Uiversity of Missouri-Columbia Departmet of Electrical ad Computer Egieerig ECE 7330 Itroductio to Mechatroics ad Robotic Visio Fall, 2010 PROJECT #2 GENERIC ROBOT SIMULATOR Luis Alberto Rivera Estrada ID # 14103824 December 17 th, 2010
2 Abstract The objective of this project is to develop a geeric robot simulator. Several simulators of specific robots have bee implemeted. The program developed creates robots accordig to the well kow D-H represetatios. It has several predefied robots available for the user to try. New robots are easily created by iputtig the correspodet D-H parameters. To evaluate the performace of the proposed simulator, a compariso is made agaist Peter Corke s Matlab Robotic Simulator. Itroductio Havig a simulator ca be very helpful whe desigig a system. I the particular case of a robot, a simulatio ca help, for istace, i determiig a suitable workspace for it. There are some robot simulators available. [1] is a ice Matlab Toolbox that allows forward ad iverse kiematics aalysis, amog others. It also allows simulatig some robots. For istace, the Puma 560. [2] is aother simulator that offers a ice user iterface ad a more detailed CAD like visualizatio of the robot. But it is restricted to oe robot, the Puma 762 from the WWU Robotics Lab. A simulator for a particular robot may iclude more details, like actual lik dimesios ad shapes, physical limitatios of the robot or the workspace, special fuctios or tasks that the robot is programmed to do, etc. A geeric robot simulator, o the other had, is probably limited i terms of specific details, but it allows simulatig importat aspects like joit movemets, positio ad orietatio of ed effectors, etc. of a virtually ulimited umber of differet robots.
3 The proposed simulator is based o the stadard D-H represetatio. It allows the user to create his/her ow robot by iputtig the D-H parameters. The differet features ad limitatios of the simulator will be explaied throughout the report, which icludes sectios o techical backgroud, descriptio of the simulator ad methods, results, coclusios ad future work. Problem Statemet ad Techical Backgroud The Deavit-Harteberg (D-H) model of represetatio is a simple way of modelig robot liks ad joits. It is assumed that a robot is made of a sequece of joits ad liks. The joits ca be either prismatic (liear) or revolute (rotatioal). They ca be i ay order ad i ay plae. The liks may be of ay legth (icludig zero), may be twisted or bet, ad may be i ay plae. So, ay geeral set of joits ad liks may create a robot. [3] To model the robot a referece frame is assiged to each joit. Matrices are defied to trasform from oe joit to the ext. A total trasformatio matrix is obtaied combiig all the trasformatios from the base of the robot to the last joit (ad/or possibly the ed effector). [3] [3]
4 The ecessary motios to trasform from oe referece frame z, x to the ext z x are the followig:, 1 1 1. Rotatio of a agle 1 about the z axis, which will make x ad x 1 parallel to each other. 2. Traslatio of a distace d 1 alog the z axis to make x ad x 1 colliear. 3. Traslatio of a distace a 1 alog the x axis to brig the origis x ad x 1 together. 4. Rotatio of the z axis a agle 1 about the x 1 axis to alig z with z 1 axis to fially make frames ad 1 be exactly the same. [3] The matrix represetig the four movemets is obtaied by postmultiplyig the four matrices represetig the four movemets, as follows: T 1 Where A 1 Cx Rot C S 0 0 z, Tras0,0, d Trasa,0,0 Rotx, 1 1 1 S C 1 1 S C 1 0 C 1 1 cosx ad Sx six. 1 S 1 C 1 C S 0 1 The total trasformatio betwee the base (frame 0) ad the last frame (frame, usually the had or ed effector) is 0 T 1 S 1 1 a a 1 1 C d S 1 1 1 1 0 1 1 T1 T2 T A1 A2 1 A. A table of joit ad lik parameters (D-H table) summarizes the characteristics of a robot. The values are determied from a schematic drawig of the robot after assigig proper frames for each of the joits that costitute the robot. I essece, such a D-H table describes a robot. This is the mai idea behid the geeric simulator developed for this project assigmet. All it takes to create ad simulate a robot is to have a D-H table. I the ext sectio I describe the actual simulator.
5 Descriptio of the Simulator The Puma3D simulator [2] was used as a base for creatig the simulator for this project. The graphical iterface is illustrated ext: It has the followig features: D-H table for defiig the robot.
6 Robots with up to six joits (degrees of freedom) ca be defied. The joits ca be revolute or prismatic. Additioal to the four parameters for each joit (, d, a, ) it is possible to set the miimum ad maximum value for the correspodet variable ( for revolute joits ad d for prismatic joits). After the parameters are iput, by clickig o the Set butto the robot is created. The positio determied by the D-H parameters (i particular, determied by the values of variables) becomes the Home positio of the robot. There are various pre-defied robots for the user to try. Clickig o the Default, Puma 560, Example 1, Example 2 ad Example 3 will put D-H parameters i the correspodet boxes. Clickig o the set butto will create the correspodet robot. Buildig the Robot. The robot cosists of joits ad liks. Geeric shapes are used for the joits. Cyliders are used for the revolute joits ad prisms are used for the prismatic joits. Sice there is o detailed descriptio of the liks (shape, width, etc.), thick lie segmets are used. Those lies coect cosecutive frame origis. A simple ed effector is placed at the last frame of the robot. The first origi (frame 0, correspodig to the base) is placed at the world s origi. For visualizatio purposes, a (gree) coical base completes the structure of the robot.
7 Robot s Workspace The scales of the axes adjust to the dimesios of the robot to have a good visualizatio of the robot. The last origi (show i red) is projected to the groud ad to the backgroud walls. This helps i the visual localizatio of the ed effector. Movig the Robot: Kiematics cotrol.
8 The idividual joits ca be maipulated i order to move the robot. A slider bar ad a edit box allow chagig the correspodig variables. The maximum ad miimum values specified i the D-H table are reflected i the kiematics cotrol pael. The Radom butto will produce a radom movemet of the robot, ad the Home butto will brig the robot to the home positio. Positio ad Orietatio of the Ed Effector The Homogeeous trasformatio matrix represetig the pose of the last coordiate frame is displayed i the table show above (with the exceptio of the last row). Vectors, o ad a are the directio vectors of the frame, ad vector P is the positio vector of the frame s origi. Results Next I show some of the example robots predefied. Moreover, I show a compariso betwee my proposed simulator ad the simulator proposed i [1] for the Puma 560 robot.
9 Example 1: 3 joit robot (revolute, prismatic, revolute). [4]
10 Example 2: 4 joit robot (revolute, prismatic, prismatic, revolute). [4]
11 Example 3: 6 joit robot (all revolute joits). [4]
12 Puma 560: compariso betwee simulators. The D-H table for the Puma 560 robot accordig to the toolbox proposed i [1] is the followig (all joits are revolute): # d a 1 0 0 0 90 2 0 0 0.4318 0 3 0 0.15005 0.0203-90 4 0 0.4318 0 90 5 0 0 0-90 6 0 0 0 0 Show above is the home positio. Note the x, y ad z coordiates of the last frame ad its a directio vector. The home positio accordig to my simulator is ext: Note that both the positio vector ad the directio vector coicide with the correspodet vectors i Corke s simulator. Now, cosider some other cofiguratio of the joit variables.
13 Compariso cofiguratio 1: 1 60, 2 30, 3 10, 4 20, 5 90, 6 180 Note how the positios ad orietatios coicide.
14 Compariso cofiguratio 2: 1 150, 2 45, 3 30, 4 45, 5 0, 6 90 Note agai how both simulators give the same positio ad orietatio.
15 Coclusios ad Future Work The proposed simulator allows creatig ad simulatig a large variety of robots, with up to six degrees of freedom. Its user friedly iterface ad simple D-H parameters ad cotrol paels make it easy to defie ad build robots, ad the to move them. It offers several features that ehace the visualizatio of the robot ad the positio of the ed effector. This simulator may be a useful tool for desigig real robots or for academic purposes. Future versios of the simulator may iclude some of the followig features: Allow the user to save D-H parameters ad to load previously saved oes. Allow iteractig with the workspace (e.g. zoomig, rotatig, maipulatig the axes, etc.). Optio to place the base of the robot i differet locatios with respect to the world. Iclude more details of the joits ad liks. Costrai the joit variables to take physical limitatios ito accout. Others. Refereces 1. P.I Corke A Robotics Toolbox for MATLAB. IEEE Robotics ad Automatio Magazie. No. 1, Vol. 3, March, 1996. Pp. 24 36. 2. PUMA3D Simulator of the Puma robot located i the Robotics Lab of Walla Walla Uiversity. 3. S. B. Niku. Itroductio to Robotics: Aalysis, Systems, Applicatios. Pretice Hall. Uited States of America, 2001. 4. G. DeSouza. Lecture otes from the course Itroductio to Mechatroics ad Robotic Visio. Uiversity of Missouri Columbia. Fall, 2010.