Mechatronic approach for control of 2 DOF mini parallel robots.

Lapusan, Ciprian ; Maties, Vistrian ; Balan, Radu 等

Abstract: The paper addresses the issues of optimal control algorithms for mechatronics systems. For a given system the designer has to use a mechatronic approach which takes into account all the system components. Because of the complexity of the real systems the traditional modeling approach using classical methods can be a very hard task. The paper presents an integrated mechatronic environment for modeling and simulation. This method is applied for two mechatronic systems which consist of two planar micro parallel robots with two degrees of freedom (DOF).

Key words: mechatronics, integration, control, simulation, mini parallel robots.

1. INTRODUCTION

Due to the increasing demands of the modern economy, the development of new products must reach new levels concerning the complexity and the implemented intelligence while saving resources and reduce time needed for designing and production. An answer in satisfying these needs is to simulate using computer software the behavior of the designed structure in similar real world conditions. The development of the computers performance and the software applications complexity in the past few years, offers adequate tools for simulating complex engineering systems.

In most industrial cases, the system design process is divided into two sequential phases: the mechanical design and the control system design; usually, the mechanical design is not influenced by the control system conception: the designer simply tries to obtain high structural stiffness, because a very stiff machine is easily controllable by means of decoupled linear loops applied separately to each axis (Bruzzone, 2003).

The mechatronic approach the mechanical architecture is conceived in parallel with a more sophisticated control strategy's (Isserman, 2005). Like this it is possible to study exhaustively the behavior of the overall system, emphasizing the peculiar properties of the mechanical architecture itself. This approach allow, if the results of the system simulations do not offer the desired results, changes to the mechanical parts or control algorithm from the first phases of the design process. Also technical functions that in the traditional approach were executed by mechanical parts can be replaced with software functions.

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In order to simulate the behavior of a system, a model of it must be built. In the classic approach, the model of the system is built using mathematics. That is, real-world physical processes are described by mathematical relationships that are solved using suitable analytical or numerical techniques. As real engineering systems are very complex, it is not an easy task to create a valid model and solve it (Maties, 2001).

In the new approach, described in the paper, the model of the system is created by using three programs: SolidWorks[c], Visual Nastran[R] and Matlab[TM]/Simulink.

The integration of these applications offers a new perspective on the first phases of design. The model of the system is created automatically after the mechanical structure is defined in SolidWorks[c] and Visual Nastran[R]. Using Matlab[TM]/Simulink, the model of the system is developed. The control algorithm, the actuators, the sensors and the dynamic model of the mechanical structure are created using blocks from Simulink. Matlab permit to create and test different control methods in order to determine the optimal solution.

In order to illustrate the integrated approach proposed here, the design and control of two plan parallel micro robots with two DOF is studied.

2. PARALLEL ROBOTS

This section presents two micro parallel robots and their kinematics. Also the dynamic model is developed using the proposed method. First structure is a two DOF parallel micro robot also known as Biglide. Actuation of the robot is made using two dc electric motors. The transmission between the motor and the actuated joints is made using a screw nut mechanism as shown in Fig 2.a. The second structure is a two DOF parallel micro robot also known as the five bar mechanism (Fig. 2.b.).

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2.1 Inverse Kinematics

The equations resulted from the inverse kinematic problem are used in the system simulation for trajectory implementation. Inverse Kinematic Problem (IKP) is defined as the inverse problem of finding the joint variables in terms of the end-effector position and orientation of a manipulator (Merlet, 2000). Inverse kinematics problem of the Biglide robot can be solved by the following equations:

[q.sub.1] = [y.sub.p] - [square root of (([l.sub.1.sup.2] - [x.sub.p.sup.2]))] [q.sub.2] = [y.sub.p] - [square root of (([l.sub.2.sup.2] - (d- [x.sub.p]).sup.2]))] (1)

In order to simplify the computation for the Inverse Kinematic Problem, for the second robot, two symmetrical cinematic chains of the mechanism are considered (Fig. 2.b). The basic relations for IKP are:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

The [[psi].sub.1] and [[psi].sub.2] represents the generalized coordinates of the robot.

2.2 Dynamics

The dynamic model of the mechanical structure, for both robots, was created using Solid Works and Visual Nastran. The assembly and all the components were modeled using Solid Works (fig. 1.a and 1.b). The assembly created is then imported in Visual Nastran where the joints, the actuators and the sensors are defined. The actuators will became the inputs and the sensor will became the output of the model for the mechanical system. In order to import the model as a block with inputs and outputs in Simulink the component VNPlant is used.

3. SIMULATION OF MECHATRONIC SYSTEMS

In a mechatronic system the integration of mechanical engineering, electrical engineering and information technology creates critical dependences between all the components of the system. The simulation of a system must take into account all the modules that create the structure of the robot.

3.1 Control System

The control of the both robots is implemented using a joint-based control scheme. In such a scheme, the end effecter is positioned by finding the difference between the desired quantities and the actual ones expressed in the joint space (Lapusan, 2006). The command of the robot is expressed in cartesian coordinates of the end effecter. Using the inverse kinematic problem, these coordinates become displacements. These displacements will become the reference for the control algorithm.

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3.2 The model of the robots

The models of the robots were made using the module Simulink from Matlab Fig. 4 and Fig. 5. Simulink is a widely used tool for modeling and simulating dynamical systems. A model in Simulink is represented graphically by means of a number of interconnected blocks.

In both cases for each robot, the actuators were controlled using first a PI controller and then a PID controller.

The response at a step signal for Biglide robot is presented in Fig. 6.

4. CONCLUSION

In the paper was presented a mechatronic approach for designing and simulating a technical system. The model of the system was build using the software's Solid Works, Visual Nastran and Matlab. The response of the robots at step signal was simulated using a PI and PID controller.

5. REFERENCES

Bruzzone, E., Molfino, M., Zoppi, M. (2003). Mechatronic design of a parallel robot for high-speed, impedance-controlled manipulation, Proc. of the 11th Mediterranean Conference on Control and Automation, June 18-20, 2003, Greece

Isermann, R.(2005). Mechatronic Systems, Fundamentals, Springer, Londra, Anglia, 2005

Lapusan, P., Maties, V, Balan,R., Hancu, O.(2006). "Integrated design of the mechanism for mechatronics" COMEFIM'8 8th--10th June 2006, Cluj-Napoca

Maties, V., Mandru, D., Balan, R., Tatar, O., Rusu, C.(2001). Mechatronich Technology and Education, Ed. TODESCO, Cluj-Napoca, Romania, 2001

Merlet, J-P.(2000). The Parallel Robots, Kluwer Academic Publ., The Netherland, 2000.