1. Bayesian Filtering for Robot Localization
CSE-473

2. Probabilistic Robotics
Key idea: Explicit representation of uncertainty
(using the calculus of probability theory)
Perception = state estimation
Control = utility optimization

3. Localization
“Using sensory information to locate the robot in its environment is the most fundamental problem to providing a mobile robot with autonomous capabilities.” [Cox ’91]
Given
Map of the environment.
Sequence of sensor measurements.
Wanted
Estimate of the robot’s position.
Problem classes
Position tracking
Global localization
Kidnapped robot problem (recovery)

4. Bayes Filters for Robot Localization

5. Bayes Filters: Framework
Given:
Stream of observations z and action data u:
Sensor model P(z|x).
Action model P(x|u,x’).
Prior probability of the system state P(x).
Wanted:
Estimate of the state X of a dynamical system.
The posterior of the state is also called Belief:

6. Graphical Model of Localizationu u u 1
t-1
... x x x x 1 2 t m z z z 1 2 t

7. Markov Assumption Underlying Assumptions Static world
Independent noise
Perfect model, no approximation errors

8. Two Time Slice Representation of Dynamic Bayes Netu u
t-1 t x x x
t-1 t z z
t-1 t

9. Belief Update u t x x
t-1 t z t

10. Bayes Filters z = observation u = action x = state Bayes Markov
Total prob.
Markov

11. Representations for Bayesian Robot Localization
Kalman filters (late-80s?)
Gaussians
approximately linear models
position tracking
Discrete approaches (’95)
Topological representation (’95)
uncertainty handling (POMDPs)
occas. global localization, recovery
Grid-based, metric representation (’96)
global localization, recovery
Robotics AI
Particle filters (’99)
sample-based representation
global localization, recovery
Multi-hypothesis (’00)
multiple Kalman filters
global localization, recovery

12. Particle Filters

13. Particle Filters Represent belief by random samples
Estimation of non-Gaussian, nonlinear processes
Monte Carlo filter, Survival of the fittest, Condensation, Bootstrap filter, Particle filter
Filtering: [Rubin, 88], [Gordon et al., 93], [Kitagawa 96]
Computer vision: [Isard and Blake 96, 98]
Dynamic Bayesian Networks: [Kanazawa et al., 95]d

14. Sample-based Density Representation

15. Importance Sampling
Weight samples: w = f / g

16. Particle Filters

17. Sensor Information: Importance Sampling

18. Robot Motion

19. Sensor Information: Importance Sampling

20. Robot Motion

21. Particle Filter Algorithm
Importance factor for xit:
draw xit from p(xt | xit-1,ut-1)
draw xit-1 from Bel(xt-1)

22. Motion Model Reminder
Start

23. Proximity Sensor Model Reminder
Sonar sensor
Laser sensor

24. Sample-based Localization (sonar)

44. Using Ceiling Maps for Localization
[Dellaert et al. 99]

45. Vision-based Localization
h(x) z
P(z|x)

46. Under a Light
Measurement z:
P(z|x):

47. Next to a Light
Measurement z:
P(z|x):

48. Elsewhere
Measurement z:
P(z|x):

49. Global Localization Using Vision

50. Localization for AIBO robots

51. Adaptive Sampling

52. Example Run Sonar

53. Example Run Laser

54. Example Run

55. Tracking with a Moving Robot

56. Ball Tracking in RoboCup
Extremely noisy (nonlinear) motion of observer
Inaccurate sensing, limited processing power
Interactions between target and environment
Interactions between robot(s) and target
Goal: Unified framework for modeling the ball and its interactions.

57. Dynamic Bayes Network for Ball Trackingz l z l z l
Landmark detection
k-2
k-1 k
Robot localization r r r
Map and robot location
k-2
k-1 k u u
Robot control
k-2
k-1 m m m
k-2
k-1 k
Ball motion mode b b b
Ball location and velocity
Ball tracking
k-2
k-1 k z b z b z b
Ball observation
k-2
k-1 k

58. Rao-Blackwellised PF for Inference
Represent posterior by random samples
Each sample contains robot location, ball mode, ball Kalman filter
Generate individual components of a particle stepwise using the factorization

59. Ball-Environment Interaction

60. Nokia 6600 Java Cell Phone with Bluetooth GPS unit
GPS Receivers We Used
Today the GPS receivers become much smaller and cheaper than a few years ago.
Nokia 6600 Java Cell Phone with Bluetooth GPS unit
GeoStats wearable GPS logger

61. Geographic Information Systems
The second related system is …. The kernel of such systems is the database about geographic information.
GIS technology has been used for tens of years and today there are a large number of different kinds of geographic data available.
In this project we rely on two kinds of geographic data.
The first data is the street map. The left picture shows….
The second is the bus route and bus stop data. The picture on the right…
Street map
Data source: Census 2000
Tiger/line data
Bus routes and bus stops
Data source: Metro GIS

62. Adding Mode of Transportation
Say something about the dependence between mode and x. How to model the dependence.
mk-1 mk
Transportation mode
xk-1 xk
Edge, velocity, position
qk-1 qk
Data (edge) association
zk-1 zk
GPS reading
Time k-1
Time k

63. Infer Location and Transportation
Measurements
Projections
Bus mode
Car mode
Foot mode
Green
Red
Blue
Explain why it switches from foot to bus, not car: because of the bus stops
If people ask why no car particle at all (there are car particles, just their weights are too small that can not be displayed).

64. Hierarchical Model gk-1 gk tk-1 tk mk-1 mk xk-1 xk qk-1 qk zk-1 zk
Goal
tk-1 tk
Trip segment
mk-1 mk
Transportation mode
xk-1 xk
Edge, velocity, position
qk-1 qk
Data (edge) association
zk-1 zk
GPS reading
Time k-1
Time k

65. Predict Goal and Path
Predicted goal
Predicted path

66. Application: Opportunity Knocks
Finally I’ll give an application of our technique.
The client side includes a cell phone and a GPS receiver. The cell phone can transmit GPS measurements to a server. Our learning and inference engines are run on the server side and transmit the inference results back to the cell phone.
In this episode, suppose an elder person carries … Then the inference engine instantiate the goal as home.

67. Detect User Errors Untrained Trained Instantiated
In this episode, the person takes the bus home but missed the usual bus stop.
The black disk is the goal and the cross mark is where the system think the person should get off the bus. The probability of normal and abnormal activities are represented using a bar here. The black part is the probability of being normal while the red part is the probability of being abnormal. At here, the person missed the bus stop and the probability of abnormal activity jump quickly.
Untrained Trained Instantiated

68. Application: Opportunity Knocks

69. Particle Filter Algorithm

70. Resampling Given: Set S of weighted samples.
Wanted : Random sample, where the probability of drawing xi is given by wi.
Typically done n times with replacement to generate new sample set S’.

71. Resampling Stochastic universal sampling Systematic resamplingw2 w3 w1 wn
Wn-1 w2 w3 w1 wn
Wn-1
Stochastic universal sampling
Systematic resampling
Linear time complexity
Easy to implement, low variance
Roulette wheel
Binary search, log n

72. Resampling Algorithm

73. Probabilistic Kinematics
Robot moves from to
Odometry information

74. Noise Model for Motion
The measured motion is given by the true motion corrupted with noise.
To predict sample position, just sample from “noisy version” of measured motion.

75. Gaussian Noise Model
Normal distribution

76. Examples (odometry based)

77. When does this approximation fail?
Motion Model with Map
When does this approximation fail?