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

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

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

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

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)

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

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

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 :

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

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

Simple RCS model : Boolean Models 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 :

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

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

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

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

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

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

Simulation results (1)

Simulation results (2)

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

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