1. Statistical environment representation to support navigation of mobile robots in unstructured environments Sumare workshop 13.12.00 Stefan Rolfes Maria Joao Rendas rolfes,rendas@i3s.unice.fr

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

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

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

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

8. Random Closed Set Each model is defined by a parameter vector Family of models : 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

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

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

11. 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 9 Simple RCS model : Boolean Models Already used in biological / physical contexts to model natural scenes Analytical expression for the hitting capacity :

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

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

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

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

16. Perceptual observations memoryless ? Observation window Overlapping observation area 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 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 on individual feature description) by RCS models based on these descriptions