Real-time implementation of a dynamic fuzzy neural networks controller for a SCARA

This paper presents the design, development and implementation of a Dynamic Fuzzy Neural Networks (D-FNNs) Controller suitable for real-time industrial applications. The unique feature of the D-FNNs controller is that it has dynamic self-organising structure, fast learning speed, good generalisation and flexibility in learning. The approach of rapid prototyping is employed to implement the D-FNNs controller with a view of controlling a Selectively Compliance Assembly Robot Arm (SCARA) in real time. Simulink, iterative software for simulating dynamic systems, is used for modelling, simulation and analysis of the dynamic system. The D-FNNs controller was implemented through Real-Time Workshop (RTW). RTW generates C-codes from the Simulink block diagrams and in turn, the generated codes (object codes) are downloaded to the dSPACE DS1102 floating-point processor, together with the supporting files, for execution. The performance of the D-FNNs controller was found to be superior and it matches favourably with the simulation results. INTRODUCTION The promise of robots being able to replace menial, tedious, or dangerous human tasks has motivated many engineers to design and develop more sophisticated and intelligent controllers for robotics. Numerous intelligent control methodologies have been devised to solve a number of complicated problems in robot manipulators, which are represented by a multivariable non-linear coupled dynamic system with uncertainties (Takagi, 1992) – (Neo and Er, 1996). Due to uncertainties, it is difficult to obtain an accurate mathematical model for robot manipulators. Conventional control methodologies find it difficult or impossible to handle unmodelled dynamics of a robot manipulator. To accommodate system uncertainties and variations, learning or adaptive techniques must be incorporated. Most conventional methods, e.g. PID controllers, are based on mathematical and statistical procedures for modelling the system and estimation of optimal controller parameters. In practice, the plant to be controlled is often highly non-linear and a 1 School of Electrical and Electronic Engineering Nanyang Technological University Nanyang Avenue, Singapore 639798. REPUBLIC OF SINGAPORE Tel : (65) 67904529, FAX : (65) 67912687 Email : [email protected], [email protected] and [email protected] Journal of The Institution of Engineers, Singapore Vol. 44 Issue 3 2004 2 mathematical model may be difficult to derive. As such, conventional techniques will not be able to handle modelling errors and are lack of robustness. Fuzzy logic, however, offers a promising approach towards designing robot controllers. In contrast with conventional controller design techniques, fuzzy logic formulates control of a plant in terms of linguistic rules drawn from the behaviour of a "human operator" instead of an algorithm synthesised from a rigorous mathematical model of the plant. Due to the growing popularity of Neural Networks, much research effort has been directed towards design of intelligent hybrid controllers using Fuzzy Logic and Neural Networks. Design of robust adaptive controllers suitable for real-time control of robot manipulators is one of the most challenging tasks for many control engineers. Robot manipulators are multivariable non-linear coupled systems and are frequently subjected to structured and/or unstructured uncertainties even in a well-structured setting for industrial use. The Dynamic Fuzzy Neural Networks (D-FNNs) algorithm developed in (Er and Wu, 2002) is a newly developed algorithm that has the following salient features: dynamic self-organising structure, fast learning speed, good generalisation and flexibility in learning. The D-FNNs controller is employed to compensate for environmental variations such as payload mass and disturbance torque during the operation process. By virtue of on-line learning, it is able to learn the robot dynamics and make control decisions simultaneously. In effect, it offers an exciting on-line estimation scheme of the plant. The approach of Rapid Prototyping is used to implement the D-FNNs controller in realtime through Real-Time Workshop (RTW) using the Texas Instruments TMS320C31 floating-point processor, together with some supporting files. In addition, Simulink is used for modelling, simulation and analysis of the dynamic system. DYNAMIC MODEL OF THE SEIKO TT-3000 SCARA The SEIKO D-TRAN 3000 Series robot used in this work is a four-axis, closed-loop DC servo Selectively Compliance Assembly Robot Arm (SCARA). Each of the four axes provides a different motion and contributes to one degree of freedom of the robot (see Figure 2-1). The main characteristics of the TT-3000 SCARA are its high precision, repeatability and speed. The basic SCARA geometry is realised by arranging two revolute joints (for simplicity, they will be called Joint T1 and Joint T2 herein) and one prismatic joint (for simplicity, it will be called Joint Z herein) in such a way that all axes of motion are parallel. The acronym SCARA characterises mechanical features of a structure offering high stiffness to vertical loads and compliance to horizontal loads. The dynamic equations of the SCARA can be represented by a set of highly non-linear coupled differential equations given by ( ) ( , ) ( ) ( ) V C M C G F F θ θ θ θ θ θ θ τ •• • • • + + + + = (2.1) Journal of The Institution of Engineers, Singapore Vol. 44 Issue 3 2004 3 where M(θ) is the n×n inertia matrix of the manipulator, C(θ, ̇θ) is the n×n matrix of Centrifugal and Coriolis terms, G(θ) is the n×1 vector of gravity terms, Fv( ̇θ) is the n×1 vector of viscous friction terms, Fc is the n×1 vector of coulomb terms and τ is the n×1 vector of the input torque (generated by the joint motor). The terms θ, ̇θ, ̇ ̇θ, are the nx1 vectors of the output link position, velocity and acceleration respectively. The dynamic model of the TT-3000 SCARA has been developed in [6], with most of its parameters determined and verified through experiments. Based on this known mathematical model of the robot, training of the D-FNNs controller was carried out using MATLAB simulation tools. Figure 2.1: The SEIKO TT-3000 SCARA DESIGN OF THE D-FNNS CONTROLLER Architecture of D-FNNs The architecture of the D-FNNs developed in (Er and Wu, 2002) is depicted in Figure 31. It is constructed based on the Radial Basis Function (RBF) and functionally, it is equivalent to an TSK model-based fuzzy system. In Figure 3-1, Layer 1 defines the input variables layer. This is the layer where the input signals first enter the D-FNNs. Layer 2 represents the membership functions associated with the input variables. The Journal of The Institution of Engineers, Singapore Vol. 44 Issue 3 2004 4 membership function is chosen as a Gaussian function of the following form: 2 2 -( ) exp 1, 2,3 1, 2, 3 i ij ij i j x c MF (x ) i r j u σ ⎡ ⎤ = = = ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ... ... (3.1) where r is the number of input variables and u is the number of membership functions. Layer 1 Layer 2 Layer 3 Layer 4 x i ij MF φ j j w y Figure 3.1: Architecture of D-FNNs Layer 3 is the rule layer. The number of RBF units in this layer indicates the number of fuzzy rules. The outputs are given by ∏ = = r i j MF 1 ij φ (3.2) Layer 4 defines the output variables. Each output variable is a weighted sum of incoming signals. Corresponding to a fuzzy system, this layer performs defuzzification that considers effects of all membership functions of the input values on the output, i.e., 1 u j j j y w φ = = ∑ (3.3) The weight is chosen as follows in the TSK model: x x w r rj j j j α α α + + + = ... 1 1 0 (3.4) where αi ’s are real-valued parameters. It is not difficult to see that Eq. (3.3) can be Journal of The Institution of Engineers, Singapore Vol. 44 Issue 3 2004 5 re-written as y W = Φ (3.5) Where [ ] 01 11 1 02 12 2 0 1 r r n n rn W α α α α α α α α α = (3.6) [ ] 1 1 1 1 2 2 1 2 1 T r r u u u r x x x x x x φ φ φ φ φ φ φ φ φ Φ = (3.7) Adaptive Fuzzy Neural Control Scheme The proposed adaptive fuzzy neural control scheme is depicted in the following figure.