A General Deterministic Sequence for Sampling d-Dimensional Configuration Spaces
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- Rosell, J., Roa, M., Pérez, A. et al. J Intell Robot Syst (2007) 50: 361. doi:10.1007/s10846-007-9170-9
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Previous works have already demonstrated that deterministic sampling can be competitive with respect to probabilistic sampling in sampling-based path planners. Nevertheless, the definition of a general sampling sequence for any d-dimensional configuration space satisfying the requirements needed for path planning is not a trivial issue. This paper makes a proposal of a simple and yet efficient deterministic sampling sequence based on the recursive use, over a multi-grid cell decomposition, of the ordering of the 2d descendant cells of any parent cell. This ordering is generated by the digital construction method using a d×d matrix Td. A general expression of this matrix (i.e. for any d) is introduced and its performance analyzed in terms of the mutual distance. The paper ends with a performance evaluation of the use of the proposed deterministic sampling sequence in different well known path planners.