Depth Space Collision Detection for Motion Planning

Depth maps are an efficient representation of 3D free space. Encoding distance-to-camera in each pixel permits a dense, regular 2D representation of the space between a camera and the scenery it observes, which may be inspected to fulfill a useful class of object collision queries. In the proposed method, candidate poses of arbitrary 3D geometry are rendered into a depth map with depth testing as a fast way of determining if the geometry is fully contained by the free space implicitly encoded in the depth map. For efficiency, raw depth maps representing a spatial discretization of the world are transformed into a discretization of the configuration space of collision geometry elements. The result is a collision checker that requires 0.4% of the memory and 56% of the CPU resources used by an existing high-performance distance field 3D collision checker.