1. Statistical environment representation to support navigation of mobile robots in unstructured environments
Stefan Rolfes
Maria Joao Rendas
Sumare workshop

2. Short introduction to the problem
Outline
Short introduction to the problem
Novel environment representation (RCS models)
Navigation using RCS models as a map
Simulation results
Conclusion

3. Mobile robot navigation Basic requirement: localisation capacities
Global supervision (GPS, beacons, cameras)
Feature based approach (mapping and recognition)
Common approaches :
Map
Recognition
Estimation of
True robot pose
deviation
Observations
Estimated robot pose

4. Navigation in unstructured environments
Problems
(1) in unstructured environments (unreliable feature description)
mismatch leads to erroneous pose estimation
(2) in underwater scenarios (no GPS available)
no external pose information
Solution under study
Statistical environment description of natural scenes

5. Natural scenes
Observation : Objects that occur in natural scenes tend to form patches (alga, stone fields, …)
We consider that natural, unstructured scenes can be described as a collection of closed sets:
(family of closed sets)

6. Statistical versus feature based description
Feature description :
Mapping individual features
Statistical description :
Captures global characteristics
(Shape description of salient features)
Spatial distribution
Morphological characteristics
(size, boundary length,…..)
p(size)
size

7. Statistical environment description: Example Posidonie (Villefranche)
Image processing
Distribution of the orientation
Statistics

8. Random Closed Set Doubly stochastic process :
1) Random point process (germ process)
describes spatial distribution of objects
2) Shape process (grain process)
determines the geometry of the objects
Each model is defined by a parameter vector
Family of models :

9. Examples of Random Closed Sets
Uniform distribution
Non isotropic distribution
Cluster process
Line process

10. The hitting capacity
Theorem : Knowledge of the hitting capacities for all compact sets
is equivalent to knowledge of the model parameter
Analytical forms of can be found for some model types

11. Simple RCS model : Boolean Models9
Simple RCS model : Boolean Models
Already used in biological / physical contexts to model natural scenes
The sequence of locations (germs) of the closed sets is a stationary Poisson process of intensity
The sequence (grains) are i.i.d. realisations of random closed sets with distribution
Analytical expression for the hitting capacity :

12. Map of the environment Map of the environment
Segmentation of the workspace :
Non isotropic
isotropic
Map of the environment

13. Pose estimation : Bayesian approach
Dynamic model:
An optimal estimate of the robot’s state is obtained by (MMSE):
Past observations :
memoryless observations:

14. Optimal filter The a-posteriori density is obtained : Prediction
Filtering
Assuming and to be uncorrelated
Need to be characterized

15. Good approximation by Gaussian densities
Characterisation of
Good approximation by Gaussian densities
Approximation of the optimal filter by an Extended Kalman Filter (easy computation)

16. Perceptual observations memoryless ? Overlapping observation area
Observation window
Observations not memoryless :
Requires random sampling of the image
Observations memoryless :
Use of perceptual observations periodically

17. Simulated environment
Bolean model (discs of random radii)
Map (RCS model parameters):
Generation
Realisation

18. Simulation results (1)

19. Simulation results (2)

20. Simulation results (3) Pose estimation Use of perceptual observations
Only odometry

21. Conclusions We proposed a novel environment description (not relying
and demonstrated the feasibility of mobile robot navigation
on individual feature description) by RCS models
based on these descriptions
A lot of future work
Characterisation of more complex RCS models suitable to
Address the Model testing (using MDL or ML)
Solve the problem of joint mapping and localisation
describe natural scenes