Probabilistic Estimation of Multi-Level Terrain Maps

Recent research has shown that robots can model their world with Multi-Level (ML) surface maps, which utilize 'patches' in a 2D grid space to represent various environment elevations within a given grid cell. Though these maps are able to produce 3D models of the environment while exploiting the computational feasibility of single elevation maps, they do not take into account in-plane uncertainty when matching measurements to grid cells or when grouping those measurements into 'patches.' To respond to these drawbacks, this paper proposes to extend these ML surface maps into Probabilistic Multi-Level (PML) surface maps, which uses formal probability theory to incorporate estimation and modeling errors due to uncertainty. Measurements are probabilistically associated to cells near the nominal location, and are categorized through hypothesis testing into 'patches' via classification methods that incorporate uncertainty. Experimental results comparing the performances of the PML and ML surface mapping algorithms on representative objects found in both indoor and outdoor environments show that the PML algorithm outperforms the ML algorithm in most cases including in the presence of noisy and sparse measurements. The experimental results support the claim that the PML algorithm produces more densely populated, conservative representations of its environment with fewer measurements than the ML algorithm.