Describing moving spherical obstacle in a configuration space

A way of parameterizing a spherical obstacle in the configuration space (C-Space) and the properties of a moving spherical obstacle are described. A spherical obstacle in a work space (W-Space) is transformed into a characteristic region in C-Space, and can be approximated as a set of geometric objects. The transformation of a complex work space into C-Space is described in terms of unifying the transformation of each element of a set of spheres. A collision-free path is made by using a penalty-function-method. for a moving spherical obstacle in the work space, the penalty-function is modified according to the factors of the velocity along axes in polar coordinates system. Simulation results are presented for the case of two manipulators in W-Space