A sphere world is a mathematical concept used in robotic motion planning. Essentially, if the environment is represented as a sphere, and the robot and obstacles within the environment are represented as spheres, then it is possible to construct navigation functions which create paths from a start position to a goal position. Although the real world is rarely composed of spheres, sphere worlds are still useful for motion planning, as they are topologically equivalent to star worlds.
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Sphere world Wikipedia(Text) CC BY-SA