A simple and practical model with applications in 3D motion planning is presented. The new model is based on a double spherical hierarchy of detail to represent solid bodies.

First, each element making up the robot and the obstacles is approximated by means of 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 spherical model leads to a simple treatment for the problem of dynamic collision detection, and it is further applied to collision-free path planning for robot manipulators in 3D.

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