Generation of Homotopic Paths for a Size-Changing Sphere

A new and fast technique for generating collision-free paths for a mobile sphere, whose size (radius) dynamically changes, is introduced in this paper. A collision between the mobile-sphere motion and an obstacle is predicted by computing its minimum translational distance. This distance parameterizes an intermediate configuration for the sphere, which is in contact with the obstacle or separated a configurable distance. Collision with a given obstacle is then avoided by forcing the mobile sphere to pass through a selected intermediate configuration. This paper describes a technique to reduce or to grow this configuration (sphere) in order to bring it into contact (or as close as desired) with a second obstacle. This fact provides the path planner some remarkable properties like it really generates a set of homotopic paths in narrow environments for not only a sphere but any other mobile object which always keeps inside the volume represented by the generated path.