Statistical environment representation to support navigation of mobile robots in unstructured environments

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Statistical environment representation to support
navigation of mobile robots in unstructured
environments
Stefan Rolfes
Maria Joao Rendas
rolfes,rendas_at_i3s.unice.fr
Sumare workshop 13.12.00
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Outline

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

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Mobile robot navigation
Basic requirement localisation capacities
Map

• Recognition
• Estimation of

True robot pose
deviation
Observations
Estimated robot pose
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Navigation in unstructured environments
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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)
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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
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Statistical environment description Example
Posidonie (Villefranche)
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Random Closed Set
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Examples of Random Closed Sets
Uniform distribution
Non isotropic distribution
Cluster process
Line process
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The hitting capacity
Theorem Knowledge of the hitting capacities for
all compact sets is
equivalent to knowledge of the model parameter
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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
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Map of the environment
Segmentation of the workspace
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Pose estimation Bayesian approach
Dynamic model
An optimal estimate of the robots state is
obtained by (MMSE)
Past observations
memoryless observations
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Optimal filter
The a-posteriori density is obtained
Filtering
Prediction
Assuming and to be uncorrelated
Need to be characterized
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Characterisation of
Good approximation by Gaussian densities
Approximation of the optimal filter by an
Extended Kalman Filter (easy computation)
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Perceptual observations memoryless ?
Overlapping observation area
Observation window
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Simulated environment
Bolean model (discs of random radii)
Map (RCS model parameters)
Generation
Realisation
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Simulation results (1)
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Simulation results (2)
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Simulation results (3)
Pose estimation
Use of perceptual observations
Only odometry
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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