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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 robotics or how the world became to be one big bayes network

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

Sebastian Thrun

Carnegie Mellon University

University of Pittsburgh

slide2

This Talk

Robotics

Research Today

Particle Filters

In Robotics

4 Open Problems

slide6

This Talk

Robotics

Research Today

Particle Filters

In Robotics

4 Open Problems

robotics @ cmu 1997
Robotics @ CMU, 1997

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

robotics @ cmu 1998
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
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
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

bayes filter localization
Bayes Filter Localization

[Nourbakhsh et al 94]

[Simmons/Koenig 95]

[Kaelbling et al 96]

what is the right representation
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
Monte Carlo Localization (MCL)

With: Wolfram Burgard, Dieter Fox, Frank Dellaert

monte carlo localization
Monte Carlo Localization

With:

Frank

Dellaert

particle filter in high dimensions
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

ekf approach
EKF Approach

O(N2)

[Smith, Self, Cheeseman, 1985]

eks slam for underwater mapping courtesy of stefan williams and hugh durrant whyte univ of sydney
EKS-SLAM for Underwater MappingCourtesy of Stefan Williams and Hugh Durrant-Whyte, Univ of Sydney
insight conditional independence
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
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
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
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 log n
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
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

3 examples
3 Examples

Particles +

Kalman filters

Particles +

Point Estimators

Particles +

Particles

outdoor mapping no gps
Outdoor Mapping (no GPS)
  • 4 km excursion

With Juan Nieto, Eduardo Nebot, Univ of Sydney

3 examples36
3 Examples

Particles +

Kalman filters

Particles +

Point Estimators

Particles +

Particles

indoor mapping
Indoor Mapping
  • Map: point estimators (no uncertainty)
  • Lazy
importance of particle filters
Importance of Particle Filters

Non-probabilistic

Probabilistic, with samples

multi robot exploration
Multi-Robot Exploration

DARPA TMR Texas

DARPA TMR Maryland

With: Reid Simmons and Dieter Fox

3 examples41
3 Examples

Particles +

Kalman filters

Particles +

Point Estimators

Particles +

Particles

tracking moving features
Tracking Moving Features

With: Michael Montemerlo

map based people tracking
Map-Based People Tracking

With: Michael Montemerlo

autonomous people following
Autonomous People Following

With: Michael Montemerlo

advantage of structured pf solution46
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
Worst-Case Environment ?

N landmarks

robot path

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

relative map error simulation
Relative Map Error (Simulation)

Kalman Filter

Kalman Filter

250 particles

error

steps

relative map error simulation49
Relative Map Error (Simulation)

Kalman Filter

Kalman Filter

250 particles

250 particles

100 particles

100 particles

2 particles

error

steps

robot to map error simulation
Robot-To-Map Error (Simulation)

Kalman Filter

error

250 particles

100 particles

2 particles

steps

summary results
Summary Results

O(N2)

O(logN)

  • O(N2)  O(MN)  O(M logN)  O(logN)
  • Scalable(?) solution to data association problem
slide52

This Talk

Robotics

Research Today

Robotics

Research Today

Particle Filters

In Robotics

4 Open Problems

can we factorize better
Can We Factorize Better?

Static Factorization

Dynamic Factorization

#1

example multi robot localization55
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
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
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, …

implications for planning control
Implications for Planning & Control

MDP Planner

POMDP Planner

N. Roy et al

can we exploit procedural knowledge
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

and can we actually do something useful
…And Can We Actually DoSomething Useful?

#4

See poster by Anguelov et al.

the nursebot project
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
Wizard of Oz Studies

By Sara Kiesler, Jenn Goetz