Spatial reasoning for robot navigation using the Helmholtz-Hodge decomposition of omnidirectional optical flow

The Helmholtz-Hodge decomposition separates a vector filed into translation, rotation, and divergent vector fields. In this paper, using the Helmholtz-Hodge decomposition of omnidirectional optical flow field, we develop geometric algorithms for the detection of free space and navigation direction. For free space direction and navigation, we use catadioptric image sequences and spherical image sequence, respectively.