Robot Visualization System for Windows (RVS4W) User's Manual
Contents
1. 445465 usu Figure 20 The Conditioning dialog is known as the forward problem Khan and Angeles 2006 the inverse problem con sisting in the computation of all DH parameters of an optimum robot with maximum conditioning under user specified constraints RVS4W attempts to solve the above mentioned problem using the Nelder Mead simplex method This is done when the robot is loaded RVS4W displays a besides the robot name upon convergence The characteristic length is displayed in the Characteristic length text box Should the Nelder Mead method fail to converge a sign is displayed besides the filename and a value of 1 is put in the Characteristic length text box For cases where evaluation of the characteristic length is either irrelevant or undefined e g in the case of spherical robots RVS4W displays 0 in the Characteristic length text box 2 8 The Environment Menu 2 8 1 Set Work Environment Creating and editing the work environment The Set Work Environment command allows the user to set the work environment Click Environment gt Set Work Environment from the menu Fig 21 This brings up the Set Work Environment dialog Fig 22 to select and place objects in the work environment follow the steps below 1 Input the required number of objects in the Total text box 2 Select the first object by choosing 1 from the ID list 24 8 9 fim Robot Yisualization System for Windows 3R2. It is also possible to save a robot posture Please refer to Subsection 2 5 3 below to find how this can be done To move to a previously saved posture select Posture gt Select Configuration from the menu Fig 11 The Select Configuration dialog will popup on the screen 14 Minimum Maximum Joint 4 0 00 a 0 00 gt Joint 2 0 00 0 00 Joint 3 0 00 Soo Figure 12 The Joint Limits dialog Fig 13 All the saved postures of the loaded robot are displayed in a list box The Select Configuration dialog offers three functions e To move the robot to a saved configuration select the desired configuration from the list box e Spline When this option is selected the robot translates from the current posture to the selected posture e Jump Select this option if you want the robot to jump to the selected configu ration Click close to hide the Select Configuration window 2 5 3 Forward Kinematics To change the posture of the robot by changing the value of the joint coordinates for ward kinematics or to save the current joint configuration click Posture gt Forward Kinematics Fig 11 This brings forth the Forward Kinematics dialog Fig 14 The symbol th represents the joint number Next to the joint number is the respective joint coordinate value e To change the value of the joint coordinate do one of three actions 1 Input the new value of the joint coordinate in the appropria
3. John Darcovich the author of RVS is the brain behind this project RVS4W like RVS was made possible thanks to the sustained support of NSERC to the third author s research Disclaimers RVS4W and RVS are intended for research and education use only The authors cannot be held responsible for any errors or damage caused by the use of this software packages Contents 1 Introduction 1 1 1 2 RVS4W Features Document Conventions Li 2 RVS4W Basics 2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 Startin RVSAW rusa abr die dle Rodio Ae aria E ad eae We Mosconi ceh ASE A AA UMTS AAA Sa E AERO Ode Men ta e ds dea de de ee ds ath ase 2 4 1 New Robot Creating a robot cier isla Do AS 2 4 2 Load Robot Loading an existing robot 2 4 3 Edit Robot Editing the robot lt tc one be awe oe 2 4 4 The Link Settings dialog ooa oaa ge ee 2 4 5 Displaying the DH parameters of the current robot 2 4 6 End Effector Selecting an end effector 24T Saver Sane A TOOT o s aose Gla SERIA AI 2 4 8 Save As Saving a robot with another name 220 Exit bomme RVSAW a pena A ST SSG 5 SSE are The Posture Menu sosia sri Gass REA ai 2 5 1 Joint Limits Setting joint limits cesa aldo 2 5 2 Select Configuration Moving the robot to a saved posture 2 5 3 Forward Kinematics aoaaa a e karat 2 5 4 Iny se Kinematics o o a sa cuts e Gen pesi e e kr d The Trajectory Menea Susa nanne ae e 2
4. Hllo yt HWH7 W 1 2 m Hence the weighted Frobenius norm of a m x n matrix with n gt m yields the rms value of the set of m singular values of H Strang 1986 The conditioning lies in the interval 0 1 with 1 being best and 0 worst 22 li Transform Trajector loj xj Transform Trajectory Position Orientation aj Rx 10 000 aj Ry 0 000 aj Rz 0 000 ni Scale Scale 1 000 m Traj Fief save close Figure 19 The Transform Trajectory dialog If the robot at hand is redundant with n gt m joints then H is am x n matrix formula 1 still applying but with H replaced by the right Moore Penrose gener alized inverse of H namely H7 HH Strang 1986 It is not difficult to prove that the Frobenius norm of the foregoing generalized inverse reduces to H HH 7 y ion 3 In order to avoid dimensional inhomogeneity RVS4W evaluates the characteristic length of the robot The numerical value of the characteristic length is shown in the Characteristic length display box in the Conditioning window in usu Further details on conditioning characteristic length and the optimum posture can be found in Angeles 2007 Khan and Angeles 2006 The evaluation of the characteristic length given the DH parameters of a robot That is a Jacobian with entries bearing disparate physical units 23 oix kappa osasose Charactenstic Length 0 890525 usu Madamum Reach
5. Of xj Filename Ri 1 D DH Parameter Fe AER ES EA a 0 0 0 D b o o fo o al o o o o th o o fo o Prismatic i i O L i Limits I Limits Limits Limits Limits I Limits I min 0 0 O 0 O 0 max 0 O 0 D 0 0 oO o o o o 0 Oo ao Description Save M close Figure 4 The Robot Parameter dialog 2 4 2 Load Robot Loading an existing robot Select Robot gt Load Robot from the main menu Fig 2 to display the Load Robot dialog Fig 5 In this dialog a list box displays the list of existing robots The user has several options e Select a robot to view its description e To load a robot choose the desired robot and click Load e To delete a robot select the robot to be deleted and click Delete The con firmation dialog appears Click OK to delete the robot or Cancel to keep it Notice that when a robot is deleted all the relevant data are erased from the system This includes the architecture configuration and trajectory files of the selected robot This means that if the user is to try a given trajectory on var ious robots then the user must save the trajectory in a separate data file then copy and paste it on the data file of every robot to be assigned this trajectory for tracking laa Select Architecture Cuatro vrist CuatroNew DIESTRO Description Load Delete close Figure 5 The Load Robot dialog 2 4 3 Edit Robot E
6. Robot Posture Trajectory Conditioning Environment PE Export About Figure 26 Menu Setting e Inverse Kinematics This group allows the user to fine tune the inverse kine matics engine Please refer to the Appendix for further details To exit the dialog click close 2 10 Export Exporting a scene RVS4W can export the current scene to various file formats To export a scene 1 Select Export gt Export Fig 28 The Export dialog will popup on the screen Fig 29 2 Input the filename in the Filename text box 3 Select the desired file format from the drop down list and click Save 2 11 About The About command provides some information about RVS4W Select About gt About Fig 30 to display the About dialog on the screen Fig 31 Configurations 29 lal Setting System Mei Background Color x A grey view Axes fim Robot Visualization System for Windows 3R Figure 28 Menu Export 30 fal OpenGL Scene Export mi 215 xi Figure 29 The Export dialog i N iu 0 N AN i eo a ZE i n mi W X X i N DA i i I ON ne AY Y LE Figure 30 Menu about 31 201 Robot Visualization System for Windows Version Beta Version 1 0 Built March 2007 Department of Mechanical Engineering amp Centre for Intelligent Machines McGi
7. 6 1 Joint Trajectory Making the robot follow a joint trajectory 2 6 2 Cartesian Trajectory Making the robot follow a Cartesian TAJO ci bh gin ur And fe the a ai area e 2 6 3 Transform Trajectory Transform a displayed trajectory 2 6 4 Converting joint trajectories to Cartesian trajectories Conditioning fcc wen rt pc a Shree ea Ses The Environment Menu fs ala fa Ker Go ee Dh Ee ee ele 2 8 1 Set Work Environment Creating and editing the work envi FORME sa dad ka see t E kes 4 2 8 2 Load Work Environment Loading a work environment 2 8 3 Obstacle Creating and editing obstacles 2 8 4 Payload Creating and editing payloads Sy gite Ma ae ARA ALL 2 10 Export Exporting a scene adrede Pe Urs RR A ah tel a ee a dol 3 Joint Configuration 24 26 26 26 27 29 29 32 4 Trajectories 4 1 Cartesian Trajectories sara ea SUE AE AS G 4 2 Joint Trajectory Bibliography Appendices 32 32 33 34 34 1 Introduction RVS4W is a 3D visualization tool to be used to determine the feasibility of a new robot or of a new path plan This tool is an updated version of its IRIX predecessor RVS Darcovich Angeles Montagnier and Wu 1999 In the skeleton mode the Denavit Hartenberg DH parameters of the robot at hand are read from a data file and rendered as a kinematic chain using a standard set of skeleton primitives This set includes an L shaped link with dimensions in proportio
8. Journal of Robotics Research Vol 4 No 2 pp 21 87 Angeles J 2007 Fundamentals of Robotic Mechancal Systems Theory Methods and Algorithms Third edition Springer New York Darcovich J Angeles J Montagnier P and Wu C J 1999 RVS A robot visual isation software package in Batoz J L Chedmail P Cognet G and Fortin C editors Integrated Design and Manufacturing in Mechanical Engineering Kluwer Academic Publisher Dordrecht pp 265 272 Strang G 1986 Introduction to Applied Mathematics Wellesley Cambridge Press Wellesley Khan W A and Angeles J 2006 The kinetostatic optimization of robotic ma nipulators the inverse and the direct problems ASME Journal of Mechanical Design No 128 pp 168 178 Appendix Here we provide a brief account of the numerical procedure that RVS4W uses to solve the inverse kinematics displacement problem For details the reader is referred to 34 Angeles 1985 as a basic reference We have fine tuned the numerics behind the algorithm therein We set the task as a nonlinear least square problem in the six joint variables O as min 306 4 where vect AQ p tr AQ AQ QQ6 1 Ar r r 5 Ar Furthermore 1 is the 3 x 3 identity matrix Q is the rotation matrix that represents the current orientation of the end effector with respect to that of the base frame Qc being the target counterpart of Q i e the representation of the desired E
9. 4 13 A lale File contig save close Figure 14 Dialog Forward Kinematic 2 6 The Trajectory Menu 2 6 1 Joint Trajectory Making the robot follow a joint trajectory The Joint Trajectory command allows the robot to follow a pre stored joint trajec tory To activate the Joint Trajectory command select Joint Trajectory from the Trajectory menu Fig 16 The Joint Trajectory dialog will popup on the screen Fig 17 In this dialog a list box displays the stored joint trajectories for the loaded robot e Click on the desired trajectory to load it The corresponding Cartesian trajec tory is evaluated and displayed in the main RVS4W window in blue e Points Click once to display the corresponding Cartesian position points of the trajectory Click again to switch the option off e Frames Click once to display the Cartesian frames of the trajectory Click again to switch the option off e Cont To make the robot follow the trajectory continuously check the Cont text box e Step To make the robot follow the trajectory step by step check the Step text box 17 E Inverse Kinematics ol xj Cartesian Configuration amp Jacobian J Display Position Orientation E E Rx 66 038 i R aj Ry 36 094 si i aj RZ 134 665 i Figure 15 The Inverse Kinematics dialog e Reset Click to move the end effector to the initial position e Clear Click to unload the selected trajectory clear th
10. 4W Basics This section introduces the user into the basic features of RVS4W After reading this section the user should be able to load RVS4W and use its main functions 2 1 Starting RVS4W To start RVS4W go to install directory rs and double click RVS4W EXE The RVS4W main window will appear as shown in Fig 1 RVS4W commands are grouped in the main menu displayed at the top of the RVS4W window To activate a command navigate through the menu system and select the required menu item The corresponding dialog is invoked and displayed on the screen Notice that to activate some commands the user must load a robot in RVS4W 2 2 Mouse Controls Once a robot is loaded the user can rotate zoom and translate the rendering e Press and hold the left mouse button and drag the mouse to rotate the workspace with respect to the viewer e Press and hold the middle mouse button and drag the mouse upwards down wards to zoom in zoom out e Press and hold the right mouse button and drag the mouse to translate the workspace in the corresponding direction 2 3 Units With regards to the geometric dimensions of the robot and the work environment RVS4W does not incorporate a unit manager The user is free to decide on the units of length while interacting with RVS4W Whenever units of length are needed in this document the legend usu for user specified units is included The user is encouraged to indicate the selected units in the corresp
11. DI x Robot Posture Trajectory Conditioning aa Setting Export About e k Environment Load Work Environment Obstacle Payload Figure 21 Menu Environment Turn on the Visible button Select the type of object from the Object drop down list Enter the dimensions of the selected object in the Length Height and Width text boxes Enter the position of the selected object in the Position x Position y and Position z text boxes Orient the object by selecting an axis of rotation and inputting the desired angle of rotation by using the Rotation text box From the Color list select the color of the object Select the next ID from the ID list and repeat steps 3 to 8 To save the environment input the filename in the File text box and click Save Click close to exit the dialog 25 1513 Object rable y File Enviroment A E n 3 Position x 0 00 E Length 1 00 El ition y zi i F Position y 0 00 z Height 11 00 F PRA E al idth aj Position z 0 00 2 Width j1 00 gt Ratation o k Color crey T visible wf Totat 1 m save close Figure 22 The Set Work Environment dialog 2 8 2 Load Work Environment Loading a work environment To load the work environment of a robot select Load Work Environment from the Environment menu Fig 21 The Load Work Environment dialog will popup on the screen Fig 23 The types of Work environment available are displayed in a list box Select
12. E orientation while r is the homogenized position vector of the end effector That is r is a dimensionless position vector obtained upon dividing the current position vector in usu by the robot characteristic length in usu as well Notice that the characteristic length is calculated by RVS4W upon loading a given robot The iterative procedure involved can be either successful or unsuccessful in reaching convergence If successful the computed value is transferred to the inverse kinematics routine otherwise this routine uses the mean value of the link lengths in lieu of the characteristic length As well rc is the target position vector of the operation point Both Q and r are defined in the base frame Finally vect and tr are correspondingly the vector and the trace Angeles 2007 of the argument matrix a 3 x 3 rotation matrix RVS4W uses the Newton Gauss method to solve problem 4 iteratively Given an initial guess 0 a sequence 0 02 0 is generated which produces a monotonically decreasing sequence of values 21 22 2 PY with z defined as i 5120 4 0 6 The sequence is generated in the form with the correction AG computed as the least square approximation of an over determined linear system of seven equations in six unknowns namely BAO p 0 8 where 96 0 0 59 10 0 9 is the 7 x 6 Jacobian matrix of the nonlinear system 5 Notice that problem 8 is
13. Robot Visualization System for Windows RVS4W User s Manual W Khan H Zhuang and J Angeles Centre for Intelligent Machines CIM Department of Mechanical Engineering McGill University Montr al Qu bec Canada June 11 2007 Abstract Visualization plays an important role in the design of new robots or work environments Robot Visualization System for Windows RVS4W is an up dated cross platform version of its predecessor the Robot Visualization System RVS RVS was developed at the Centre for Intelligent Machines McGill Uni versity in the 1990s It was developed on IRIX the UNIX dialect of Silicon Graphics Inc SGI Since IRIX is native to SGI workstations RVS does not run on Intel based PCs Therefore the source code of RVS had to be modified in order to use this tool on an Intel based PC Based on the two important attributes of RVS4W i e open source and platform independent the proper development tools were chosen RVS4W is an updated version of RVS The user interface was rewritten from scratch We have made an effort to keep the user interface consistent and user friendly The existing kinematics engine was also debugged and improved RVS4W incorporates many new features including routines to evaluate the char acteristic length maximum reach optimum posture for minimum condition number and robot conditioning This manual introduces the user to the window driven environment of RVS4W Acknowledgements
14. a linear system of seven equations in six unknowns At each iteration the correction A is computed using Householder reflections 35 The process terminates when the termination criterion lt e is met for a given tolerance e Notice that e is dimensionless Actually the convergence criterion for a nonlinear least square problem is A lt eo for a prescribed tolerance eg The criterion adopted in RVS4W is stricter in that it imposes the vanishing of 0 which is possible in our case because the four scalar orientation equations are not independent they obey a quadratic constraint Angeles 2007 The Set System Subsection 2 9 dialog provides access to the above mentioned tolerance via the Error Tolerance text box In this dialog the maximum number of iterations can also be set 36 Index Cartesian trajectory convert to joint trajectory 20 follow 19 characteristic length 5 22 23 condition number 23 conditioning 5 22 DH parameters display 11 edit 11 input 7 dialog About 29 Cartesian Trajectory 19 Conditioning 22 Create Robot Parameters 7 Create Robot 7 DH Parameters 11 Edit Robot 10 End Effector 11 Export 29 Forward Kinematics 15 Inverse Kinematics 16 Joint Limits 13 Joint Trajectory 17 Link Settings 10 Load Robot 9 Load Work Environment 26 Obstacle 26 Payload 26 Robot Save As 13 Select Configuration 15 Set System 27 Set Work Environment 24 Transform Tra
15. diting the robot Selecting Robot gt Edit Robot Fig 2 brings up the Edit Robot dialog on the screen Fig 6 e To change the display geometry click the appropriate radio button Up Down or Full The full geometry option is available only for those robots whose detailed link geometry has been previously input e To modify the robot parameters click the appropriate link button This brings up the corresponding Link Settings dialog The reader is referred to Subsec tion 2 4 4 for details on the Link Settings dialog Click close to exit the Edit Robot dialog 2 4 4 The Link Settings dialog The Link Settings dialog Fig 7 can be accessed through the Edit Robot dialog There is a separate Link Settings dialog associated with each link of the robot The link number is displayed at the top of the dialog The dialog displays a set of options organized in three groups 10 lola 3R Geometry J r fue 1 Link 2 fr Down Link 3 close Figure 6 The Edit Robot dialog e Joint To select the required joint type revolute or prismatic check the corre sponding check box e DH Parameters The DH parameters of a link that can be edited depend on the selected joint type To change the DH parameters of the link input the desired value or use the arrow buttons to increase or decrease the value of the corresponding parameter The robot is updated dynamically i e as soon as the new value is input in the spinner e Joi
16. e trajectory display from the workspace and reset the dialog e Forward Click the forward button to start the animation in the forward direction If the Cont option is selected the end effector will move to the initial point of the trajectory and follow the trajectory to the end Click the forward button again to stop the animation in between If the Step option is selected the end effector will move to the next step in the trajectory e Backward Click the backward button lt to start the animation in the backward direction e Use the scroll bar to drag the robot along the trajectory manually e Click close to exit the dialog 18 E Robot Visualization System for Windows 3R zi Dj xl Robot Posture file Conditioning Environment Setting Export About Joint T ry Cartesian Trajectory Transform Trajectory Figure 16 Menu Trajectory 2 6 2 Cartesian Trajectory Making the robot follow a Cartesian trajec tory The Cartesian Trajectory command allows the robot to follow a pre stored end effector trajectory that is described in the Cartesian coordinates In order to activate the Cartesian Trajectory command select Trajectory gt Joint Trajectory from the menu Fig 16 This brings up the Cartesian Trajectory dialog Fig 18 The list box in this dialog displays the Cartesian trajectories available for the loaded robot e Click on the desired trajectory to load it The Cartesian trajectory is displayed i
17. ectory type in the filename in the Traj File text box press Save e Click close to hide the dialog window 2 6 4 Converting joint trajectories to Cartesian trajectories The Transform Trajectory command can also be used to convert a joint trajectory to its corresponding end effector Cartesian trajectory This is done by following the steps below 1 Load the desired joint trajectory Sec 2 6 1 2 Activate the Transform Trajectory dialog 3 Input the filename for the corresponding Cartesian trajectory in Traj File and click save 2 7 Conditioning For a detailed account of the theoretical issues pertaining to this subsection the reader is referred to Khan and Angeles 2006 The Conditioning dialog provides useful information to the user namely the conditioning the characteristic length and the maximum reach of the robot at hand Select Conditioning from the main menu to activate the Conditioning command The Conditioning dialog will popup on the screen Fig 20 In RVS4W the robot conditioning is computed as the reciprocal of the minimum condition number kr of the dimensionless also termed homogeneous Jacobian H defined as 1 ke HI BH 1 where r is the Frobenius norm of the matrix argument m is 3 for planar and spherical robots 6 for spatial moreover we assume n joints with n gt m The factor 1 m in the right hand side of eq 1 stems from the use of the weighted Frobenius norm of H namely 1
18. h a different name select Robot gt Save As Fig 2 The Robot Save As dialog will appear on the screen Fig 10 Input the new filename and click Save The robot will be saved under the new filename 2 4 9 Exit Exiting RVS4W To exit RVS4W select Robot gt Exit 2 5 The Posture Menu 2 5 1 Joint Limits Setting joint limits RVS4W allows the user to set joint limits When active the joint limits are considered in the forward and inverse kinematics of the robot Select Posture gt Joint Limits Fig 11 to activate the Joint Limits dialog Fig 12 e To activate joint limits check the Joint Limits On check box 13 fim Robot Yisualization System for Windows 3R 0 x GENES Trajectory Conditioning Environment Setting Export About Joint Limits Select Configuration Forward Kinematics Inverse Kinematics Figure 11 Menu Posture e To deactivate joint limits check the Joint Limits Off check box e To specify joint limits input the maximum and minimum values in the corre sponding joint limit spinner e To exit the dialog click close 2 5 2 Select Configuration Moving the robot to a saved posture The robot can be moved to previously saved postures RVS4W provides two postures automatically 1 lt robotname gt Characteristic The characteristic posture is that with the best conditioning See Subsection 2 7 for further details 2 lt robotname gt Maxreach A posture at the maximum reach of the robot
19. i are the position coordinates of the origin of the frame F i and Qmn i are the nine entries of the 3 x 3 rotation matrix Q z expressed in the base frame For positioning robots the structure of the text file must be 18 Qui Qui Q13 1 Qa 1 QA Q23 1 Q31 1 Q32 1 Qg3 1 Qii 2 Q12 2 Q13 2 Q21 2 Q22 2 Q23 2 2 Q32 2 2 The trajectory file must be stored in the RVS CTraj directory The filename must be in the form lt Robot name gt Cartesian trajectory name 4 2 Joint Trajectory RVS4W allows the robot to follow a pre stored joint trajectory The trajectory file must be stored in the RVS JTraj directory The filename must be in the form lt Robot name gt Joint trajectory name 33 The joint trajectory file must be provided in text format with the structure where 0 j is the variable of the i joint given in degree or usu at sample time j An example of the joint trajectory file is shown below as applicable to a redundant seven revolute robot Note that the text file contains correspondingly seven columns 101 7014 17 6766 98 9590 88 8606 25 0257 119 4901 113 3444 101 6753 17 6985 98 8462 88 9656 25 2299 119 6729 113 5423 101 6438 17 7185 98 7321 89 0719 25 4328 119 8611 113 7414 101 6070 17 7365 98 6165 89 1794 25 6346 120 0545 113 9415 References Angeles J 1985 On the numerical solution of the inverse kinematic problem The International
20. jectory 21 display geometry down 10 full 5 10 skeleton 5 up 10 end effector 11 exiting RVS4W 13 files Cartesian trajectory 32 joint configuration 32 joint trajectory 33 forward kinematics 15 inverse kinematics 16 iterations 36 settings 29 tolerance 36 Jacobian 5 joint limits 7 deactivate 14 activate 13 input 13 maximum 7 minimum 7 joint trajectory convert to Cartesian trajectory 22 follow 17 joint type prismatic 7 revolute 7 mouse controls 7 Nelder Mead method 24 obstable create 26 edit 26 payload create 26 edit 26 posture characteristic 14 maximum reach 5 14 22 37 optimum 5 23 pre stored 14 robot conditioning 22 create 7 delete 9 description 7 edit 10 DH parameters 11 joint limits 11 joint type 11 load 9 save 11 save as 13 save joint configurations 15 scene export 29 rotate 7 snapshot 5 translate 7 zoom in out 7 spline 15 starting RVS4W 6 system settings 27 background color 27 projection 27 trajectory rotate 21 scale 21 transform 21 translate 21 units 7 angular 7 user specified units 7 work environment create 24 edit 24 load 26 38
21. ll University 817 Sherbrooke West Montreal QC Canada H3A 2K6 http Awww cimn megill ca rmslindexindex htm Authors In Alphabetical Order Angeles Jorge angeles acim mcgill ca Bauer Frank Darcovich Jan Khan Waseem Ahmad wakhan cim megill ca Zhuang Haijun zhuanghi cim mcgill ca Figure 31 The About dialog 3 Joint Configuration RVS allows the user to move the robot to pre stored postures configurations The pre stored configurations must be described in terms of the joint coordinates The filename must be in the form lt Robot name gt Configuration name The joint configuration file must be provided in text format with the structure th 01 4 63 where 6 is the variable of the ith joint given in degree or in usu for prismatic joints The file must be stored in the RVS JConfig directory 4 Trajectories 4 1 Cartesian Trajectories RVS4W allows the end effector to follow pre stored Cartesian trajectories In this vein the trajectory is discretized to the desired resolution thereby obtaining a set of frames F Each frame F i then represents the desired end effector pose with respect to the base frame at sample time 32 The Cartesian trajectory file must be provided in text format with the structure rd y z 1 Qull Qu 1 Q13 1 Qa 1 Qo2 1 Q23 1 Q31 1 Q32 1 Q33 1 r 2 yQ 2 Q11 2 Q12 2 Q13 2 Q21 2 Q22 2 Q23 2 3102 Q32 2 Q33 2 where x i y i and z
22. n dictated by the corresponding DH parameters a revolute joint a prismatic joint and an end effector EE No geometric details on the actual shape of the links is provided in the skeleton mode Full rendering of the actual robot can also be made Of course this requires that a database with the details of the robot link geometry be supplied by the user 1 1 RVS4W Features Currently RVS4W supports the following main features e Forward kinematics e Inverse kinematics e Individual joint limits e Posture pre storing e Trajectory tracking in joint space e Trajectory tracking in Cartesian space e Maximum reach characteristic length optimum posture evaluation for a given robot e Robot Jacobian evaluation at a given posture e Robot conditioning evaluation at a given posture e A snapshot of the scene to be saved in Encapsulated PostScript EPS Portable Document Format PDF or Scalable Vector Graphics SVG formats e Display of reference frame the moving frames and the EE frame e Creation and visualization of work environments E Robot Yisualization System i DI x Robot Posture Trajectory Conditioning Environment Setting Export About Figure 1 RVS4W Main Window 1 2 Document Conventions Conventions used throughout the manual e Typewriter fonts are used to represent RVS4W commands shell commands directory paths and code C scripts e Uppercase ITALICS fonts are used to represent file names 2 RVS
23. n the main RVS4W window in pink e Points Click once to display the corresponding Cartesian position points of the trajectory Click again to switch the option off e Frames Click once to display the Cartesian frames of the trajectory Click again to switch the option off e Cont To make the robot follow the trajectory continuously check the Cont text box e Step To make the robot follow the trajectory step by step check the Step text box 19 fa Joint Trajectory iol x Points Frames M Cont Step Figure 17 The Joint Trajectory dialog Reset Click to move the end effector to the initial position Clear Click to unload the selected trajectory clear the trajectory display from the workspace and reset the dialog Forward Click the forward button P to start the animation in the forward direction If the Cont option is selected the end effector will move to the initial point of the trajectory and follow the trajectory to the end Click the forward button again to stop the animation in between If the Step option is selected the end effector will move to the next step in the trajectory Backward Click the backward button lt to start the animation in the backward direction Use the scroll bar to drag the robot along the trajectory manually RVS4W can save the corresponding joint trajectory to a file This is done by following the steps below 1 Load the desired Cartesian trajecto
24. nt Limits To specify joint limits check the Limits check box and enter the maximum and the minimum joint values Click close to exit the Link Settings dialog 2 4 5 Displaying the DH parameters of the current robot To display the DH parameters select Robot gt DH Parameter Fig 2 The DH Parameters dialog will appear on the screen Fig 8 showing the relevant parameters of the loaded robot Click close to exit the dialog 2 4 6 End Effector Selecting an end effector To select the required end effector choose Robot gt End Effector Fig 2 This activates the End Effector dialog Fig 9 The available end effectors for the loaded robot are displayed in a list box Select the desired end effector and click close to hide the dialog 2 4 7 Save Saving a robot Select Robot gt Save to save the current robot Notice that the current posture of the robot is saved as the default posture The default posture of a robot is one that is used to render the robot when the robot is loaded 11 fis Link Settings Figure 7 The Link Settings dialog DH Parameters DH Parameter Description ix revolute robot for arc welding with a decoupled architecture Figure 8 The DH Parameters dialog 12 EET ici xi Select EE None Figure 9 The End Effector dialog Da Filename II Save Figure 10 The Robot Save As dialog 2 4 8 Save As Saving a robot with another name To save the robot wit
25. onding Description text box Sec 4 as an aide m moire All angles must be specified in degrees 2 4 The Robot Menu 2 4 1 New Robot Creating a robot Select Robot gt New Robot Fig 2 to invoke the Create Robot dialog Fig 3 Next input the desired number of links for the new robot and press OK The Create Robot Parameters dialog Fig 4 is displayed This dialog has four main groups 1 Filename Input the name of the new robot 2 DH Parameters Input the corresponding robot dimentions using the DH con vention described in Angeles 2007 i e a b al a and th 0 By default a joint is taken as revolute To specify a prismatic joint check the corresponding Prismatic check box Notice that RVS4W does not support the conditioning evaluation for robots with prismatic joints 3 Joint limits To specify the physical limits of a joint check the corresponding Limits check box and input the minimum and maximum values in the min and max text boxes The limits must be specified in degrees for the revolute joint in agreement with the DH convention adopted at the outset For a prismatic joint the limit must be specified in usu 4 Description Input the description of the robot in this text box Click Save to save the robot and render its skeleton on the screen Click close to exit the dialog I im Robot Visualization System Figure 2 Menu Robot Figure 3 The Create Robot dialog imi Create Robot Parameters
26. ry and check the Cont check box 2 Make the robot follow the complete trajectory by clicking the forward but ton and letting it run to the end This step evaluates the corresponding joint angle trajectory of the Cartesian trajectory at hand 20 limi Cartesian Trajectory JE xj SR test Points Frames M Cont Step zapa Joint Traj File Save JT Figure 18 The Cartesian Trajectory dialog 3 Specify a filename for the corresponding joint trajectory in the Joint Traj File text box and click Save e Click close to exit the dialog 2 6 3 Transform Trajectory Transform a displayed trajectory The Transform Trajectory command allows the user to transform a pre stored tra jectory in the workspace Notice that the user must load a trajectory joint or Carte sian into the system before activating the Transform Trajectory command To activate the Transform Trajectory command select Transform Trajectory from the Trajectory menu Fig 16 the Transform Trajectory dialog then popping up on the screen Fig 19 e Position To translate the trajectory input the x y and z translation compo nents in the corresponding text boxes e Orientation To rotate the trajectory about the origin of the base frame input the relevant Rx Ry and Rz components e Scale To scale the trajectory with respect to the origin of the base frame input the required scaling in the Scale text box 21 e Traj File To save the traj
27. t for K1207 Enviroment for Puma Figure 23 The Load Work Environment dialog spherical by default Its radius is modified by using the scroll bar or typing in the new value in the Radius text field To visualize the payload click on the Visible button When the payload is visible the user will see a green sphere inside the workspace Click on the close button to exit the dialog 2 9 Setting Use the Set System dialog to change various global settings in RVS4W These include the background color projection axis display and settings related to the inverse kinematics engine Select Setting gt Set System from the menu Fig 26 The Set System dialog will appear on the screen Fig 27 The dialog is divided into four groups e Background Color the R G or B slider to change the color of the background A palette of three colors is also provided e View Use the radio buttons to select the type of projection perspective or orthogonal e Axes There three options in this group i e Reference Joint and End Effector which allow the user to display or hide the coordinate axes The user who wants to develop a feature allowing for user defined payload shapes is invited to request the source code by writing to the address provided in the RVS4W Web site 27 ll Obstacle Of x Obstacle Data al Payload Payload Data Figure 25 The Payload dialog 28 E Robot Visualization System for Windows 3R zi Dj xl
28. te text box 2 Use the arrow buttons to increase or decrease the joint coordinate value 3 Drag the horizonal scroll bar of the corresponding joint e To save the joint coordinate values of the current posture input the desired filename in the File text box and click Save 15 2 5 4 li Select Configuration ioj x Joint Configuration 3R 1 3R 2 3R 3 3R 4 3R Characteristic 3R config SR Maxreach 3R Sol1 3R Sol2 3R Sol3 3R Sol4 Spline F Jump close Figure 13 The Select Configuration dialog To exit the dialog click close Inverse Kinematics To change the pose of the end effector and hence change the posture of the robot in verse kinematics select Posture gt Inverse Kinematics from the menu Fig 11 The Inverse Kinematics dialog will popup on the screen Fig 15 Position To change the position of the end effector input the desired value in the x y and z text boxes or use the arrow keys to increase or decrease the value Orientation To change the orientation of the end effector input the desired value in the Rx Ry and Rz text boxes or use the arrow keys to increase or decrease the value To view the orientation matrix click on the Q button To view the robot Jacobian click on the J button Click close to exit dialog An outline of the inverse kinematics algorithm is available in the Appendix 16 i Forward timer Forward Kinematics i th2 68 55 I th3 3
29. the desired work environment to load and display it in the main window 2 8 3 Obstacle Creating and editing obstacles RVS4W allows the user to place obstacles in the workspace to detect collisions visually Select Obstacle from the Environment menu Fig 21 The Obstacle dialog will pop up on the screen Fig 24 The position and velocity of the obstacle can be specified from the Obstacle Data group The position of the obstacle is defined with respect to the base frame Currently the obstacle velocity option is not operational The shape of the obstacle is spherical Its radius can be modified by dragging the Radius scroll bar or by entering the new values in usu in the corresponding text fields To display the obstacle click the Visible push button When the obstacle is visible the user will see a grey sphere inside the workspace Click close to exit the dialog 2 8 4 Payload Creating and editing payloads RVS4W allows the user to mount a payload at the tip of the end effector Select Payload from from the Environment menu Fig 21 The Payload dialog will appear on the screen Fig 25 The user can position the payload with respect to the end effector frame The default position is the origin of the end effector frame To modify type in the new value in the appropriate text box The shape of the payload is 26 iix Select Workspace Enviroment for 3R Enviroment for 3R2R2R Enviroment for 6RND Enviroment for FanucS300 Enviromen
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