Title: Sebastian Thrun
1Probabilistic Algorithms forMobile Robot Mapping
- Sebastian Thrun
- Carnegie Mellon Stanford
- Wolfram Burgard
- University of Freiburg
- and Dieter Fox
- University of Washington
LEP Adapted, combining partially with Thruns
Tutorial
2- Based on the paper
- A Real-Time Algorithm for Mobile Robot Mapping
- With Applications to Multi-Robot and 3D Mapping
- Best paper award at 2000 IEEE International
Conference on Robotics - and Automation (1,100 submissions)
- Sponsored by DARPA (TMR-J.Blitch, MARS-D.Gage,
MICA-S.Heise) - and NSF (ITR(2), CAREER-E.Glinert,
IIS-V.Lumelsky) - Other contributors Yufeng Liu, Rosemary Emery,
Deepayan Charkrabarti, Frank Dellaert, Michael - Montemerlo, Reid Simmons, Hugh Durrant-Whyte,
Somajyoti Majnuder, Nick Roy, Joelle Pineau,
3This Talk
Motivation
SLAM (Kalman filters)
Expectation Maximization
Real Time Hybrid
3D Mapping with EM
Open Problems
4Museum Tour-Guide Robots
With Greg Armstrong, Michael Beetz, Maren
Benewitz, Wolfram Burgard, Armin Cremers, Frank
Dellaert, Dieter Fox, Dirk Haenel, Chuck
Rosenberg, Nicholas Roy, Jamie Schulte, Dirk
Schulz
5The Nursebot Initiative
With Greg Armstrong, Greg Baltus, Jacqueline
Dunbar-Jacob, Jennifer Goetz, Sara Kiesler,
Judith Matthews, Colleen McCarthy, Michael
Montemerlo, Joelle Pineau, Martha Pollack,
Nicholas Roy, Jamie Schulte
6The Localization Problem
- Estimate robots coordinates s(x,y,q) from
sensor data - Position tracking (error bounded)
- Global localization (unbounded error)
- Kidnapping (recovery from failure)
- Ingemar Cox (1991) Using sensory information
to locate the robot in its environment is the
most fundamental problem to provide a mobile
robot with autonomous capabilities.
see also Borenstein et al, 96
7Mapping The Problem
- Concurrent Mapping and Localization (CML)
- Simultaneous Localization and Mapping (SLAM)
8Mapping The Problem
- Continuous variables
- High-dimensional (eg, 1,000,000 dimensions)
- Multiple sources of noise
- Simulation not acceptable
9Milestone Approaches
Mataric 1990
Elfes/Moravec 1986
Kuipers et al 1991
Lu/Milios/Gutmann 1997
103D Mapping
Moravec et al, 2000
Konolige et al, 2001
Teller et al, 2000
11Take-Home Message
- Mapping is the
- holy grail in
- mobile robotics.
12Robots are Inherently Uncertain
- Uncertainty arises from four major factors
- Environment stochastic, unpredictable
- Robot stochastic
- Sensor limited, noisy
- Models inaccurate
13Probabilistic Robotics
14Probabilistic Robotics
- Key idea Explicit representation of uncertainty
- (using the calculus of probability theory)
- Perception state estimation
- Action utility optimization
15Advantages of Probabilistic Paradigm
- Can accommodate inaccurate models
- Can accommodate imperfect sensors
- Robust in real-world applications
- Best known approach to many hard robotics
problems
16Pitfalls
- Computationally demanding
- False assumptions
- Approximate
17This Talk
Motivation
SLAM (Kalman filters)
Expectation Maximization
Real Time Hybrid
3D Mapping with EM
Open Problems
18The Localization Problem
- Estimate robots coordinates s(x,y,q) from
sensor data - Position tracking (error bounded)
- Global localization (unbounded error)
- Kidnapping (recovery from failure)
- Ingemar Cox (1991) Using sensory information
to locate the robot in its environment is the
most fundamental problem to provide a mobile
robot with autonomous capabilities.
see also Borenstein et al, 96
19Probabilistic Localization
Simmons/Koenig 95 Kaelbling et al 96 Burgard
et al 96
20Bayes Filters
d data o observation a action t
time s state
Kalman 60, Rabiner 85
21Markov Assumption
used above
- Knowledge of current state renders past, future
independent - Static World Assumption
- Independent Noise Assumption
22Bayes Filters are Familiar to AI!
- Kalman filters
- Hidden Markov Models
- Dynamic Bayes networks
- Partially Observable Markov Decision Processes
(POMDPs)
23Localization With Bayes Filters
24What is the Right Representation?
25Idea Represent Belief Through Samples
- Particle filters
- Doucet 98, deFreitas 98
- Condensation algorithm
- Isard/Blake 98
- Monte Carlo localization
- Fox/Dellaert/Burgard/Thrun 99
26Monte Carlo Localization (MCL)
27MCL Importance Sampling
28MCL Robot Motion
motion
29MCL Importance Sampling
30Particle Filters
Represents b(st) by set of weighted particles
s(i)t,w(i)t
31Monte Carlo Localization
32Performance Comparison
Monte Carlo localization
Markov localization (grids)
33Monte Carlo Localization
- Approximate Bayes Estimation/Filtering
- Full posterior estimation
- Converges in O(1/?samples) Tanner93
- Robust multiple hypothesis with degree of belief
- Efficient focuses computation where needed
- Any-time by varying number of samples
- Easy to implement ?
-
34Pitfall The World is not Markov!
35Probabilistic Localization Lessons Learned
- Probabilistic Localization Bayes filters
- Particle filters Approximate posterior by random
samples
36The Problem Concurrent Mapping and Localization
37Concurrent Mapping and Localization
- Is a chicken-and-egg problem
- Mapping with known poses is simple
- Localization with known map is simple
- But in combination, the problem is hard!
- Todays best solutions are all probabilistic!
38Mapping Outline
Maximum likelihood EM
Posterior estimation EKF (SLAM)
Maximum likelihood ML
Posterior estimation with known poses Occupancy
grids
39Mapping as Posterior Estimation
40Kalman Filters
- N-dimensional Gaussian
- Can handle hundreds of dimensions
41Underwater Mapping
By Louis L. Whitcomb, Johns Hopkins University
42Underwater Mapping - Example
Autonomous Underwater Vehicle Navigation, John
Leonard et al, 1998
43Underwater Mapping with SLAMCourtesy of Hugh
Durrant-Whyte, Univ of Sydney
44Mapping with Extended Kalman Filters
Courtesy of Leonard et al 1998
45The Key Assumption
- Inverse sensor model p(stot,m) must be Gaussian.
- Main problem Data association
- In practice
- Extract small set of highly distinguishable
features from sensor data - Discard all other data
- If ambiguous, take best guess for landmark
identity
46Mapping Algorithms - Comparison
SLAM (Kalman)
Output Posterior
Convergence Strong
Local minima No
Real time Yes
Odom. Error Unbounded
Sensor Noise Gaussian
Features 103
Feature uniq Yes
Raw data No
47Mapping Outline
Maximum likelihood EM
Posterior estimation EKF (SLAM)
Maximum likelihood ML
Posterior estimation with known poses Occupancy
grids
48Mapping with Expectation Maximization
Dempster et al, 77 Thrun et al, 1998
Shatkay/Kaelbling 1997
49Uncertainty Models for Motion
50CMUs Wean Hall (80 x 25 meters)
51EM Mapping, Example (width 45 m)
52Mapping Algorithms - Comparison
SLAM (Kalman) EM
Output Posterior ML/MAP
Convergence Strong Weak?
Local minima No Yes
Real time Yes No
Odom. Error Unbounded Unbounded
Sensor Noise Gaussian Any
Features 103 ?
Feature uniq Yes No
Raw data No Yes
53Mapping Outline
Maximum likelihood EM
Posterior estimation EKF (SLAM)
Maximum likelihood ML
Posterior estimation with known poses Occupancy
grids
54The Goal
EM data association Not real-time
Kalman filters real-time No data association
?
55Real-Time Approximation (ICRA paper)
56Incremental ML Not A Good Idea
mismatch
path
robot
57ML Mapping, Online
Idea step-wise maximum likelihood
1. Incremental ML estimate
2. Posterior
Gutmann/Konolige 00, Thrun et al. 00
58Mapping withPoor Odometry
DARPA Urban Robot
raw data
map and exploration path
59Mapping Without(!) Odometry
map
raw data (no odometry)
60Localization in Multi-Robot Mapping
613D Mapping
two laser range finders
623D Structure Mapping (Real-Time)
633D Texture Mapping
raw image sequence
panoramic camera
643D Texture Mapping
65Underwater Mapping (with University of Sydney)
With Hugh Durrant-Whyte, Somajyoti Majunder,
Marc de Battista, Steve Scheding
66Mapping Algorithms - Comparison
SLAM (Kalman) EM ML
Output Posterior ML/MAP ML/MAP
Convergence Strong Weak? No
Local minima No Yes Yes
Real time Yes No Yes
Odom. Error Unbounded Unbounded Unbounded
Sensor Noise Gaussian Any Any
Features 103 ? ?
Feature uniq Yes No No
Raw data No Yes Yes
67Mapping Outline
Maximum likelihood EM
Posterior estimation EKF (SLAM)
Maximum likelihood ML
Posterior estimation with known poses Occupancy
grids
68Occupancy Grids From scans to maps
69Occupancy Grid Maps
Assumptions poses known, occupancy
binary, independent
Elfes/Moravec 88
70Example
The Tech Museum, San Jose
71Mapping Algorithms - Comparison
SLAM (Kalman) EM ML Occupan. Grids
Output Posterior ML/MAP ML/MAP Posterior
Convergence Strong Weak? No Strong
Local minima No Yes Yes No
Real time Yes No Yes Yes
Odom. Error Unbounded Unbounded Unbounded None
Sensor Noise Gaussian Any Any Any
Features 103 ? ? ?
Feature uniq Yes No No No
Raw data No Yes Yes Yes
72Mapping Lessons Learned
- Concurrent mapping and localization hard
robotics problem - Best known algorithms are probabilistic
- EKF/SLAM Full posterior estimation, but
restrictive assumptions (data association) - EM Maximum Likelihood, solves data association
- ML less robust but online
- Occupancy grids Binary Bayes filter, assumes
known poses ( much easier)
73The Obvious Next Step
EM for object mapping
EM for concurrent localization
?
74This Talk
Motivation
SLAM (Kalman filters)
Expectation Maximization
Real Time Hybrid
3D Mapping with EM
Open Problems
75Take-Home Message
- Mapping is the
- holy grail in
- mobile robotics.
Every state-of-the-art mapping algorithm is
probabilistic.
76Open Problems
- 2D Indoor mapping and exploration
- 3D mapping (real-time, multi-robot)
- Object mapping (desks, chairs, doors, )
- Outdoors, underwater, planetary
- Dynamic environments (people, retail stores)
- Full posterior with data association (real-time,
optimal)
77Open Problems, cont
- Mapping, localization
- Control/Planning under uncertainty
- Integration of symbolic making
- Human robot interaction
- Literature Pointers
- Robotic Mapping at www.thrun.org
- Probabilistic Robotics AI Magazine 21(4)