localization
DESCRIPTION
Localization. David Johnson cs6370. Basic Problem. Go from thisto 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 - PowerPoint PPT PresentationTRANSCRIPT
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