This paper considers a grasp planning scheme for dextrous hands. The
grasp is assumed to be a precise one, which means that only the fingertips of the
hand are in contact. The most important algorithm of the grasp planner is the
placement of contact points in the presence of friction. Based on a heuristic
search, a number of grasp configurations are generated. A proposed method for
evaluation of the configurations and determination whether a grasp is a force
closure, is introduced. These algorithms are used in the experimental control
system of an industrial robot, which the dextrous hand is attached to. A two-level
robot programming language, which was written for the robot-hand system, is
briefly introduced

Tóth, Ervin

English

Periodica Polytechnica (Budapest University of Technology and Economics)

PERIODICA POLYTECHNICA SER. EL. ENG. VOL. 43, NO. 3, PP. 207–214(1999)STABLE OBJECT GRASPING WITH DEXTROUS HAND INTHREE-DIMENSIONErvin TÓTHDepartment of Control Engineering and Information TechnologyBudapest University of Technology and EconomicsH–1117 Budapest, Pázmány Péter sétány. 1/D, Hungarye-mail: ervin@sch.bme.huReceived: Nov. 30, 1999AbstractThis paper considers a grasp planning scheme for dextrous hands. The grasp is assumed to be a preciseone, which means that only the fingertips of the hand are in contact. The most important algorithm ofthe grasp planner is the placement of contact points in the presence of friction. Based on a heuristicsearch, a number of grasp configurations are generated. A proposed method for evaluation of theconfigurations and determination whether a grasp is a force closure, is introduced. These algorithmsare used in the experimental control system of an industrial robot, which the dextrous hand is attachedto. A two-level robot programming language, which was written for the robot-hand system, is brieflyintroduced.Keywords: grasp planning, grasp evaluation, robot programming.1. IntroductionForm and force closure have been discussed in the literature for many years. How-ever, the distinction between the two has often been unclear. The difference liesin the way how the contact between the object and the constraining bodies is mod-elled. Form closure means that if enough constraints are placed in a motion ofan object, then the object is immobilized. Force closure means that any externalwrench (i.e. force and torque) can be balanced by the proper combination of fin-ger forces. RIMON and BURDICK have shown that in certain circumstances forceand form closure are equivalent to each other [5]. In this paper we focus on thecomputation of the force closure.At our institute a language called SRPS (Simple Robot Programming System)has been developed for the TUB-PC three-fingered dextrous hand attached to aNOKIA-Puma 560 industrial robot. The most important feature of the language isthat it has two levels: a high, task-oriented level and a low, motion-oriented one. Onthe higher level indirect commands exist, such as ‘Grasp a given object’ or ‘Movethe dextrous hand above a given object without colliding with the environment’.The language is upwardly compatible, that is, on the high level all the instructions ofthe low level can be used. The high-level part, naturally, contains commands which208 E. TÓTHrequire sophisticated algorithms. This paper demonstrates the grasp planning andevaluating algorithms in detail.2. The Object ModelA virtual reality display is used to visualize the actions of the robot for the humanoperators and this usually has to be done in real-time. It is also a requirement todetermine that the robot can do the desired action, so that it does not clash withitself and/or the surrounding items of the environment. Hence an efficient multi-level collision-detection algorithm was implemented.There are two fundamentally different ways to view the robot during thevisualization: it can be an overlaid image with the real camera images or can be aview from an arbitrary viewpoint. In order to put the virtual world together withthe real environment, the calibration of the system is required. It means that theparameters of a camera, e.g. position, orientation, focal length, etc. are identifiedbased on pictures taken by a real camera, and used in the visualization stage [1]. Thsystem runs on a Windows NT workstation and was developed using the OpenGLgraphic library for realtime display and Visual C for all the other computations.Our system uses boundary representation (B–Rep) scheme to describe objects.For grasp computations the fingertips are treated as a sphere. The normal vector ofthe surface element touched by the fingertip, however, not necessarily equals thenormal of the triangle. For curved objects vertex normals are defined, which arethe weighted sum of the triangle normals in a vertex shared by the neighbouringtriangles. The weighting factors are the areas of the triangles (the vertex normalsare not of unit length). The computed normal of a surface element of a triangle is thelinear combination of the three surrounding vertex normals. The arbitrary surfacenormal in a certain point is generated by linearly interpolating and normalizing thevertex normals along the surface.The contact force computation for simulation is based on the penetration ofthe fingertip model to the object model. Let the penetration vector, which is parallelwith the surface element normal and points from the surface to the deepest pointof the finger, bep. The contact force isF = −(Kc + Bc · dpdt)· √|p| · s whereKcspecifies the nonlinear stiffness of the material andBc is the damping [2].3. The SRPS LanguageOur goal was to develop a robot programming language which is capable of describ-ing complex motions, e.g. the robot should be controlled either in joint coordinatesand as a functionf (x, y, z, t), too. If the system is used without external infor-mation, that is, for simulation, the contact forces have to be simulated. In our caseit means collision and minimum-distance computations between the model of thedextrous hand and the surrounding objects. The language is a frame system, whichSTABLE OBJECT GRASPING 209means that certain actions do not need to be directly defined, only the starting andending positions and the path and grasp planner will do the rest automatically.Some parts of the functions implemented in the SRPS can be found in theARPS, the programming language of the NOKIA Puma robot. Certain programswritten in SRPS can (with minor modifications) be transmitted to the ARPS inter-preter. The new functions mainly deal with the control of the robot hand (high-levelgrasp synthesis) because the ARPS is not applicable for this task. Since the robotcarries items during its movement, condition-systems had to be developed whichdetermine them in a given configuration if the hand holds the object or not.With the graphic model the reference points of the robot track can be gen-erated. It is especially important when the robot cannot move free because theenvironment contains obstacles. The virtual robot can be positioned near the de-sired end positions, then collision-free configurations must be manually found.From now on, the path planning algorithm can find the movement between the endpoints so the operator does not have to find and teach it. In SRPS level this meansthat there are indirect moving commands between endpoints. The output of the pathplanning is the complete SRPS program, which contains simple (direct) instructionsonly, which can be directly transmitted to the robot controller. The reference pointsin both stages are collision-free of course.To demonstrate the possibilities of the SRPS, a few low-level functions arelisted below.LOAD – used to load pre-defined coordinates. These are the Denavit–Har-tenberg joint (wrist) coordinates. In the SRPS program a coordinate-configurationrecord is referred to with its number.FRAME/UNFRAME – defines/deletes a new coordinate system in which thefollowing commands work. This is used for navigation close to the manipulableobjects, using their own coordinate system.GO, GOS – moves the robot between two reference points. WithGO the pathplanning is done in joint coordinates, withGOS is along a straight line in 3D. Thestarting position is the actual position of the robot, the end coordinate is given withits number. If a collision is found during the movement, the program stops with anerror message.GRASP – directs the hand into one of the loaded hand positions. If a segmentof a finger collides with an object, the phalanx stops. The other phalanxes andfingers move further until another collision or the desired position. The commandhas several parameters, such as maximum contact forces, and list of the segmentswhich can touch the object. There are three simplified versions of this command,such asPINCH, SNAP and GRIP [3]. These commands move the fingers intopredefined positions, so these do not need to be taught. Furthermore, these havemuch smaller numbers of parameters.OPEN – straightens the fingers and translates them to the edge of the palm.During the movement collision must not occur. (If so, the program shows an errormessage.)210 E. TÓTHThe high-level functions:GOIN (Go indirect) – this command is not interpreted by the ARPS but isreplaced by the path planning algorithm with series ofGO andGOS commands.GRASPIN (Grasp indirect) – directs the grasp planner to develop a grasp. Thegrasp planning algorithm tries to find a prehensile grasp on the object. It takes intoaccount the properties of the object, e.g. frictional coefficient, center of gravity,parts of its surface that can be touched, and orientation constraints. Furthermore, itconsiders the obstacles around the object with respect to the initial and final positionof the robot arm before approaching and after grasping the object.4. Contact Point GenerationThe theory of grasp planning is also studied for a long time. Generally, the objectto be grasped has arbitrary shape, given in a form of geometric model, transformedfrom a modeller software (CAD) or derived from sensor data. Because of thebig amount of data required to describe even a medium-complex object, a direct(closed-form) solution for finding the optimal grasp does not exist. To overcomethis, we assume that using heuristics to locate contact points on the object, a numberof grasp candidates can be found, the best of which is selected. Precision graspsare considered (only the fingertips, which are hemisphere-shaped, touch the object).Unfortunately, it cannot be told how close our best candidate is to the optimal grasp.However, a number of measures to qualify grasps has been proposed, e.g. [4] , thatmeasures which external forces can be balanced by a grasp. From this point ofview, the best ones are the force-closure grasps, which resist all external forces andtorques. This induces a special problem: the TUB-PC hand has three fingers, and a3D force-closure grasp requires at least four contact points. The solution is to finda concave corner on the object, which can provide more than one contact point fora single fingertip.Our contact point generator has two fundamentally different algorithms, onefor the form-closure grasp generation, the other for arbitrary grasps. The plannerdecides whether a form-closure grasp is possible, and if not, runs the second algo-rithm. First, concave corners are searched. A corner (vertex) is concave, if all theedges meeting in the vertex are on the same side of a plane, and the plane, in thevicinity of the vertex, lies inside the object. The resulting grasps can be divided intothree categories: a) which contain only concave corners as grasp points, b) whichcontain no concave corners, c) mixed. The latter ones can be either form or forceclosures. Only those concave vertices are considered which are accessible for thefingertip of the dextrous hand. Next, the vertex normals of the concave corners aresearched for tripletsv1, v2, v3, where(v1 · v2), (v2 · v3), (v3 · v1) are all close to−0.5, which means that these vectors span a quasi-regular triangle. (The tripletsare assigned a valuew:∑i=1,2,3j=2,3,1(−0.5− (vi · v j ))2 and are sorted in ascending order.)If the smallestw is larger than a givenwmax value, the algorithm fails. We foundSTABLE OBJECT GRASPING 211out that a reasonable value forwmax is 1. The remaining ones (w < wmax) becomegrasp candidates.P′QRCPϕψ αβχdFig. 1. Parameters that alter the grasp starThe second algorithm tries to place a Y-shaped ‘grasp star’ so that the pene-tration points on the object surfaces are the contact points. First, a surface is picked.Through its center pointP a ray is shot inside the object which is parallel to thesurface normal. Between the (farthest) penetration pointP′ on the opposite side,and the starting position, aC point is picked so thatPC = 2P′C. FromC two raysare shot, their intersection point with the object isQ andR (the angles betweenCP,CQ andCR are 120 degrees, seeFig. 1). At this point, we constructed a three-tipstar whose tips are the contact points. The algorithm checks whether theCP, CQandCR lines are inside the corresponding friction cones. If so, a grasp candidateis ready; if not, we try to compensate with altering the star. There are a number ofpossibilities: theC point can be altered, the angles of the star can be modified, andthe star can be rotated around theCP, CQ andCR lines. These operations take intoaccount the surface normal in the contact points so that the accumulated deviationfrom the surface normals becomes smaller. Random modification is also applied,thus the algorithm resembles the simulated annealing optimization method. Duringthe algorithm, the following criteria are checked: a) two contact points cannot betoo close to each other, b) the contact points must be reachable for the hand, c) acontact point cannot be too close to an edge.We generate several grasp candidates. If possible, the starting position is notonly a surface point, but also a vertex normal of a concave corner, resulting a mixedtype grasp. Finally, the palm position of the dextrous hand is calculated for thegrasp candidates. The palm position is selected so that the accumulated distance212 E. TÓTHof the palm and the surrounding objects is maximal. The calculation of the fingerpositions is an inverse geometry task: a finger has 3 degrees of freedom.5. Grasp EvaluationThe necessary and sufficient conditions of stable grasp are checked. The staticequilibrium of fingertip forces and Coulomb friction are considered. The necessaryand sufficient conditions are: a) total moment of fingertip forces is zero, b) totalforce of fingertip forces is zero, c) each fingertip force is in the friction cone. Thefirst condition is satisfied by selecting the fingertip forces so that they intersect inC. The necessary and sufficient condition for the second is:eTi (e j + ek) ≤ 0; eTj (ei + ek) ≤ 0; eTk (ei + e j ) ≤ 0,whereei is the unit vector of theith fingertip force. The third condition is a restrictionabout Coulomb friction. The method we use, proposed in [6], calculates a measureby determining the set of external wrenches (grasp wrench space, GWS) that can beresisted by distributing one unit force over all grasp points. For linear computations,the set of forces within the friction cones at contact pointi are approximated bya linear combination of a finite set ofn unit force vectorsfi, j at the friction coneboundaries:fi =n∑j=1αi, j · fi, j , αi, j > 0,n∑i=1k∑j=1αi, j ≤ 1.The resulting generalized force (wrench) at theith contact can be expressed aswi =n∑j=1αi, j · wi, j , wi, j(fi, jλ · (ri × fi, j )),wi, j is called primitive contact wrench. TheGWS can be calculated asGWS =ConvexHull(⋃ni=1{wi,1, . . . , wi,m}). The time-consuming calculation of the con-vex hull can be sped up applying incremental calculations [6]. This means that inthe beginning of the convex hull computation each friction cone is represented onlyby three primitive contact wrenches. Those cones which take part in spanning theweakest surface of the convex hull, will be supplemented by additional primitivecontact wrenches, thus making the cone approximation more precise. (The weak-est surface is the one which lies closest to the origin.) This process continues untilthe weakest plane converges. The grasp measure is the radius of the maximal ballwhich can be drawn inside the convex hull. To establish whether a grasp is a forceclosure, the following condition is checked [7]: if the origin of the wrench space(R6) lies exactly inside the convex hull of the primitive contact wrenches, then thegrasp is a force closure.STABLE OBJECT GRASPING 213wi, jnFig. 2. Primitive contact wrenches6. ConclusionThis paper proposed a method for finding and evaluating stable grasps on an arbitraryshaped object. Extended polygonal models supplied by material properties areapplicable for contact force simulation. A two-level robot programming languagehas been introduced to describe complex operations. As a part of this language, agrasp planning algorithm was introduced, which generates many grasp candidatesbased on a heuristic search. Finally, an evaluation function for grasp stability wasshown. So far we assumed that the geometric object model is fully known. Inreal environments, this requirement often cannot be satisfied. In the near future thegeneration of a partial object model from sensor (mainly visual) data is considered.AcknowledgementSupport for the research for stable object grasping is provided by the Hungarian NationalResearch Programs under grant No. FKFP 0417/1997 and OTKA T 029072.References[1] TÓTH, E. – TÉL, F.: Intelligent Robot Control System with Graphic Model Based Programmingand Stereo Vision. In:Proc. IEEE Int. Conference on Intelligent Engineering Systems, Poprad,Slovakia, 1999, pp. 57–62.[2] M AEKAWA , H. – HOLLERBACH, J. M.: Haptic Display for Object Grasping and Manipulatingin Virtual Environment. In:Proc. IEEE Int. Conference on Robotics & Automation, Leuven,Belgium, 1998, pp. 1586–1592.[3] L ANTOS, B.: Some Possibilities to Increase the Intelligence in Robot Control Systems.Proc.IEEE Conference on Intelligent Engineering Systems, Vienna, Austria, 1998, pp. 7–18.214 E. TÓTH[4] FERRARI, C. – CANNY, J., PlanningOptimalGrasps. In:Proc. IEEE Int. Conference on Robotics& Automation, Nice, France, 1992, pp. 2290–2295.[5] RIMON, E. – BURDICK, J.: On Force and Form Closure For Multiple Finger Grasps.IEEETrans. on Robotics and Automation, 1996.[6] BORST, C. – FISCHER, M. – HIRZINGER, G., A Fast and Robust Grasp Planner for Arbitrary3D Objects. In:Proc. IEEE Int. Conference on Robotics & Automation, Detroit, Michigan, 1999,pp. 1890–1896.[7] M ISHRA, B. – SCHWARTZ, J. T. – SHARIR, M.: On the Existence and Synthesis of MultifingerPositive Grips. Algorithmica, Special Issue:Robotics, 2 (1987), pp. 541–545.

Stable Object Grasping With Dextrous Hand In Three-Dimension

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Stable Object Grasping With Dextrous Hand In Three-Dimension

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