Smidt, D.

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KfK 4120 August 1986 Automatie Path-Pianning for a Multilink Articulated Boom Within the Torus of a Fusion Reactor D. Smidt Institut für Reaktorentwicklung . Kernforschungszentrum Karlsruhe KERNFORSCHUNGSZENTRUM KARLSRUHE Institut für Reaktorentwicklung KfK 4120 Automatie Path-Planning for a Multilink Articulated Boom Within the Torus of a Fusion Reactor D. Smidt Kernforschungszentrum Karlsruhe GmbH, Karlsruhe Als Manuskript vervielfältigt Für diesen Bericht behalten wir uns alle Rechte vor Kernforschungszentrum l<arlsiUhe GmbH Postfach 3640, 7500 l<arlsruhe 1 ISSN 0303-4003 Automatische Bahnplanung für ein mehrgliedriges Trägersystem im Torus eines Fusionsreaktors Zusammenfassung Für Wartungsarbeiten im Torus eines Fusionsreaktors wird ein Manipula-tor durch ein mehrgliedriges Trägersystem an seinen Einsatzort gebracht. Das Trägersystem wird als "articulated boom" bezeichnet. Trägersysteme dieser Art haben vier bis fünf Glieder und bewegen sich in der Mittel-ebene des Torus. Sie sind kinematisch redundant und haben einen sehr be-grenzten Bewegungsspielraum. In dieser Art werden automatische Verfahren für das kollisionsfreie Anfahren beliebiger Positionen innerhalb der Reichweite durch das letzte Glied beschrieben. Sie schließen das Ein- und Ausfahren des Trägersystems in bzw. aus dem Torus ein. Mit Hilfe der CAD-Simulation kann eine Tabelle sicherer Konfigurationen aufgebaut werden, die durch einen Feinpositionie-rungsalgorithmus ergänzt wird. Abstract For in-torus maintenance of fusion machines a manipulator is conveyed to the working area by a mul tilink-transporter 1 also called "articulated· boom". Systems of this type have in general four to five· links and move in the midplane of the torus. They are kinematically redundant and have a very restricted working space. In this paper automatic methods for the collision free approach of any position of the final joint within the reach of the transporter are presented, including insertion and removal. By automatic teach-in with the CAD-simulation a table of safe configura-tions can be generated and supplemented by a fine-posi tioning algorithm. - 1 -1. Introduction For maintenance purposes within a torus of a fusion reactor an endeffec-tor or manipulator will be conveyed to its working area by a transporter. In most cases the transporter is a multilink system, also called "articu-lated boom". It is mounted on a trolley by which it can be inserted into and removed from the torus. The axes of the joints are parallel to one another and so the transporter always moves in the torus midplane. Posi-tions outside the midplane will only be reached by movement of the endef-fector or manipulator. As an example Fig. 1a) shows the articulated boom for the JET (Joint European Torus), Fig. 1b) depicts a typical working position of the transporter within the torus. The JET transporter consists of four links with five joints. The fifth joint carries the endeffector. As movement in a plane requires only two degrees of freedom to reach a certain target position, the system is kinematically undefined. The redundant degrees of freedom are required to avoid collisions between transporter and torus. However, these con-straints do not completely resolve the problern of kinematic uncertainty. · joint on Trolley link I joint 2 link 2 joint 3 link 3 joint 4 link 4 joint 5 Fig. 1a): Transporter (articulated boom) with endeffector for JET (Joint European Torus) - 2 -Originally each joint was to be controlled separately by the operator, who observes the transporter with one or more videocameras. This is ra-ther difficult 1 and therefore our group has developed a method /2/ which gives the operator a CAD image coupled with the transporter showing him a clear display of the whole transporter-scenario. The CAD model of the articulated boom is coupled to the movement of the transporter. Collision warning is generated on the basis of a CAD environment model. The permitted angular positions of the joints for moving the endeffector step by step to the target position can be generated by a teach-in and stored for further use. However, such teach-in is a lengthy procedure. It must be supplemented by an interpolation procedure for fine positioning or continuous movement (e.g. for continuous driving along a surface for any cleaning or treatment). If the teach-in could be done automatically, it would be faster and more independent from human error. Fig. 1b): Articulated boom inserted into the torus (orthographic representation) - 3 -In this connection it is helpful that with the given geometry the enaef-fector can be controlled independently, when the required position for joint No. 5 has been reached. The control of the endeffector is not subject of this report but shall be treated in later research. In this report I will describe an automatic method for the teach-in, for the path-planning of the transporter. It is supplemented by an interpola-tion algorithm. Within the range of the boom joint No. 5 can be moved to any position without collision. This is done for two principal opera-tions, namely a) Insertion of the transporter into the torus to full length (respectively vice versa the removal of the transporter) b) Approach to the target position of joint No. 5 - 4 -2. Collision free Insertion and Removal of the Transporter 2.1 Collision Detection To detect a collision or penetration between two objects is a basic prob-lern of all CAD-methods and quite a nurober of solutions is available. In this work the torus and the transporter, moving in a plane, are coded as seenarios of polygons each modelled as a "quadtree". Object representa-tion by quadtrees (octrees for the case of three dimensions) is in use since some years /3 - 5/. At edges or corners of objects the range of definition is subdivided into four quadrants (or eight octants). If ne-cessary this subdivision can be recursively continued until a minimum scale is reached. Tree structures generated by this method permit in a simple way set operations as negation, intersection 1 and union. If the two trees generated from the torus and from the transporter have a not vanishing intersection, collision of the objects is indicated. For this report I have implemented a quadtree method reported by Ayala et al. /6/. In this algorithm edges need not be resolved to the minimal scale, but are directly included into the tree with their line-parame-ters. Only corners require complete resolution. The knots of the tree, representing the quadrants of a region, are of the type W white, free area B black, inside of object X contains just one straight edge, characterized by the parameters of the line equation G grey, contains more than one edge and will be subdivided until minimum scale is reached or until it is described by w, B, X only. A tree with four W-quadrants represents the empty set. For the torus the quadtree has to be generated only once, for the transporter this has to be done for each new configuration. With a Pascal program on the Intel 80286/8087 processors this takes about 100 secs for the torus configura-tion, about 20 secs for the transporter configuration. - 5 -The intersection operation is comparatively fast. If the intersection set is not empty, it delivers the origin coordinates XS and YS of the minimum scale quadrant finally encountered. Having the property X or B in quad-rants of minimal scale with XS and YS the position of the collision at the torus and at the transporter and the evasive motion of the transpor-ter can be determined. In general a minimal scale of 1/256 of the total display width was sufficient for the required accuracy. 2.2 Strategy for the removal of the transporter from the torus The task of moving an object through an area cluttered with obstacles from a start to a target position is the central problern for the next generation of manipulating systems. Here Lozano-Perez, Brooks, Brady and other workers at the Artificial Intelligence Laboratory of the MIT have done pioneer work /7- 11/. However, since their work refers to simple moving objects or conventional roboters in their typical environment, it could not be applied to the present problem. The transporter problern is characterized by a large nurober of joints, a very restricted workspace and the two-dimensionality which facilitates the solution. Therefore a new method had to be developed. In the case considered here the transporter enters the torus by the upper opening and moves either into the right or into the left-hand side (Fig. 2). All links must be controlled in such a way that the fully inserted position can be reached without collisions. One can easily see that in-sertion and removal can be understood as the same procedure in opposite direction. Also the insertion and removal on the right-hand side of the torus are mirror-symmetrical to the respective procedures on the left-hand side. Therefore, one needs only to determine one of the four proces-ses in-out and right-left and to generate a table of collision-free in-termediate positions. This solution then can respectively be transferred to the other Operations. For this purpose I use the pull-out from the fully inserted starting position. It is the only hand-made configuration. Pulling is reasonable since the transporter behaves kinematically as a chain and pulling a chain requires less additional constraints than pu-shing. By this, beginning with the shoulder, stepwise link after link is oriented parallel to the input-output-channel and pulled out. The other - 6 -links follow according to the kinematic conditions as defined by the Denavit-Hartenberg-matrices. In case of a collision with the torus an evasive motion of the transporter is generated. This algorithm will be described in the following section. 2.3 Algorithms for the removal of the transporter (generation of a table of configurations) The starting position is depicted in Fig. 2. The transporter is fully inserted on the right-hand side of the torus. The joints are numbered from 1 to 4 from shoulder to wrist, the respective angles are a 1 to a 4• The fifth joint, carrying the endeffector, is controlled independently by local criteria and is not considered here. The links have lenths 11 to 14• Stepwise a link is rotated by an angle ßa 1 which has a predefined value, until it is parallel to the exit channel. Fig. 2: Boom fully inserted at the right-hand side (endeffector omitted) This and all subsequent figures are screen-photographs. The torus consists of 4 polygons. The 45-degree gaps are plan-ned as channels for the insertion of narrow objects. They are not used in the present work. - 7 -begin i: = 1 ; While i < 4 do begin While a.<>3*n/2 do 1. begin a.: = a.-ßa; (*rotation of link i to get parallel to trolley*) ]_ ]_ new kinematic computation of transporter build new quadtree for transporter collision test with torus-tree if collision then begin intersection operator generates intersection coordinates xs, ys from xs, ys get closest joint j also determine wether collision with inner or outer wall of torus + sign of movement to avoid collision if j < = i+l then j: = j+l; ( *only joints > i may be changed*) repeat a . : = a . + !:lign * (la, J J until not collision end if; endwhile; (a. = 3 *n/2) ]_ (*now similarly pull out link No. i+l*) i: = i+l; end while; end procedure. Algorithm for generation of collision free positions at removal of the boom the torus - 8 -All configurations without collision are stored. Using ßa = TI/16 results in 27 configurations which are generated in about 4 minutes. This is quick compared to a teach-in controlled by the operator. Fig. 3: Articulated Boom removed except link No. 4 3. Collision free Movement to a Target Position 3.1 General procedures The required target position is entered into the system as a radius R and angle~. Joint No. 5 must be transferred to this position. The orienta-tion of the endeffector again is not considered here. The approach of a position is executed in three steps: 1 • Full insertion of the transporter on the required side 2. Coarse approach of position according to an automatically gene-rated table of collision free positions - 9 -3. Fine positioning Step No. 1 has been described in the preceeding chapter. The remaining steps will subsequently be detailed. 3.2 Algorithm for the coarse positioning (generation of a table of configurations) A table of collision free configurations, which later can be used in both directions and in both sides, is generated by a pulling operation. The chain will be pulled from the fully inserted position on the right by turning away link No. 1 until it nearly touches the outer wall of the torus on the left-hand side. Afterwards link No. 2 can be turned in the same direction if necessary. This is shown in Fig. 4 for a sequence of steps. In all other respects the processes are analog to the one des-cribed in chapter 2.3. After each step the system is examined for colli-sion and moved away if necessary. The generated collision free configura-tions of the ai are attached to the corresponding angular position ~of link No. 5 in the torus. Once the table is available, for any start and target position f the closest entries in the table have to be found. Between them they define the sequence of configurations which has to be passed. In principle this automatic teach-in results in moving of the joints and 2 and pulling the chain along the inner wall of the torus to the target positon. For safety reasons the inner radius can be increased com-pared to the real value to obtain additional distance. - 10-Fig. 4: Series of intermediate positions to reach the target configu-ration visible as the leftmost boom position a) Sequence turning link No. 1 to the left b) After link No. 1 is in the final position, link No. 2 is turned, collisions are repaired by turning other links - 11 -Fig. 5: Insertion and positioning on the left are based on the same table and a mirrar transformation 3.3 Fine positioning Using the procedures described in the preceding chapter the end joint 5 can be moved into the proximity of the required angular position within the torus. So far the radial position is random, but close to the inner wall of the torus. For the final approach to the target position a cor-recting algorithm has been developed, based on the Jacobian of the confi-guration. Generally the cartesian coordinates x, y of joint 5 depend on the angles of the other links. With x0 and y0 as coordinates of the shoulder joint we have (2) y - 12 -Cerreetions in the positions x and y can be described as displacements dx and dy. While the change is reasonably small one gets {3) dx = (4) dy = The C3f ää. ]_ af af af ~da aa 1 , 1 + --aaz daz + aa3 da3 + aa4 da4 ag_ d -- a + aa 1 1 ag and -aa. J ag + ~~3 da3 + ag da4 aa2 da2 aa~ are known sin and cos functions. As it is wellknown the Jacobian is the coefficient matrix From (3) and (4) the coefficients of maximal size (3f ag a"' 1 aa . and neglecting all other coefficients one gets "'i J (5) af da. dx aa. ]_ ]_ ( 6) dy ag da. ää."" J J of (3) and (4). are determined .For any desired displacements dx and dy a very simple equation for the change of some angles dai' daj can be determined. This algorithm must be repeated until the target position has been reached. Fig. 6 shows an example. However, for certain configurations this method fails. As an example the configuration in Fig. 7a) results in maximal coefficients for joint 3 and 4. Since both links are oriented in the same direction to-wards the target position, the iteration will not converge. Therefore after a certain nurober of unsuccessful iteration steps the presently moved joints are stopped and the others moved. Now the target position is reached ( Fig. 7b). - 13-Fig. Ga): By coarse positioning (table) the transporter is moved to the position ~ = 45° Fig. Gb): By fine positioning another radial position at ~ = 45° can be approached without further collision control - 14 -Fig. 7a): In this example the use of the Jacobian with maximal coefficients fails, if an outer radial position must be reached Fig. 7b): By using other joints, it succeeds -15 -The starting position for the fine adjustment is the end position of the coarse approach. According to the principle of the method this generally is close to the inner wall of the torus. Therefore the fine adjustment moves joint 5 generally outward and away from the nearest collision ran-ge. Therefore it is not necessary to test for collisions in connection with the fine adjustment. This results in a faster computation. 4. Future Work The described method permits the automatic generation of the complete field of movements of the transporter in the torus. In a next step the respective steps shall be done for the endeffector to enable the system to do arbi trary and complex operations. References I 11 P.D.F. Jenes, D. Maisonnier, T. Raimondi, Design and Operation of the JET Articulated Boom, 11th Symp. on Fusion Engineering, Austin, Texas, Nov. 1985 I 21 K. Leinemann, E.G. Schlechtendahl, Computer Graphics Support for Remote Handling Simulation and Operation, Proc. 32nd Conf. on Remote Systems Technology, New Orleans, June 3-7, 1984, Vol. 1, pp. 10-16 I 31 G.l-t. Hunter, K. Steigli tz, Operations on Images Using Quadtrees, IEEE Trans. on Pattern Analysis and Machine Intelligence 1, p.145-153, April 1979 I 41 G.M. Hunter, K. Steiglitz, Linear transformation of pictures represented by quadtrees, Computer Graphics and Image Processing, Vol. 10, 289-296, 1979 - 16 -I 51 C.L. Jackins, S.L. Tanimdo, Oct-trees and their use in represen-ting three-dimensional objects, Computer Graphics and Image Processing, Vol. 14, 249-270, 1980 I 61 D. Ayala, P. Brunet, R. Juan, I. Navazo, Object Representation by Means of Nonminimal Division Quadtrees and Octtrees, ACM Trans-actions on Graphics, Vol. 4 1 No. 1 1 11-59, Jan. 1985 I 71 Tomas Lozano-Perez, Spatial Planning, A Configuration Space Approach, IEEE Transactions on Computers C-32, Febr. 1983, 1 08-120 I 81 Tomas Lozano-Perez, Automatie Planning of Manipulator Transfer Movements, IEEE Transactions on Systems, Man, and Cybernetics, SMC-11, No. 10, 1981, 681-698 I 91 J.M. Brady et al., Robot Motion: Planning and Control, MIT Press, Cambridge, MA, 1983 1101 Rodney A. Brooks, Solving the Find-Path-Problem by Good Representation of Free Space, IEEE Transactions on Systems, Man, and Cybernetics, SMC-13 1 1983, 190-197 1111 Bruce R. Donald, Motion Planning with Six Degrees of Freedom, Thesis, Report AI-TR-791, MIT, Cambridge, MA 

Automatic path-planning for a multilink articulated boom within the torus of a fusion reactor

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Automatic path-planning for a multilink articulated boom within the torus of a fusion reactor

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