MATLAB Toolbox for Motion Control of KUKA Robot Manipulators

2010 IEEE International Conference on Robotics and AutomationAnchorage Convention District May 3-8, 2010, Anchorage, Alaska, USA KCT : a MATLAB toolbox for motion control of KUKA robot manipulators Francesco Chinello, Stefano Scheggi, Fabio Morbidi, Domenico Prattichizzo Abstract— The Kuka Control Toolbox (KCT) is a collection it does not support graphical interfaces and advanced mathe- of MATLAB functions for motion control of KUKA robot matical tools (such as, matrix operations, optimization and manipulators, developed to offer an intuitive and high-level filtering tasks), and it does not allow an easy integration of programming interface to the user. The toolbox, which is compatible with all 6 DOF small and low payload KUKA external modules and hardware (such as, e.g., cameras or robots that use the Eth.RSIXML, runs on a remote computer embedded devices using common protocols: USB, Firewire, connected with the KUKA controller via TCP/IP. KCT includes PCI, etc.). A possible way to overcome these drawbacks is more than 30 functions, spanning operations such as forward to build a MATLAB abstraction layer upon the KRL. A first and inverse kinematics computation, point-to-point joint and step towards this direction has been recently taken by a MAT- Cartesian control, trajectory generation, graphical display and diagnostics. The flexibility, ease of use and reliability of the LAB toolbox called Kuka-KRL-tbx [11]. The authors in [11] toolbox is demonstrated through two applicative examples. use a serial interface to connect the KUKA Robot Controller (KRC) with a remote computer including MATLAB. A KRL I. I NTRODUCTION interpreter running on the KRC, establishes a bi-directional MATLAB [1] is a powerful and widely used commercial communication between the robot and the remote computer software environment for numerical computation, statistic and it is responsible for the identification and execution of analysis and graphical presentation available for a large all instructions that are transmitted via the serial interface. number of platforms. Specific toolboxes (i.e., collections Kuka-KRL-tbx offers a homogeneous environment from the of dedicated MATLAB functions) have been developed in early design to the operation phase and an easy integration the past few years for support in research and educa- of external hardware components. In addition, it preserves tion, in almost every branch of engineering, such as, e.g., the security standards guaranteed by the KRL (workspace telecommunications, electronics, aerospace, mechanics and supervision, check of the final position switches of every control. As far as robotics is concerned, several toolboxes robot axis, etc.). However, Kuka-KRL-tbx suffers from some have been presented in the last decade for the modeling limitations: of robot systems [2]–[7]. These simulation tools have been • The MATLAB commands of the toolbox are one-to- inspired by various applicative scenarios, such as vision- one with the KRL functions: this lack of abstraction based robotics [5], [6] and space robotics [3], and have may hinder the user from designing advanced control addressed different targets ranging from industrial [4] to applications. academic/educational [2], [5]–[7]. • The serial interface may represent a limit in real-time A more challenging problem is to design MATLAB control applications. toolkits, offering versatile and high-level programming envi- • The toolbox does not include specific routines for ronments, for motion control of real robots. Some work has graphical display. been done in this field for one of the first industrial robots, the Puma 560 manipulator [8], [9]: however this robot is known This paper presents a new MATLAB toolbox, called to have some intrinsic software limitations, especially in real- KUKA Control Toolbox (KCT), for motion control of KUKA time applications, which have been overcome by more recent robot manipulators. The toolbox, designed both for aca- manipulators. demic/educational and industrial purposes, includes a broad In this paper we will focus on the manipulators produced set of functions divided into 6 categories, spanning opera- by KUKA [10], one of the world’s leading manufacturers of tions such as, forward and inverse kinematics computation, industrial robots. KUKA manipulators are designed to cover point-to-point joint and Cartesian control, trajectory genera- a large variety of applications in industrial settings, such tion, graphical display, 3-D animation and diagnostics. as, e.g., assembly, material handling, dispensing, palletizing KCT shares with Kuka-KRL-tbx the same advantages and and welding tasks. A specific C-like programming language, improves it in several directions: called KRL (KUKA Robot Language), has been developed • The functions of KCT are not a MATLAB counterpart by KUKA for robot motion control. This language is sim- of the corresponding KRL commands. This makes the ple and allows comfortable programming. However, it is toolbox extremely flexible and versatile. not suited for critical real-time remote control applications, • KCT runs on a remote computer connected with the KRC via TCP/IP. A multi-thread server runs The authors are with the Department of Information Engineering, University of Siena, Via Roma 56, 53100 Siena, Italy. List of e-mails: on the KRC and communicates via Eth.RSIXML {chinello,scheggi,morbidi,prattichizzo}@dii.unisi.it (Ethernet Robot Sensor Interface XML) with a client 978-1-4244-5040-4/10/$26.00 ©2010 IEEE 4603 RSIXMLv1.RSIXML (a KUKA software package for or 7. . thus enabling real-time control 1) A remote computer running KCT under MATLAB.src xo ≡ x1 θ6 z6 Fig.dii. d32 d43 d54 z0 ≡ z1 1 θ1 KUKA Control Toolbox TCP/IP protocol z4 MATLAB θ4 d65 kctserver.RSIXML) of the manipulator. the communication scheme between KCT and the robot manipulator. script which runs the eth. The server sends the web page: http://sirslab. .src or kctsetbound joint of the robot (note that d10 ≡ 0). 2. Communication scheme between KCT and the manipulator. next page).src is II. θ6 ]T denotes the collection of the joint angles hand. Mac and Linux. The KUKA robot KR5arc KR5arcHW KR6-2 KR6-2KS KR15SL KR16-2 KR16-2S KR16-2KS KR16L6-2 KR16L6-2KS models currently supported by KCT are listed in Table I: up to now. θ2 .unisi. lator. applications.0: the controllers KR C2. II commands to the manipulator via kctrsiclient. all the matrix H60 ∈ SE(3) relates the coordinates of a 3-D point angles will be in degrees and distances in millimeters.0 time loop limit: drawn and future research directions are highlighted. a soft real-time loop of 15±1 ms (the communication has Two examples are reported in Sect. KR5sixxr850 and KR16-2 robots. In the following. y0 . On the other [θ1 . a KRL (equipped with a real-time 10/100 card) are currently sup. 3-D animation. z6 . 2 illustrates 6 DOF KUKA ROBOTS CURRENTLY SUPPORTED BY KCT. managing the information exchange with the mani- pulator. To establish a connection between the remote computer KCT is fully compatible with all small and low payload and the robot controller. Small Robots (from 3 to 5 kg) KR3 KR5sixxr650 KR5sixxr850 In the interest of clarity. Reference robot: 6 DOF elbow manipulator with spherical wrist. II-A for more details). . in provides a comprehensive overview of the functions of KCT. . z0 . Fig. the ±1 ms uncertainty is currently due to the lack of a hard real-time support platform). KCT can be easily integrated with other MATLAB manages the information exchange with the robot manipu- toolboxes and it has been successfully tested on multiple plat. 3 Robot manipulator Fig. 5. . 5. The homogeneous (see Sect. with the coordinates of the same point written in the end-effector frame x6 . The toolbox and kctserver using specific MEX-files (default option) or via the relative documentation can be freely downloaded from MATLAB Instrument Control Toolbox. the commands of KCT have been subdivided into 6 categories. . kctrsiclient. 2) The KUKA Robot Controller (KRC). 1. It consists of three parts: 4604 . Two classes of constraints affect robot’s of KCT.src.5 municates via Eth. OVERVIEW OF THE TOOLBOX also used to define a HOME position (starting position) for In this section we will be briefly describe the functions the manipulator. and dkk−1 ∈ R3 .RSIXML with KSS (Kuka System Software) v. KCT provides kctserver. and includes a graphical user interface. kctserver com- Eth. .RSIXML client on the KRC and ported. conclusions are margin over the 12 ms Eth. In Sect. 2. This communication scheme guarantees high transmission rates. KR C2 ed05 and KR C3 TCP/IP-robot interface) with kctrsiclient.RSIXML KRC yo ≡ y1 kctrsiclient. according to the task Low Payloads (from 6 to 16 kg) they perform (see Table II. The hardware constraints depend on manipulator’s will be used as a reference along the paper: vector q = physics and cannot be modified by the user.exe d21 z2 θ2 z3 θ3 z5 θ5 2 Eth.src. 1 motion. written in the base reference frame x0 . • KCT has several dedicated functions for graphics and 3) The robot manipulator. a C++ 6 DOF KUKA robot manipulators which make us of the multi-thread server running on the KRC. y6 . The 6 DOF robot manipulator shown in Fig. IV. 6} the can be configured at the beginning of each working session displacement between the center of the (k − 1)-th and k-th via the functions kctrsiclient.it/vision/kct the robot’s current state to the computer and the velocity The rest of the paper is organized as follows: Sect.4. The MATLAB functions of KCT communicate with forms. k ∈ {1. . the software constraints (established by Eth. including Windows. III to show the flexibility been temporized to 15 ms in order to have a suitable of the toolbox in real scenarios. the toolbox has been successfully tested on the TABLE I KR3. Graphics kctdisptraj Plot the 3-D trajectory of the end-effector 2) Select kctrsiclient. containing the current position and by KCT is stored in the MATLAB file kctrobotdata. return to step 2. 12. M A T . The matrix. X XM Y m Y M Zm ZM >> q' = kctikine(H06). transform for translation 5) Start kctrsiclient. 15]. This matrix can >> kctrobot(). The function kctsetbound(B) can be used to set the software bounds of the robot. it is sufficient to kinematics and the inverse kinematics solution expressed as write kctinit(’KR3’). transform for rotation about z-axis kcttran Hom. 54. as a vec- differently from kctrsiclient. Kinematics A.mat roll-pitch-yaw orientation of the end-effector (first row). transform for rotation about y-axis is the IP address of the KRC real-time network card. kctrotoz Hom. the function q = ables a MATLAB warning message in the motion control kctikinerpy(p) computes the inverse kinematics solution functions (see Sect. Initialization The state of the manipulator is stored in a 2 × 6 matrix. θ4m θ4M θ5m θ5M θ6m θ6M The command p = kctfkinerpy(q) is analogous to contains the bounds on the position and orientation (limited kctfkine. ψ]T .0’). where the argument is a string a joint angles’ vector q. ’name’ KR3 KR5sixxr650 KR5sixxr850 ··· Initialization kctrobot Show the list of supported KUKA robots ’link1’ [mm] 350 335 335 kctinit Load the parameters of the selected robot ’link2’ [mm] 100 75 75 kctsetbound Set the workspace bounds kctgetbound Visualize the workspace bounds ’link3’ [mm] 265 270 365 ··· ’link4’ [mm] 0 90 90 Networking kctclient Initialize the client ’link5’ [mm] 270 295 405 kctcloseclient Terminate the client ’link6’ [mm] 75 80 80 Kinematics TABLE III kctreadstate Return the current configuration of the robot DATA STORED IN THE FILE K C T R O B O T D A T A .155.src on KSS. where 193.src by pressing the run button kctchframe Change the reference frame on the KUKA control panel and keep pushing until the line ST SKIPSENS is reached. (see Table III) and can be accessed by typing. >> q = [13. and the current joint angles (second row). Note that orientation of the end-effector of the robot. kctdispdyn Plot the time history of the joint angles 3) Start kctserver. TABLE II 6) Check whether the communication is established. Finally. The bounds can be graphically visualized using kctsetjoint Set the joint angles to a desired value the function kctgetbound. L IST OF KCT FUNCTIONS DIVIDED BY CATEGORY. C. The information relative to the KUKA robots supported called robotstate. Networking and angular velocity profile After the initialization step. 4605 . θ5 and θ6 ) of the end-effector. II-D). Z. transform for rotation about x-axis kctclient(’193. If it is not. when the workspace’s bounds from the vector p. φ. To close the TCP/IP communication is sufficient to write kctcloseclient(). 32. -43. kctpathjoint Generate a trajectory (joint space) The main steps necessary to initialize the connection are the kcthome Drive the robot back to the initial position following: kctstop Stop the robot in the current position kctdemo Demonstration of the toolbox 1) Put the mode selector on T1 (automatic execution) in the KUKA control panel (teach pendant). tor p = [X.1.0 kctrotoy Hom.1. kctsetbound en. but returns the position and roll-pitch-yaw to the joint angles θ4 . To compute the matrix H60 of the forward To initialize a particular robot model. kctanimtraj Create a 3-D animation of the robot 4) In the MATLAB workspace start the TCP/IP Homogeneous transforms communication with kctserver by typing kctrotox Hom.  m  >> H06 = kctfkine(q). kctfkine Compute the forward kinematics kctikine Compute the inverse kinematics kctfkinerpy Compute the forward kinematics (give the pose) kctikinerpy Compute the inverse kinematics (from the pose) Motion control are violated. KCT provides the following two containing the name of the robot selected as specified in functions: kctrobotdata.src.mat. B= . γ. Y. the TCP/IP communica- kctdrivegui GUI for robot motion control kctpathxyz Generate a trajectory (operational space) tion between KCT and kctserver must be established. be accessed using the following command: robotstate = kctreadstate(). kctsetxyz Move the end-effector in a desired position kctmovejoint Set the joint velocities to a desired value kctmovexyz Move the end-effector with a desired linear B.155. zw . γ. φi . 11. zw  as new reference frame. Yi . >> [robotinfo. viewpoint. z-axes. functions using ctrl-c. of the robot is diplayed via a 3-D animation. for A graphical user interface. 35. . kctdispdyn(robotinfo) (poly or prop. 12. whose rows are vectors of joint angles: >> Q = [23. The first argument of kctpathjoint is a n × 6 matrix Q. Zi . θ6 ]T be the final desired joint config. uration of the robot. 14. zw  kctmovexyz(pdot). 15]. n}. 0. It is very frequent in the applications to deal with >> H0w = kctrotoz(alpha)*kcttran(d). respectively). D. .1). -21. 20. >> [robotinfo. z0 . warn] = kctsetjoint(qf. pn ]T . 0. should first terminate the execution of the motion control Let qf = [θ1 . . Homogeneous transforms moves to robot from the initial to the desired pose pf KCT provides a set of transformation functions of frequent using a proportional controller. 12. KCT provides the function kcthome(). . 40. >> 10. . >> -15. -23.tp. z0 . is to move the robot from an initial to a final configuration To immediately stop the robot in the current position. the linear and angular velocities of the end- Let us now suppose we wish to move the robot’s end-effector effector necessary to achieve the goal are computed via with respect to an external reference frame xw . warn] = kctpathjoint(Q. yw . >> -50. -5. Hx = kctrotox(alpha). 100. operational space. move the end-effector of the robot from point p1 to point p3 using a linear interpolation method: a time step tp of 2 seconds between two consecutive points is considered. Graphics moves the robot from the current to the final configuration Three functions are available in KCT for graphical display. using either a polynomial approach [12. E. 60]. The third argument of kctpathxyz is a Boolean variable enabling or disabling the visualization of the 3-D trajectory of the end-effector and the time history of the joint angles at the end of the task. When >> Htr = kcttran(d). yw . as specified by the second argument trajectory of the end-effector. 10. trajectories defined by a sequence of Cartesian frames >> kctchframe(H0w). 21. Note that kctsetjoint and use in robotics.2] or a The function kctdisptraj(robotinfo) plots the 3-D proportional control.1). . 54. (see the help of the single functions for more details). inspired by Robotics Tool- example. -2. i ∈ {1. level functions: kctmovejoint and kctmovexyz. 12. -21. The following referred to xw . 35. p2 . to drive the robot back to the initial position. Hz = kctrotoz(alpha). >> pf = [412.tp. 3). warn] = kctpathxyz(P. A suite of robot’s motion. The matrix robotinfo con. 200. . φ. 5. . Motion control >> 42. the KUKA controller computes the >> Hy = kctrotoy(alpha). γi . . III-B). -10. (see Fig. Finally. commands. The function. and then type kctstop(). tp = 2. 20. Z. . 12. The function. >> qf = [23. should be referred to the camera frame (see Sect. Let now pf = [X. warn] = kctsetxyz(pf). kctsetjoint is called. zw  and x0 . 2. 24. different from the base x0 . yw . y0 . . yw . tp = 2. y0 . and trajectory planning. in an eye-in-hand framework where robot’s motion box’s drivebot GUI [2]. >> [robotinfo. -15. 31. The function. is loaded by kctdrivegui(). 12. The joint angles of the robot can be easily Let Hw 0 be the homogeneous matrix defining the rigid motion regulated here using six sliders: the corresponding motion between xw . or joint angles. stacked into specified by commands executed after kctchframe are the n × 6 matrix P = [p1 . F. -10. joint velocities necessary to accomplish the requested task provide the basic homogeneous transformations generating using kctmovejoint(qdot). 3. when kctsetxyz SE(3) for translation and rotation about the x-. 50. 4606 . plots the time history of the joint angles and tains the time history of the joint angles and warn is a kctanimtraj(robotinfo) creates a 3-D animation Boolean variable that is set to 1 when an error occurs during of the robot executing the requested task. The interface loaded by the function kctdrivegui. KCT provides several functions for point-to-point control >> [robotinfo. 20. 54. etc. Let d ∈ R3 be a translation vector and α kctsetxyz are user-level routines relying on two lower an angle. frame’s dimension. ψ]T be the final options (frame’s and trajectory’s color.) is available to customize the plot. 150. θ2 . y-. one defined by robot’s joint angles or by end-effector’s poses. The functions. The function kctpathjoint is analogous to kctpathxyz: the only difference is that the trajectory is defined here in the joint space instead of the Fig. is called. All the operations [Xi . >> P = [100. 350. This could be useful.'poly'). 60. Sect. Y.5. The simplest task one could require. . Similarly. 80]. -30. desired pose of the end-effector. ψi ]T . 32]. Consider a sequence of n points pi = fixes xw . has been called. zc  and the mirrors’ reference catadioptric stereo (PCS) sensors [13] is tested using KCT. mirrors.it/vision/kct d = [−100. 90]. The value of the >> P = [x'. qinit is the vector of the joint angles the following lines of code: of the robot in the initial point of the trajectory. 850]T ): 4607 . 90. 8]. A pinhole camera mounted example shows an elementary application of the trajectory on the effector of the KUKA manipulator. i. kctdrivegui has been used to drive the eye-in-hand >> x = 600*ones(1. 0.length(k).z'.0. kctclient(’192. zw  while the camera moves with time. 3π/2]. >> kctchframe(H0c).dii. 0]. with a pen mounted motion with respect to xc . zc  in the initial point of the on the flange of the KUKA KR3 manipulator. on a paper board.0) with tp = 1. z(k) = 150 sin(k) + 310. we moved the camera along a Suppose we wish to draw the circle.] −55 20 y z y −65 0 300 −20 (c) t = 0s (d) t = 28s Z −75 200 x 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70 100 samples samples 600 60 z0 θ6 [deg. -90. 650. and between the end-effector and base frames. given trajectory and compared the estimated and actual roll- pitch-yaw angles of Rcw (see Fig. 4(b) the time history of the joints angles.] 40 0 20 −20 0 y z 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70 500 t=0 samples samples x θ3 [deg. reflected scenes were clearly visible. To draw the circle. >> B = [450. 0.] θ5 [deg. Fig. The second example reflects authors’ personal inte. the effectiveness of a camera the visual information).1. in [13.7. 90. -90. Planar catadioptric stereo: camera rotation estimation This section presents two examples demonstrating the Let us consider the Planar Catadioptric Stereo (PCS) flexibility and ease of use of KCT in real scenarios. The experiments we will present in the next subsections1 . The software bounds are set >> H06 = kctfkine(qinit). 90. 4.repmat([0. joint angles in the via points has been collected in the We finally called the function kctpathxyz(P. = kctpathjoint(Q.tp. with the commands.1 under mirrors. robot through other 14 points. III. 5(a). yc . the rotation matrix Rcw between rotation estimation method based on the geometry of planar the camera’s frame xc . (b) Time history of the joint angles (solid).] 400 θ4 [deg. In order to test the robustness of this solu- A. sted in the camera’s rotation. effector and Fig. frames. 20 θ2 [deg.y'. Prop. 4(a) shows the trajectory of the end. We then performed the following this goal. To achieve trajectory.168. for painting. welding or assembling tured 3-D scene directly and reflected through two planar tasks). -200. a closed-form formula for Rcw has been determined Windows XP. The TCP/IP communication between kctserver and KCT is then established with >> H6c = kctrotoz(-90)*kcttran([0. formation matrices between the camera and end-effector >> kctsetbound(B). A PPLICATIVE EXAMPLES B. yc . 4(c)-(f) show four snapshots of the real robot during motion between xc .. Since we are intere- x(k) = 600. been measured in the real setup: it corresponds to a rotation 1 The videos of the experiments are available at the web page: of an angle α = 90◦ about the x-axis and to a translation http://sirslab. yw . it is convenient to refer robot’s k ∈ [0. warn] time step tp = 1. where Hc6 (known) and H60 are the homogeneous trans- >> -90. been obtained using the following commands (the rigid Figs.length(k)). The actual rotation matrices Rcw along the trajectory have as returned by kctpathxyz setting to 1 its third argument.e.1). observes a struc- control functions (e. 50]'). zc  for t = 0 and xw .0’). Drawing a circle tion in a real-world setting. 200. frame xw .. for t = 0.] θ1 [deg.] 500 20 0 y0 x0 400 40 200 0 300 100 200 0 100 X 20 −20 Y −100 0 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70 −200 samples samples (e) t = 55s (f) t = 83s (a) (b) Fig. >> k = [0:pi/50:3*pi/2]. By taking advantage of the epipolar geometry between the have been performed using the KUKA KR3 manipulator real camera and the virtual cameras associated to the two with KR C3 controller: KCT run on MATLAB v. with 15 × 6 matrix Q and the function [robotinfo. we have first to initialize the robot using the change of frame after the initialization/connection step: command kctinit(’KR3’). yc .tp. (c)-(f) Snapshots from the experiment. 0. In fact. y(k) = 150 cos(k). where the real and mirror- >> y = 150*cos(k). Let us suppose we wish to estimate (using only rest in robot vision. Example 1: (a) Trajectory of the end-effector. H0c = H06*H6c. yw . 500. The first system [14] shown in Fig.unisi. z = 150*sin(k) + 310.1)]. 5(b)). we generated a matrix P of points using respectively.g. zw  has the circular motion. [12] M. IEEE Robot. 1996. Babuška. In Proc. set of functions for kinematics computation. 17th IFAC World Cong. trajectory gene. and Visual Servoing: Robotics and Vision with Pinhole and Panoramic Cameras.:)). S. Res. Mag. 44(1):65–79. S. Catadioptric Stereo: Single and Multi-View Geometry for Calibration R EFERENCES and Localization.M.mb. and M. Lampe. We also aim to create a robot simulator Environment. Gluckman and S.L. Pawletta. Vidyasagar. and extend software/KukaKRLTbx. Planar research. http://www. D. and D. IEEE/RSJ Int. pages 1510–1515. A Simulink- control toolbox (KCT) runs on a remote computer connected Based Robotic Toolkit for Simulation and Control of the PUMA 560 with the KUKA controller via TCP/IP: it includes a broad Robot Manipulator.I. Scheggi. kuka-robotics. KCT is an ongoing software project: work is in progress [11] G. Roll Estim. IEEE Robot. Ind. A Model- to extend the compatibility of the toolbox to all KUKA Based Robot Programming Approach in the MATLAB-Simulink industrial robots. 2005. Intel. and B. Casini. 32(1):32–34. The KUKA Robotics. 5(c)-5(e). Vicino. Automat. Conf. Robot Modeling and The control of multiple robots is another subject of current Control. Conf.] 0 −30 0 −35 −4 −40 −5 −45 −8 0 10 20 30 40 50 60 −10 time [sec. Falconi and C. C ONCLUSIONS AND FUTURE WORK vision and vision-based control. [8] W. T.html. Pitch Roll Pitch 10 −15 Estim. graphical display and diagnostics. F. [2] P. EGT for Multiple View Geometry Rcw thus computed (dash). [3] K. pages 377–382. S. Prattichizzo. IEEE/RSJ Int. and D. Mag. pages 2202–2207. In Proc. [1] MATLAB and Simulink for Technical Computing.W. Manuf. lues (solid). the functionality of KCT to the Simulink environment.. Int. USA. real-word examples. Nayar.] time [sec. Robot. [Online]: http://www. Autom. Breijs. 2005. 12(4):16– 25. 2009.. Hutchinson. Robots Syst. 2005. Walker. RACT: a ration. Conf.de/˜gunnar/ for off-line validation of motion control tasks. Conf. 2006. Chinello. 2001.com/. Catadioptric Stereo using Planar Mirrors. [Online]. 12(4):26–39. and R.] [deg. and A. Example 2: (a) PCS experimental setup. (b) 3-D trajectory of the camera with respect to the mirrors. D. Robots Syst. pages 9111–9116.1:3). The time history of the roll-pitch-yaw angles of the matrices [5] G. Yaw 4 −20 Yaw 5 −25 [deg. Yoshida. is shown in Figs. Melchiorri.. 2006. B. [6] P. In Proc. Maletzki. Mag. In Proc. Mariottini and D. Comput. 5. together with the estimated va. [10] KUKA Robotics Corporation [Online]: http://www.K. The flexibility and Remote Lab for Robotics Experiments. Inc. (c)-(e) Time history of the estimated (solid) and actual (dash) roll-pitch-yaw angles of Rcw . Corke. Dawson. 1633–1638.hs-wismar.com/.. Prattichizzo. The paper describes an open-source MATLAB toolbox for [7] R. The MathWorks [14] J.L. Vision. 4608 . Spong. Autom. A Robotics Toolbox for MATLAB. Mariottini. 2008. Dixon. Morbidi. Automated design envi- >> end ronment for serial industrial manipulators.. IEEE Rob. I.] 0 10 20 30 40 50 60 0 10 20 30 40 50 60 time [sec. 17th IFAC World reliability of the toolbox has been demonstrated with two Cong. Autom. Corke. [13] G. 2001. RobotiCad: an Educational Tool for motion control of KUKA robot manipulators.] (c) (d) (e) Fig. Prattichizzo. [4] A. The SpaceDyn: a MATLAB Toolbox for Space and >> for i=1:length(robotinfo) Mobile Robots. In Proc.D.] [deg.mathworks. >> Hwc_init = kctrotox(alpha)*kcttran(d). pages >> Hwc = Hwc_init*kctfkine(robotinfo(i. >> Rwc = Hwc(1:3.E. Intel.I. The Machine Vision Toolbox: a MATLAB toolbox for IV. Wiley. Klaassens. 50 Planar mirrors 40 t = 60 30 Z t=0 xc 20 zw yc yw zc 10 xw 0 20 0 − 20 40 − 40 30 Pinhole camera Y 10 20 − 60 0 −10 − 80 − 20 X (a) (b) 8 Estim. F. Robot.. In Int. 1999. [9] M.. J. Pawletta. Moses. 2008. IEEE Int. pages 8153–8158. 3(1):24–32. 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