Localization

David Johnson

cs6370

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