Constructing an approximate representation of a configuration space without using an intersection check

Introduces the concept of configuration patches (C-patches) for representing configurations of a polyhedral robot in a point-point contact with polyhedral obstacles, and proposes an approach called the inverse mapping method for computing an approximate representation with cubic cells of the configuration space (C-space) of the robot. The configuration patches represented in a local coordinate system, have simple geometric shapes like paralleltopes. The inverse mapping method constructs the approximation of a C-space by quantizing the C-patches in the local coordinate system. There is no need to check any intersection among the robot and the obstacles. The only process needed is a coordinate transformation from discrete points on the C-patches to configurations of the robot