5-DOF Manipulator Simulation based on MATLAB- Simulink methodology

Transcription

1 5-DOF Manipulator Siulation based on MATLAB- Siulink ethodology Velarde-Sanchez J.A., Rodriguez-Gutierrez S.A., Garcia-Valdovinos L.G., Pedraza-Ortega J.C., PICYT-CIDESI, CIDIT-Facultad de Inforatica, Universidad Autonoa de Queretaro, Queretaro, Mexico. Abstract Abstract This work presents a novel siulation ethodology applied to a 5-DOF anipulator. The work includes atheatical odeling of the direct, inverse and differential kineatics as well as the dynaics of the anipulator. The ethod ipleents the path following in the 3D space and uses the Matlab-Siulink approach. Several paths were tested to verify the ethod. This ethodology can be used with different robots to test the behavior and control laws. The ain objective of the present work is to show a coplete siulation ethodology using the sae prograing platfor, where, the cobination of Matlab and Siulink is proposed. Here, the atheatical calculations are perfored at the sae tie than its virtual representation. The ethod allows to anipulate the robotic syste and to visualize the robot s behavior fro different perspectives. To test the ethodology, a anipulator robot with 5-DOF as shown on figure 1 (Thero Scientific CATALYST-5) is used, this robot has the capability to load a axiu of 1.5. A PD+G (Proportional Derivative with Gravity Copensation) control is ipleented based on a dynaic odeling. Keywords Siulation ethodology, Siulink, Manipulator 1. INTRODUCTION Robotics is one of the ain disciplines in the industry which can be used in the developent of new technologies. The synergy of robotics with the different applications like subarine task, car assebly operation, vision systes and artificial intelligence allows the innovation and reduces the anufacture costs. For this purpose, it is iportant that the robot prograers are able to visualize and test the behavior of the robots in different circustances and with different paraeters. There are several prograing algoriths to siulate robotic systes [1]; soe of the use the link and joint positions, however, ainly the path following in the Cartesian work space are visually showed by lineal plots [2]. Soe other works only ake a 3D virtual aniation [3]. Other works only show the kineatic odeling in a ixed prograing environent like C++ and OpenGL [4], also, soe ultiple interface prograing technique has been developed using Matlab, C++ and OpenGL [5][6]; in both cases, the coputational tie increases, and is quite coplicated to anage the different prograing tools. Finally, soe research that presents an interface between Matlab and Siulink is used to siulate a echatronic syste [7], however, it doesn t have a visual representation like the one proposed in this article. Figure 1. Catalyst-5 Robot The robot specifications are presented on table 1: Link 1 length Link 1 ass l Link 2 length Link 2 ass l Link 3 length Link 3 ass l Link 4 length Link 4 ass l Link 5 length Link 5 ass l Gravity acceleration G 9.81 /s 2 Table 1. Robot specifications 2. KINEMATIC MODELING The dynaic odeling of a anipulator robot with n- degree of freedo (DOF.) can be divided in four steps: Direct Kineatics, Inverse Kineatics, Differential Kineatics and Dynaics /10/$ IEEE 295

2 Direct Kineatics: The objective of the direct kineatics is to deterine the accuulative effect that coes fro the set of variables of each link, that is, to deterine the position and orientation of the end-effector. The analysis of the Direct Kineatics was ade using the Denavit Hartebrerg convention as follows: Differential Kineatics: In the previous steps, the dynaics related with the position of the end-effector as well as the location of the joints and its position with respect to the reference frae, therefore, the position proble will be changed to a speed analysis proble of a serial anipulator. The differential kineatics is defined by the next equation: (2) where J is the Jacobian atrix. This atrix depends on the robot configuration and robot degrees of freedo (DOF). A i = (1) Then, the table 2 was obtained with the results: Table 2. Denavit Hartenberg paraeters After soe calculations, the end-effector position vector is defined by: X= Y= Joint i Dynaics: The dynaic equation of an n-dof in the anipulator can be defined as:, (3) To carry out the anipulator analysis in this research, we consider the Lagrangian analysis [9], this ethod consist in the generalized coordinate analysis and it is based on the Lagrangian function, which is defined by the difference between the kinetic and the potential energies on a echatronic syste and is defined as: (4) In the case of the serial anipulators, the Lagrangian is used in a atrix for and is represented by the next equation: (5) where,,,,,,,,. V is known as the Coriolis vector, G is the gravitational force vector, and M is the inertia atrix where the analysis of the anipulator is ostly perfored. 3. PROPOSED METHODOLOGY The developent of the atheatical algoriths is carried out in Matlab and the ipleentation of the virtual siulation was ade in Siulink as shown on figures 2 (a), (b), (c) and (d): Z= Inverse Kineatics: The inverse kineatics ain proble can be reduced to both the calculus of the position and orientation inverse kineatics, where a geoetrical approach to the proble solution is based in the Method proposed by Spong [8]. (a) /10/$ IEEE 296

3 (b) (c) Matheatical odeling: This step depends on the type of the robot to be analyzed. For deonstration purposes, the dynaical calculations can be taken as a reference by considering the physical and echanical properties of the links and the ass centers, therefore, we can use a odel based control as equation (3). Control Design: The position control proble of a anipulator robot anipulator can be solved according to the following ters: Considering the dynaics of an n-dof robot as equation (5). Having a constant path desired (Reference Point). Find a function in which the q (robot links) tends to qd (desired link direction) by using a PD, PID and Adaptable Control. To solve this particularr proble, a PD + G (Proportional Derivative with Gravity Copensation) control is used as shown on figure 4. (d) Figure 2. Robot Siulation project in Siulink The block diagra that expresses the whole ethodology necessary to carry out a siulation of a robotic syste is presented as a block diagra presented on the figure 3. The process starts fro the echanical analysis, continues with the dynaics until the virtual representation of the robot and its plots. Figure 4. PD + G Control Syste Path prograing: The anipulator work space and the path to follow are known. Then, the path should be prograed to be included in the control syste. CAD Manipulator: The virtual representation is close related with the echanical visual representation, and due to this fact, the SolidWorks progra is used as a design tool, but it is necessary to use geoetric objects that are a closer approxiation to each one of the robot links as shown on figure 5. If the coplete assebly of the robot is used, the siulation process will be ore difficult to carry out due to the fact that the odel will be ore difficult to load in Siulink and also because the ass center of each link will be harder to get. Figure 3. Proposed Methodology. Figure 5. SolidWorks assebly /10/$ IEEE 297

4 VRML2: To visualize the prototype in 3D using Siulink, it is necessary to convert the file into VRML 2.0. To solve this atter, the 2009 SolidWorks version can be used and it is necessary to export the design into VRML 2.0. If the file is saved in VRML 1.0, by using the CrossRoads progra the version can be changed to the proper one. Virtual Environent: Once the previous steps have been copleted and the kineatics is prograed, the next step is to ipleent it in the virtual environent that includes; anipulator design, data showing and path following visualization. In order to successfully carry out the siulation, it is necessary to have a Matlab 2009 version that includes the full 3D aniation library. Manipulator design: Here, the prototype is loaded by using the VR Sink block, where the odel can be edited using the VRML editor. Due to the fact that the robot coing fro the echanical syste is different to the assebly, the operations on the transforation fro one link to other is different in this editor, therefore it is necessary to perfor the next tasks: Identify each links of the anipulator. Leave only 2 ain transforations: o The transforation on the base which won t be oved; o The link transforation where the oveent chain is perfored to get the atheatical paraeters (this is variable depending on the robot to be used). In this way, it can be observed the linear plots in the virtual environent at the sae tie that the dynaical behavior of the anipulator is observed. Moreover, we can use the visualization tools of the virtual interface in Siulink to odify the physical aspects of the siulation in order to get soe pictures or videos. TEST AND RESULTS In order to test the proposed ethodology, the clover shape path was selected. This trajectory is represented as: 3 ; 3 ;.3; Considering the next paraeters, we perfor the siulation: Center of the figure in X-axis: 0.3 Center of the figure in Y-axis: 0.2 Petal Clover Radius: 0.07 Angular Speed: rad/s Control gains: ; ; ; ; ; ; ; ; ; ; As can be seen in figure 6, the plots show the behavior of the desired link paths and the real link paths. It is clear that the proposed ethodology can follow the desired path in a closer way. Text Visualization: To obtain the real-tie data fro the anipulator, we can use the VR Text Output. It is necessary to reference the virtual environent, also to introduce the variable naes to be shown together with the variable forat. Path Following Visualization: To show the path that the robot follows in the siulation process, it is necessary that the desired target as well as the real target to be connected to the block naed V Tracer. We need to connect x, y and z for the data acquisition. The type of path to be followed is selected and projected on the virtual environent; also, it is necessary to reference the nae of the transforations in the anipulator s design block to be represented in the workspace. Siulation: Once the virtual environent is created, and having the calculations already solved, the interface is carried out by executing the progra in Siulink. Figure 5 Inverse Kineatics Also, the path follow is shown after the control ipleentation in the Method. Here, it can be observed that the perforance is satisfactory and the plots of the real and the desired path are shown in blue and red respectively /10/$ IEEE 298

5 Figure 7 End Effector position The 3D space path (real and desired) were plotted as well as different views of the siulator on Figures 8 to 11. Figure 10. Siulation of the 3D path (Front view) Figure 11 Virtual Reality Siulation in Siulink Figure 8 Path in 3D space CONCLUSIONS AND FUTURE WORK A siulation ethodology of the 5-DOF was proposed. The odeling of the robot includes direct, inverse, and differential kineatics as well as dynaics. This ethod was applied to test the robot CATALYST 5 by using a project in Siulink and Matlab. A proposed path was plotted in the 3D space and the ethod was applied. All the plots fro the links and the end-effector positions were obtained and clearly show the good perforance of the proposed ethodology. As the future work, this ethodology will be applied to several robotic systes in order to test its behavior. Also, ore paths in 3D space will be tested in order to get the inforation about the speed, acceleration and force of each link in the anipulator. Soe other options include the testing of ore control algoriths like optial control. Figure 9 Siulation of the 3D path follow with control /10/$ IEEE 299

6 REFERENCES [1] Felix Etienne Trepanier and Bruce A. MacDonald, Graphical Siulation and Visualization Tool for a Distributed Robot Prograing Environent, Technical Report of the Departent of Electrical and Electronic Engineering, University of Auckland, New Zealand, [2] Stephen H. Murphy, John Ting-Yung Wen and George N Saridis, Siulation of cooperating Robot Manipulators on a obile Platfor, IEEE Transactions on Robotics and Autoation, Volue 7, Issue 4, pp , Aug [3] Martin Rohreier Web Based Robot Siulation using VRML, Winter Siulation Conference Proceedings, Volue 2, pp , [4] Moreno Trejo Roberto, Cabrera Ríos Juan Salvador, Hernández Rairez Fernando, Jose Eilio Vargas Soto, Jesus Carlos Pedraza Ortega, Siulation Software of the Mitsubishi RV-2AJ Manipulator Robot, Proceedings of the 4th Mexican Conference on Mechatronics, pp , 2005 (In Spanish Language). [5] J.A. Soto, J. E. Vargas and J.C. Pedraza A New Trajectory Generation Method Using Vision for a Robot Manipulator, International Conference on Dynaics, Instruentation and Control (CDIC), [6] Maricela Gaiño, J. Carlos Pedraza Juan M. Raos, Efrén Gorrostieta. Matlab-C++ Interface for a Flexible Ar Manipulator Siulation using Multi-Language Techniques, Proceedings of the Fifth Mexican International Conference on Artificial Intelligence (MICAI), pp , [7] Nourdine Aliane A Matlab/Siulink-Based Interactive odule for Servo Systes Learning, IEEE Transactions on Education, Volue 7, Issue 4, pp. 1 7, [8] Mark W. Spong. Robot Modelling and Control, John Wiley and Sons, [9] Lung Went Tsai Robot Analysis: The Mechanics of Serial and Parallel Manipulators, Wiley, /10/$ IEEE 300