Planning 3-D collision-free paths using spheres

A scheme for the representation of objects, the Successive Spherical Approximation (SSA), facilitates the rapid planning of collision-free paths in a 3-D, dynamic environment. The hierarchical nature of the SSA allows collision-free paths to be determined efficiently while still providing for the exact representation of dynamic objects. The concept of a freespace cell is introduced to allow human 3-D conceptual knowledge to be used in facilitating satisfying choices for paths. Collisions can be detected at a rate better than 1 second per environment object per path. This speed enables the path planning process to apply a hierarchy of rules to create a heuristically satisfying collision-free path