localization david johnson cs6370. basic problem go from thisto this
Post on 19-Dec-2015
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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