Kinematics and Statics

Abstract

This chapter introduces basic notations pertinent to the kinematic structure of a humanoid robot. The main focus in the chapter is on differential kinematic relations. First, the forward and inverse kinematics problems for open-chain systems are formulated using first-order (velocity level) and second-order (accel-eration level) relationships. The existence of special (singular) configurations for robots with and without kinematically redundant limbs is clarified. Methods for instantaneous motion analysis at such configu-rations are then introduced. The role of the manipulability ellipsoid, manipulability and other kinematic performance measures is discussed. Further on, solution methods for the inverse instantaneous motion prob-lem for chains with kinematic redundancy are introduced. A detailed discussion on redundancy resolution methods under multiple motion-task constraints is provided. Also, the role of physical motion constraints is highlighted and contact joint models are introduced. Forward and inverse differential kinematic relations within chains comprising closed kinematic loops are derived. Static force relations within such chains are then discussed. Static posture stability is analyzed and the relations pertinent to internal force distribution are clarified. Finally, the complete characterization of a given posture from a kinetostatic viewpoint is presented.