Analytical solution for configuration space obstacle computation and representation

Objects within the robot´s work space impose constraints on the motion of the robot. We present a novel approach to represent these kinematic motion constraints in the robot´s configuration space. Two fundamental problems such as efficiency and completeness have also been investigated. By introducing the concept of pseudo kinematics for the robot, we demonstrate that the kinematic motion constraints in the robot´s configuration space can be analytically and completely described by a set of parametric equations. These parametric equations result from mapping the boundary of the obstacle from the work space into the configuration space using the inverse pseudo kinematics. The technique is generalized for an n-degrees of freedom manipulator operating in a 3-D work space. The closed form representation for a C-space obstacle substantially reduces the computation time needed to obtain a C-space obstacle, thus making it possible to implement on-line collision-free motion planning schemes. Simulations results are presented for computing C-space obstacles in the 3D configuration space