A new representation for collision avoidance and detection

By combining the simplicity of the sphere and the power of the motion of hierarchy of detail, a novel model is proposed with applications to collision avoidance and detection in 3D. The model is based on a double spherical representation for solid bodies. First, each element making up the robot and the obstacles is approximated by a set of exterior spheres which are automatically defined. Second, another set composed of interior spheres is generated. These representations define a hierarchy, since they can be redefined as many times as necessary; starting with two spheres per element, the approximation may be improved until it contains hundreds of spheres. Moreover, they converge to a zero-error representation. The proposed models leads to a simple treatment for the problem of collision detection, and it is further applied to collision-free path planning for manipulators in 3D