Motion planning for a knife-edge on the surface of a hyperboloid

This paper presents a motion planning strategy for a knife-edge moving on the surface of a hyperboloid. First, kinematics equations for the knife-edge are developed without the use of local coordinates so that the mathematical model is globally defined and have no singularities or ambiguities. Then, a novel motion planning algorithm has been constructed using the concept of ruled surfaces. The computer simulations demonstrate the effectiveness of the algorithm for any initial and final position/direction of the knife-edge on the surface of the hyperboloid.