1. Navigation Jeremy Wyatt School of Computer Science University of Birmingham

2. Where am I? Knowing where you are is a key problem in robotics Also hard because –Low bandwidth sensing was noisy (e.g sonar) –High bandwidth sensing (vision) is very expensive to process Problem is now partially solved –Better low bandwidth sensing –More robust interpretation methods

3. Particle Filtering State of the art method A randomised algorithm IDEA: track position using many randomised points (particles) Unlikely particles: discard Likely particles: keep and replicate

4. The kidnapped robot problem

5. Actions and observations Action model – what happens when you take an action? Observation model – how likely was your observation?

6. Particle Filtering: a sketch Generate n particles randomly Repeat 1.Take an action 2.Move particles according to the action model 3.Make an observation 4.Weight particles according to the observation model 5.Generate n new particles according to the normalised weights 6.Throw away the old particles

7. Moving particles: action model Particles are points in 3D space Action Add noise, so we sample from  xx yy

8. Action model

9. Weighting particles: observation model The observation at time t+1 is Model says how likely is given This likelihood becomes the particle’s weight

10. Resampling Old particles with weights New particles We normalise the weights and sample new particles by treating the weights as a probability distribution 2 particles here

11. Particle Filtering: the algorithm Time Generate n particles randomly Repeat 1.Take an action 2.Move each particle by sampling from 3.Make an observation 4.Weight each particle according to the observation model 5.Generate n new particles by treating the normalised weights as a probability distribution 6.Throw away the old particles

12. Applied to multiple robots

13. Applied to vision

14. Summary Problem of locating myself within a known map Particle filtering Observation & Action model Extensions and Problems