23 Model-free Subspace Based Dynamic Control of Mechanical Manipulators Muhammad Saad Saleem and Ibrahim A. Sultan University of Ballarat Australia 1. Introduction Realtime identification and dynamic control of mechanical manipulators is important in robotics especially in the presence of varying loading conditions and exogenous disturbances as it can affect the dynamic model of the system. Model free control promises to handle such problems and provides solution in an elegant framework. Model free control has been an active area of research for controlling plants which are difficult to model and time varying in nature. The proposed framework takes the objective in operational space. Benefit of specifying objective in operational space along with direct adaptive control is self evident. In this framework, subspace algorithm is used for model identification. is used for robust control of manipulator dynamics. Because of the seamless integration of identification and control modules, explicit values of dynamic parameters is not calculated. The model free control system is capable of explicitly incorporating uncertainties using μ-synthesis. Uncertainty models can be calculated from experimental data using model unfalsification. The proposed control system employs a black box approach for dynamics of mechanical systems. The chapter also presents results from a simulation of a planar robot using MATLAB® and Simulink® from MathWorks Inc. 1.1 Notations The rigid body model adopted in this chapter is given by (1) where M(q) is the inertia tensor matrix, C(q, $ q ) is the Coriolis and centripetal forces, G(q) is gravity, and ξ (q, $ q ) denotes unmodeled non-linearities. Joint variables, their velocities, and positions are donated by q, $ q , $$ q ∈ . In case of revolute joint, q is the angle while in prismatic joint, q represents the distance. The torques generated by actuators are represented by u ∈ . It is assumed that the mechanical manipulator is fully actuated, non-redundant and the Jacobian is known. If the position of endeffector is given by forward kinematics equation i.e. x = f kinematics (q). It can be differentiated by ∂q to obtain (2) Open Access Database www.i-techonline.com Source: Robotics, Automation and Control, Book edited by: Pavla Pecherková, Miroslav Flídr and Jindřich Duník, ISBN 978-953-7619-18-3, pp. 494, October 2008, I-Tech, Vienna, Austria www.intechopen.com