On the existence and synthesis of curvature-bounded paths inside nonuniform rectangular channels

Motion planners for autonomous mobile vehicles that are based on rectangular cell decompositions are often required to construct kinematically feasible path - typically curvature-bounded paths - traversing rectangular channels. In this paper, we present a numerical algorithm for determining the existence of a curvature-bounded path contained within a rectangular channel. The rectangular cells comprising the channel are assumed to be of arbitrary, non-uniform dimensions and the bounds on curvature are allowed to be different for different cells. The proposed algorithm is based on the explicit construction of the cone of feasible directions for a bounded-curvature path at the cell exit edge, given the entry point for each cell in the channel. Based on this analysis, we devise a path construction scheme that retains the convenience of cell-by-cell path synthesis but eliminates the guesswork involved in choosing terminal conditions within each cell.