ROBOTENIS: PARALLEL ROBOT W I T H VISUAL CONTROL
L. Angel, R. Saltarkn, J.M+ Sebastian, A. Hansson and R.Araci1 Dpto. de Automatica, Ingenieria Electrdnica e InformGtica Industrial, (DISAM) Escuela Tkcnica Superior de lngenieros Industriales Universidad Politkcnica de Madrid (UPM) e/ Josi Gutibrrez Abascal2,28006-Madrid, Espaiia. langel~etsii.uam.e~,rsaltareniiiretsii.ii~m.es,isebas@,etsii.upm.es, cash~kth.se,
[email protected] ABSTRACT RoboTenis is an experimental innovation platbrnl with high performance for visual control of it parallel robot with four degrecs of freedom (DOF). The platform is an open parallel structure for implementation of different strategies of visual control, that will allow the robot the play table tennis. The design o f the platform consists of the construction of the parallel robot, the integration of the visual system and the developed algorithms for the visual control. This paper presents the platform RoboTenis and describes the dcsing of the parallel robot inspired by the Delta robot. The analyse the workspacc of the robot together with the studies of the trajectories o f the ball and the dynamic simulations of the robot that use ADAM?@ allow to find the dimensions of the manipulator and information to select the motors.
KEY WORDS: Parallel robots, Visual servoing, Inverse and Forward kinematics, Workspace. 1. INTRODUCTION The realisation o f the tasks for making robotic systems in structured surroundings with presence of objects whose position and orientation are perfectly well-known, is a problem studied at the present time. Nevertheless, the realisation of tasks in dynamic surroundings presents numerous sufficiently not yet resolute difliculties. The vision systems have capacity to give useful information in the dynamic surroundings while they can give information o f the different objects in the work scene and in addition to this, probably the most important thing, to establish the precise position and orienfation of the objects. The expression visual control is applied to visual guidance systems, which make use of one or several cameras to obtain data o f the surroundings in form of images, that is used like signal o f control the final effector of the robot during the accomplishment of a task. In order to use the information contributed by 3 vision system, to model the surroundings and to obtain the control of the trajectories of robotic systems, we present 3 study and implementation o f an innovating experimental platlbrm of visual control with high performance for the control of a parallel robot with four degrees of freedom (DOF). Because of the conditions of high speed and acceleration made by thc system, the design consists of a construction of the parallel robot, integration o f a visual system and developed algorithms for visual servoing. The platform is called RoboTenis and it is an open structure for implementation of different strategies of visual control, that allows the robot the play table tennis. Recently, parallel robots have been studied because their capabilities ate superior to those of conventional serial robot in inany aspects [ I ] , [2]. The notablc characteristics o f the parallel mechanism are high accuracy, high load capacity, high rigidity, and quickness. The use o f the parallel mechanism with 6 DOFs dates back to the paper by Gough [I]. Stewart [3] proposed a 6 DOF platform targeting its application to a flight simulator. Minsky proposed
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that the parallel mechanism should be used as the motion mechanism of manipulators [4]. Then, the use o f industrial robots sprcad in the IY8Os. In the period from 1980s to present, many theoretical studies have been conducted, and new mechanisms have been proposed. Clavel proposed a high speed parallel robot DELTA equipped with 3 DOF [ 5 ] . 11 is used for tasks of pick and phcv and allows to reach accelerations of 5c10m/s2, which turns to it to the fastest robot of the world. Pierrot proposed a 6 DOF fully parallel robot HEXA [6], [7j, which is the expansion o f the DELTA robot. However, HEXA robot suffer from its high price, small tilting angle and complexity. There are a lot of applications in which 3 DOF are not enough and 6 DOF are too much. The robots with 4 DOF (3 DOF for translation and 1 DOF for rotation) are necessary and enough for pick and place tasks. Nevertheless, only few attempts have so far been made at 4 DOF parallel robots. Pierrot proposed 4 DOF parallel mechanisms called H4 [ 8 ] , [2]. In the case RoboTenis, the parallel robot shows a mechanical structure similar to the DELTA robot o f Clavel. At the moment, the Delta robot is made commercially by AB3 with the name IRB 340. An important point is to eniphasise is that the R B 340 has a closed structure which disables it to use the implementation of direct visual control strategies and justifies the added effort that causcs the construction of the RoboTenis platform. This paper presents the RoboTenis platform and the design of the parallel robot. The geometrical equations provides the models of the inverse and forward kinematics. The analyse of the workspace of the robot, the studies of the trajectories o f the ball and the dynamic simulations of the robot using ADAM%@ allow to find the dimensions of the manipulator and information to select the motors. The control hardware is a DSPACE card.
2. DESCRIPTION OF THE ROBOTENIS The platfomi consists o f a parallel robot, a vision system and control hardware. 2.1 The robot As illustrated in figure 1 , the robot consists o f two plates (one static and one dynamic) and three parallel kinematic chains separated by an an& of 120". Each chain have two links: the
(a) ADAMSB Model
(b) Real Mode1
Figure I. RoboTenis Motions of the dynamic plate are achieved by the combination o f movements of the arms which is transmitted to the static plate by the system of parallel rods through a pair o f spherical passive joints. The parallel rods, also called forearms, assure that the dynamic plate always remains parallel of the robot base and allow to position the racket according at the X, Y, Z axis. The fourth D O F is a central arm formed by two universal joints a one prismatic joint that will to tum the racket.
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2.1 Vision system The vision system will be located on the dynamic plate and will initially consist of a single camera. The controt strategy defines a scheme ofdircct visual control based on characteristics of the image and geometric knowledge of the ball. The used features will be the centre of gravity and the diameter of the batl. The diameter will estimate the depth (coordinate Z) of the ball. In order that the system fulfils the strict requirements in run time, a camera of high benefits has been selected. The modcl of the camera is XC - HRSO from Sony and the most important feature are: To capture the images at high velocity (60 fps / 120 Fps). * Progressive integration. Reduced size: 29 x 29 x 32 mm.
.
3. KINEMATICS OF ROBOT The kinematics studies the movements of a mechanism and shows its geometric restrictions and the restrictions that wilt be caused by the joints. 3.1 Geometric description The absolute reference frame Eo is chosen as shown in figure 2, at the centre o f the static plate, with i pointing upward and x being pcrpcndicular to the axis of motor I. A second reference frame En.is at the centre of the dynamic plate and represent the operational position of robot regarding to frame E,.
Figure 2. The geometric parameters of RoboTcnis Due of the triple symmetry of the robot, each arm can be treated separately. The index i ( i = I ,2,3) is used to identify the arm number. For each arm, a frame Zi is located to a distance R of the reference frame Z" and rotated by an angle a,= D", 120" and 240", Cor ann 1, 2 and 3 respectively. The length of the arm is I,, and the forearm is Lb. The joints located at the reference frames Zi are active and their positions are denoted by qi. The joints in the points B, and C, are passive. The distance of point C; to the system En.is I'. The kinematic closure of each chain (armiforearm) is obtained from the vectorial equation:
- _ _ C,B, = B & -
c&;
i=I.2,3
(1
1
that in terms o l the geometric parameters of the robot and the space position of the dynamic plate (x, y , i) can be expressed as,
m-
[ ].[.r-)]-l", L,Cur(q,)
LRz
ArCos(q)
0
(2)
LPW,)
with A r = R - r . If if i s considered that the forearms are rigid bodies and o f constant length, the constraint equations for the robat are given by:
IIqlz = Li;
i = 1,2,3
407
(3)
3.2 Inverse kinematics Developed equation (3) leads to: u.Siiin(y,) t v C u ~ ( y , = ) H
(4)
with I/
= (-2
L"Z)
v = (2L" ( R - 1.) - 2L, (xCos(n,j + ysinp, j)) w = (L;
-((R -1.y - 2 ( R -r)(*Cur(q)
+YslJl(a,) ) + x ' + y * 3-
2 + L:))
From the equation (4).the articulate position i is given as,
3.3 Forward kinematics The multibody theory consider that the robot i s formed by I I bodies: the base, the racket, the three arms and the two forearms each chain. f h c kinematics of the robot chains are modelled with a restriction vector @tu) = I ) . This vector defines all the joints (rotational, spherical) that unit the links o f the robot. In addition, it includes the restrictions imposed by the degrees of freedom of the actuatorS. The vector of restrictions and the vatuo ofthe angles in lhc joints for a given position will be used to calculate the position o f the dynamic plate using the method o f Newton-Raghson. 4. DESIGN OF THE ROBOT The analyse ofthe workspace o f the robot, thc studies of the trajectories of the ball and the dynamic simulation o f the robot using ADAMSm allow to find the dimensions o f the manipulator and information to select the motors. A precise model of the robot is constructed by ADAM'S@. It is a commercial software package for dynamic analysis of mechanical systems produced by Mechanical Dynamics, Inc. Thc conceptual modul used in the simulation is show in figure I (a). 4.1 Workspace and dimensions of the Robot The workspacc are defined as the positions where the robot can physically reach and it depends on the dinlensions o f the manipulator. The 3D representation of the workspace has been developed in Matlab@. The algorithm defines the workspace based on the dimensions of the robot. The simulations of figures 3 and 4 show the variatjon o f the workspace volume considering the variation of the diiliensions of the robot. The figure 3 shows the workspace for Lb = 800 mm y L, =350 mm, 400 nun and 450 mm respectively. The figure 4 shows the workspace for L, = 350 m m y Ln =800 mm,900 mm and 1000 mm. These are the variafion of the length o f the ann that aFFect the workspace height and the variation of the tengih of the forearm that affect the diameter. In the KoboTenis platform, the volume o f the workspace depcdds of the required movements of the racket. This volume has been dcfined as a cylinder with a diameter of 1000 mm and height o f 600 min. The result o f the simulations obtain the optiniised dimensions of the robot and are shown in Table I . Radius static plate (R) Radius dynamic plate (1.) Length ofthe arms (L,) Length of the forearms ( L A )
2.10 mm 70 m m 500 mm 900 mm
Table I . Dimensions of the robot
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Figure 3. Variation of the workspace by the variation in the length of the arm.
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w
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T
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.&L--v.
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Figure 4 Vanatlon o f the workspace by the variation in the length of the forearm
4.2 Selection of motors
The size o f the motors depends o f the wanted velocity for the racket. This velocity depends on the motion of the ball and in order to find it, a particular case has been considered. The robot plays the table tennis with itself, that is to say, the racket must be positioned considering to the movement o f the ball with aid orthe vision system, to strike the ball and to assure that it will return to the workspace ofthe robot. A study orlhe 2 0 trajectorics o f the ball establish the relation between the velocity of the ball and thc racket. The analysis considers two phases: inilialisation and continuous stage. In the initial phase determines all valid velocities and departure angles given from an extemal source (a person). This guarantees that afier the first bounce of the ball, it reaches the workspace. The initial set o f information is unique for each initial height. The model in figure 5 , shows the motion o f each trajectory and strikes. In the equations, M, /ti and e are the mass of the racket, the mass of the ball and the restitution coefficient o f the ball respectively.
i. I.
x:
__ .
.
V",)
Figure 5 . Trajectoryofthe ball, initial phase
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The equations for this phase are: For trajectory I:
For strike I :
For trajectory 2:
(9)
The continuous phase determines the veIocity of the racket that allows to impel the ball and to assure that to it retunis again and reaches the workspace. Figure 6 shows the calculations of these tnjcctorirs of the ball after each hit by the racket. The trajectories are delined by the equations IO, 1 I and 12.
For strike 2:
For trajectory 3:
For strike 3:
The equation ( I 0) shows relatioil between the velocity of the racket before and aner strike 2 (vri, v?,) and the velocity o f the ball 1'4, VJ. To find the required maximum velocity of the racket to maintain movement o f the ball, a dynamic siinulation of the robot is made in ADAMSB. This simulation verifies the niaximum velocity that requires the robot for the continuous work o f critical trajectories. This procedure also tinds the torque and allows the sclcction o f the motors.
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5. SIMULATIONS AND RESULTS Figure 7 shows the pair of velocities and departure angles that atlow the ball to reach the workspace of the robot by initial height o f 0,6 m Figure 8 shows the possible trajectories of the ball with following Initial conditions: y,,., = 0.6 m, vtlnll 2m/s and ain,,= 100" (20 iterations are considered). 5
Figure 8. Motion of the ball o f 20 strikes The minimum time o f return of the ball is 0,6 s. and the maximum velocity o f the racket is 2 . 5 d s . These parameters allows the robot to maintain the movenicnt o f the ball. 5.1 Simulation ADAMS The dynamic simulation in ADAMSB o f the continuous phase o f critical trajectories obtain the velocity o f the robot and torque required for the execution o f a movement. Figure 9 shows h e veIocity of the endeffector from the simulation o f the continuous phase and several strikes of the ball. The most relevant data are rms velocity (2.5 d s ) and the maximum velocity (8 d s ) of the endeffector. The necessary torque of the motors are to generate the previous movement are shown in figure I O . The rms torque is 2.4 N-m and the maximum torque 1 1 N-m. According to the previous results a selection of the motors has been made. They are three AC servo motors with a torque o f 7 . 7 " at 3000 rpm
cigure 9.Velocity profile of the end-effector
41 1
6. CONCLUSIONS In this paper, a novel platform based on a parallel robot, has been introduced. The platform can performs complex tasks, as in this case, play tabte tennis by using visual feedback. The design and an analysis of the platfonn RoboTenis has been made together with studies of the wctrkspacr of the robot that obtained all the dimensions of the robot. An analysis of the trajectories o f the balt along with the dynamic simulation of the robot in ADAMSB, shows the limiting velocities of the end-effector of the robot, as well as the selection of the servo motors. At this moment the physical construction o f the RoboTenis platform is about to be made. This investigation is a part of the project “Arquitecturas de Teleoperacibn en Entomos Dinhicos Modelables” (DPI 2001-3827-CO2-01) and are financed by the Ministry of Science and Tcchiiology in Spain.
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r.51 Clavel, R., “DELTA: a fast robot with panllel geometry”, Pruceeding.7
of the lgb Infcmotiorwl Syniposiunr on hdustrial Robot, 9 1-100. Sydney, Australia. (1988) [6] Pierrot, F., M. Uchiyama, P. Dauchez and A. Foumier, “A New Design of a 6 DOF Parallcl Robot”, Jorrrnd uf Rub0tic.s und Mc.chdrrmiou. v o l 2 , no 4,308-3 1.5. ( I 990) [7] Uchiyarna, M.,K. limura, F. Pierrut, P. Dauchez, K. Unno and 0. Toyama, *‘A New Design of a Very Fast 6 DOF parallel robot”, Pwceedings of the 23rd Intemafional ~i~inposiutrt on InduAtriuI robots, 771-776. (1992) [8] Pierrot, F. and 0. Company, “H4:a new family of 4 DOF parallel robots”, Pveceedittgs of the IEEE/ASME hternuliond Conjhrmce on Advanced Intelligenf Mechatronics, 508-5 13. Allantd, GA. ( 1999)
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