: Multi-Robot Localization

[Fox et al, 99]

Example: Multi-Robot Localization

x1

x2

x3

xt

Robot 1 poses

z1

z3

observations

. . .

x1

x2

x3

xt

Robot 2 poses

z2

z2

observations

x1

x2

x3

xt

Robot 3 poses

z1

observations

m

map

[Fox et al, 99]

Dynamic Factorization ??

Task: calculate E[y|x] from samples

always use joint

Robot y

error

always factorize

factorize dynamically

optimal

# samples

Robot x

Can We Learn Control?

- Not an MDP
- Not discrete or low-dimensional
- Not knowledge-free
- Only thing that matters in robotics

#2

Sondik 71,Littman/Kaelbling/Cassandra 96, …

Can we Exploit Procedural Knowledge?

Programming

Learning

See David Andre’s and Stuart Russell’s

AAAI paper this year!

prob<int> x = {{10, 0.2}, {11, 0.8}};

prob<int> y = {{20, 0.5}, {21, 0.5}};

prob<int> z = x + y;

prob<double> f = neuroNet(y);

with Frank Pfenning, CMU

#3

The Nursebot Project

University of Pittsburgh

School of Nursing

Prof. Jackie Dunbar-Jacob

Prof. Sandy Engberg

Prof. Margo Holm

Prof. Deb Lewis

Prof. Judy Matthews

Prof. Barbara Spier

School of Medicine

Prof. Neil Resnick

Prof. Joan Rogers

Intelligent Systems

Prof. Don Chiarulli

University of Pittsburgh

Computer Science

Prof. Martha Pollack

Carnegie Mellon University

Computer Science, Robotics

Prof. Sebastian Thrun

Prof. Geoff Gordon

Human Computer Interaction

Prof. Sara Kiesler

Financial Support

National Science Foundation

$1.4M ITR Grant

$3.2M ITR Grant

Wizard of Oz Studies

By Sara Kiesler, Jenn Goetz

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