Indefinite inner product-based decomposition and application to control of force and position of robot manipulators

A general algebraic framework for control analysis of constrained and compliant motion is presented. The author reviews the theory of screws, operators, and indefinite inner products to establish a mathematical formulation for a task space decomposition suitable for synthesis of constrained and compliant motion. Four components of the space of screws are identified and their mathematical properties are presented. The proposed decomposition generalizes the original hybrid force and position control. Applications to contact kinematics and system dynamics are given for illustration. The main contribution is to shed light on the issue of the hybrid control assumption of presumed orthogonality between constraint and freedom subspaces