Localization

David Johnsoncs6370

Basic Problem

• Go from this to this

[Thrun, Burgard & Fox (2005)]

Kalman Filter

[Thrun, Burgard & Fox (2005)]

Kalman Limitations

• Need initial state and confidence– Doesn’t solve global localization

• “kidnapped robot” problem• Only tracks one hypothesis at a time

– Similar landmarks confuse it

Global methods• We have used PDFs and Kalman Filter to

represent and update robot state in one position• Global methods represent probability of robot

state everywhere at once– Pick the peak as actual location

• Based on Bayes filter, Markov model– Tracks a belief “bel” about where it is

• Side note: there is a multi-hypothesis KF that tracks multiple Gaussians at once.

Markov Localization

[Thrun, Burgard & Fox (2005)]

Global Localization

• The research is how to efficiently represent the global belief

Grid Localization• Developed out of

Moravec’s occupancy maps for probabilistic mapping

Occupancy maps

• Only have to represent x,y location• Store probability that a cell is filled

– Threshold into definitely empty or filled• How is a mobile robot different?

Grid Localization

[Thrun, Burgard & Fox (2005)]

Grid Localization

[Thrun, Burgard & Fox (2005)]

Grid Localization

[Thrun, Burgard & Fox (2005)]

Grid Localization

[Thrun, Burgard & Fox (2005)]

Grid Localization

[Thrun, Burgard & Fox (2005)]

Grid Localization

[Thrun, Burgard & Fox (2005)]

Illustrative Example: Robot Localization

t=0

10Prob

Illustrative Example: Robot Localization

t=1

10Prob

Illustrative Example: Robot Localization

t=2

10Prob

Illustrative Example: Robot Localization

t=3

10Prob

Illustrative Example: Robot Localization

t=4

10Prob

Illustrative Example: Robot Localization

t=5

10Prob

1 2 3 4

Trajectory

Grid-based Localization

How do we get information to the cells?

• Pick closest obstacle– Precompute at each cell what the closest

obstacle should be and a confidence to add to the cell if a match is made.

• Only update confident cells– May cause loss of global property

• How to do motion model?– Gaussian blur of grid

• (Sequential) Monte Carlo filters

• Bootstrap filters• Condensation

• Interacting Particle Approximations

• Survival of the fittest

• …

Particle Filters

Representing Robot Location

X

Y

Sampling as Representation

X

Y

Particle Filter

[Thrun, Burgard & Fox (2005)]

Visualization of Particle Filter

unweighted measure

compute importance weights

p(xt-1|z1:t-1)resampling

move particles

predict p(xt|z1:t-1)

Particle Filters – motion model

1. Prediction Phase – motion model

u

Motion Model

2. Measurement Phase

Sensor Model

3. Resampling Step