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Abstract- A visual servoing architecture for a six degrees of freedom PUMA robot, using predictive control, is presented. Two different approaches, GPC and MPC, are used. A comparison between these two ones and the classical PI controller is performed. The implemented PUMA robot model simulator used as platform for the development of the control algorithms is presented. A control law based on features extracted from camera images is used. Simulation results show that the proposed strategies provide an efficient control system and that visual servoing architectures using predictive control are faster than those using PI control. Experimental results are obtained from an architecture using a XPC Target and Matlab Simulink. Through this technology is possible to create an operative system which allows working in real time robot control. 37006
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1. INTRODUCTION The controller has a crucial role in a visual servoing system performance. Most of the developed works in visual servoing systems do not take into account the manipulator dynamics. Nevertheless, considering these parameters could increase the precision and the velocity of the system. The term Model Predictive Control (MPC) includes a very wide range of control techniques which make an explicit use of a process model to obtain the control signal by minimizing an objective function [1]. The MPC is often formulated in a state space formulation conceived for multivariable constrained control while Generalized Predictive Control (GPC), which was first introduced in 1987 [2], is primarily suited for single variable, being the model presented in a polynomial transfer function form. Predictive control systems have been applied to different fields such as industry, medicine and chemical process control. Particularly, Model Predictive control has been adopted in industry as an efficient way of dealing with multivariable constrained control problems [3]. A developed work in the field of visual servoing systems for small displacements used a predictive controller [4]. In this work, it is given continuity to some developed works in visual servoing research [5], [6]. In order to carry out this work a toolbox that allows incorporating vision in the PUMA robot control architecture was created. Its great versatility, allowing the easy interconnection of different types of controllers, becomes this type of tool very advantageous. In this paper the results of a set of experiences in the area of the modelling, identification and control of a visual servoing system for a PUMA 560 robot are presented. This paper is organised as follows: the implemented six degrees of freedom Puma robot model simulation and its validation is presented in section 2. A brief overview of a 2D visual servoing technique is introduced in Section 3. The principles of Predictive Control (GPC and MPC) and the identification of the PUMA ARMAX model are presented in Section 4. The experimental settings and the results for a PI, GPC and MPC controllers are given in section 5. Section 6 concludes the paper and section 7 suggests the continuity of this work. 2. PUMA 560 MODEL This work started with the implementation of the PUMA 560 model [7] corresponding to a six degrees of freedom robot model (Fig.1) with all the joints revolute. In order to validate the model, real tests in joint space with some controllers and gravity compensation [8] were performed.
q'' q' qtorque 2Dqout1qoutSum6SaturationMATLAB Function Robot MATLAB FunctionKrGMATLAB Function KG 1/s 1/s MATLABFunctionDACIn1 Out1 Gravitic compensation 1torque Fig. 1. PUMA 560 model simulation The model output (q) depends of the robot dynamics, the applied torque, the current position and the velocity. The binary applied to the joints are given by [9]: () (, ) () T Mqq Cqqq Fq Gq =+ ++ (1) where M is the Inertia matrix, q is the vector joints velocities, q is the vector joints acceleration. The matrices C, F and G represent the Coriolis and centripetal effects, the viscous and Coulomb Forces, and the gravity effects respectively.