Sumare workshop 13.12.00

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

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

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

4. 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 Navigation in unstructured environments

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

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

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

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

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

11. 9 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. Non isotropic Map of the environment isotropic Map of the environment Segmentation of the workspace :

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 : Filtering Prediction Assuming and to be uncorrelated Need to be characterized

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

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

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