Study and evaluate implementation of adaptive clustering algorithm

[fbattocchia]

Feature description

The LikelihoodFieldProb model uses clustering to enhance robustness against unmapped objects. Although this significantly improves the model statistics obtained in Lamkin, it still results in twice the maximum error compared to NAV2 LFP.

The clustering algorithm implemented in Nav2 is the kd-tree. This algorithm has an adaptive structure: the way it partitions space is not fixed but adapts to the distribution of the data. In other words, the kd-tree recursively partitions the space based on how the particles are distributed. Currently, Beluga is implementing an algorithm with cells of fixed size. This can be less flexible, especially at the cell boundaries, where a small variation may cause nearby particles to end up in different cells.

Implementation considerations

After conducting tests by modifying the cell size in Beluga's clustering algorithm and observing that this modification had no effect on the results, it might be worth considering the study and implementation of a clustering algorithm with an adaptive structure, such as Adaptive Mesh Refinement (AMR): the grid is refined (subdivided) in dense areas to better capture the local structure. A Grid-based Clustering Algorithm using Adaptive Mesh Refinement

[glpuga]

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