Kenneth Y. Goldberg. Orienting polygonal parts without sensors. Algorithmica, 8(10):201--225, 1993.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... the state of a part (or set of parts) The feeder may rely solely on the geometry of specially designed fixtures interacting with a part on a conveyor belt or in a gravity field [8] 10] 29] 31] 20] 3] 5] 25] 32] 33] or specially designed motions of generic surfaces [11] 26] [12], 34] 7] 1] 6] 19] or some combination of geometry, materials, and motion (open loop or sensor based) design. In all cases, the goal is to collapse the possible initial states of the part into a smaller set (ideally a singleton) We describe a simple planar parts feeder consisting of a ....

K. Y. Goldberg. Orienting polygonal parts without sensors. Algorithmica, 10:201--225, 1993.

.... space for which the object is not immobilized but is constrained to lie within a bounded region of the free configuration space (see [10] for related work in the two dimensional, two finger case) ICS regions will allow us to plan in hand object motions as sequences of gripper configurations (see [1, 4, 5, 6, 7, 9, 10] for related work) starting from some immobilizing configuration, we can open the gripper jaws and retract the immobilizing pins, then choose another triple of pins whose ICS region contains the initial gripper configuration, lower these pins, and as the jaws close, move the object to the ....

K.Y. Goldberg. Orienting polygonal parts without sensors. Algorithmica, 10(2):201--225, 1993.

....all times in the ICS region associated with the robots, and the manipulation will succeed as long as the friction forces associated with contacts between the robots, the object and its supporting plane are not large enough to cause jamming. Unlike other techniques for manipulation planning (e.g. [1, 3, 5, 7, 8, 9]) this approach does not require that robot object contact be maintained during grasping or manipulation, nor does it rely on any particular model of friction or contact dynamics. The methods presented in [2, 10, 15] can only be used to generate plans where robots move one by one in a fixed ....

K.Y. Goldberg. Orienting polygonal parts without sensors. Algorithmica, 10(2):201--225, 1993.

.... was pioneered by Inoue [16] and Whitney [17] and techniques for re orienting parts through pushing and grasping operations have been developed by several authors, including Fearing [18] Mason [19] Mani and Wilson [20] Brost [21] Erdmann and Mason [22] Peshkin and Sanderson [23] Goldberg [24], Abell and Erdmann [25] Rao and Goldberg [26] Akella et al. 27] and Leveroni and Salisbury [28] Unlike these methods, that all assume some predictive model of the contact mechanics, our approach does not require that robot object contact be maintained during grasping or manipulation, nor ....

K.Y. Goldberg, "Orienting polygonal parts without sensors," Algorithmica, vol. 10, no. 2, pp. 201--225, 1993.

.... University Technical Report STAN CS TR 1995 1559 On the number of equilibrium placements of mass distributions in elliptic potential fields Lydia E. Kavraki Robotics Laboratory, Department of Computer Science Stanford University, Stanford, CA 94305, USA Abstract Recent papers have demonstrated the use of force fields for mechanical ....

.... University Technical Report STAN CS TR 1995 1559 On the number of equilibrium placements of mass distributions in elliptic potential fields Lydia E. Kavraki Robotics Laboratory, Department of Computer Science Stanford University, Stanford, CA 94305, USA Abstract Recent papers have demonstrated the use of force fields for mechanical ....

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K. Y. Goldberg. Orienting polygonal parts without sensors. Algorihmica, (10):201-225, 1993.

....vibratory bowl feeders [2] while the mainstream research in manufacturing has focused in developing more flexible and more robust platforms, such as programmable part feeders. This type of part feeder can be programmed to handle different parts without the need for hardware modification (e.g. [9, 12, 10, 1, 7]) A new direction in programmable part feeding that has recently gained attention in research is the use of a new class of devices for non prehensile distributed manipulation. Examples are, in microscale, the use of MEMS actuators arrays [4] and in macroscale, the use of mechanical devices ....

....as a strategy for applying a sequence of fields to bring a part from one equilibrium to another until it reaches a desired configuration. In [4] it has been shown that polygonal parts can be oriented by a sequence of squeeze fields. The sequence is planned using an algorithm similar to the one in [12] for orienting polygonal parts with a sensorless parallel jaw gripper. The number of steps in the sequence depends on the complexity of the geometry of the convex hull of the oriented part and the uniqueness of the final orientation is only upto modulo . Another research direction ....

K. Y. Goldberg. Orienting polygonal parts without sensors. Algorithmica, 10:201--225, 1993.

....designed for the orientation of a single part and need to be redesigned if the shape of the part changes. Recent work has investigated alternative ways of orienting parts in assembly workcells. Programmable part feeders are more flexible and can be adapted easily to different types of parts [1, 11]. Moreover, they are usually more robust and easier to implement. In particular, methods that do not require sensors are favored [1, 3, 7, 9, 11] 0.5 0 0.5 1 x 1 0.5 0 0.5 1 y 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Figure 1: Radial constant potential field 262 ....

....alternative ways of orienting parts in assembly workcells. Programmable part feeders are more flexible and can be adapted easily to different types of parts [1, 11] Moreover, they are usually more robust and easier to implement. In particular, methods that do not require sensors are favored [1, 3, 7, 9, 11]. 0.5 0 0.5 1 x 1 0.5 0 0.5 1 y 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Figure 1: Radial constant potential field 262 . The corresponding force field uniquely positions and orients non symmetric and some symmetric parts. One of the ....

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K. Y. Goldberg. Orienting polygonal parts without sensors. Algorithmica, 10:201--225, 1993.

....reader is referred to the survey by Bose and Toussaint [2, 5] In assembly, the emphasis is on planning tasks so as to put parts together to form the final product. Interesting geometric problems arise in almost every step of automatic assembly planning. Assembly sequencing [24] part orienting [9], fixturing [18] and welding [17] are just a few of many examples. Although these manufacturing and assembly processes may be totally different from one another, some of them raise similar geometric problems that can be generally termed separability problems [22] This is the case in the ....

K. Y. Goldberg. Orienting polygonal parts without sensors. Algorithmica, 10:201--225, 1993.

....to Bose s thesis [2] and the survey by Bose and Toussaint [4] In assembly, the emphasis is on planning tasks so as to put parts together to form the nal product. Interesting geometric problems arise in almost every step of automatic assembly planning. Assembly sequencing [27] part orienting [11], xturing [21] and welding [19] are just a few of many examples. Although these manufacturing and assembly processes may be di erent from one another, some of them raise similar geometric problems that can be generally termed separability problems [25] This is the case in the manufacturing ....

Kenneth Y. Goldberg. Orienting polygonal parts without sensors. Algorithmica, 10:201-225, 1993.

....1991] fix the number of fingers and solve a system of linear constraints in the positions of the fingers to optimally position them along the polygonal edges. A similar technique for 7 three dimensional polyhedral objects was developed by Ponce et al. Faverjon and Ponce, 1991] Goldberg [Goldberg, 1993] also details a method for choosing grasps with a parallel jaw gripper when the initial pose of the object is unknown. Other optimizing grasps techniques based on simple geometric constructions have been developed by Brost [Brost, 1988] and later Mirtich, Canny, and Ferrari [Ferrari and Canny, ....

Goldberg, K. (1993). Orienting polygonal parts without sensors. Algorithmica. Special Issue on Computational Robotics, Volume 10(3):201--225.

....are otherwise difficult to grasp and carry. It can also simplify robot hardware by allowing the robot to push with any surface available (whole arm manipulation [1] or by eliminating the need for a gripper in planar manipulation tasks. One application of pushing is parts feeding [2] 3] 4] [5], 6] Pushing also allows a mobile robot to easily manipulate large objects [7] 8] We are interested in characterizing the fundamental capabilities of pushing as a manipulation primitive. Toward that end we have studied the controllability of pushing: is it possible to push the object to the ....

.... Other related results in manipulation include the demonstration of the controllability of a ball rolling on a plane or another ball [12] bounds on the number of fingers necessary for a grasp [13] 14] 15] the classification of orientable parts by sensorless parallel jaw grasping sequences [5]; and the proof that a one joint robot operating above a fixed speed conveyor is sufficient to position and orient polygonal parts by pushing [6] Our work on characterizing controllable polygons in terms of their geometry is similar in spirit to the work of van der Stappen et al. 16] on ....

K. Y. Goldberg, "Orienting polygonal parts without sensors," Algorithmica, vol. 10, pp. 201--225, 1993.

....in configuration space. This approach applies to a new class of reconfigurabe grippers with mostly discrete degrees of freedom (Figure 1) and it is related to recent work in modular fixture planning [4, 5, 22, 47, 48, 46] and to a number of sensorless pushing and squeezing manipulation algorithms [1, 9, 12, 18, 20, 33, 35]. Indeed, the class of devices we are interested in can be seen as automatically reconfigurable fixtures, but since they are capable of both immobilizing a part and manipulating it within a grasp, we will 3 continue in the rest of this paper to call them grippers. a) b) c) d) Figure 1: A ....

.... space for which the object is not immobilized but is constrained to lie within a bounded region of the free configuration space (see [35] for related work in the two dimensional, two finger case) ICS regions allow us to plan in hand object motions as sequences of gripper configurations (see [1, 9, 12, 18, 20, 33, 35] for related work) starting from some immobilizing configuration, we can open the gripper jaws and retract the immobilizing pins, then choose another triple of pins whose ICS region contains the initial gripper configuration, lower these pins, and as the jaws close, move the object to the ....

K.Y. Goldberg. Orienting polygonal parts without sensors. Algorithmica, 10(2):201--225, 1993.

....all times in the ICS region associated with the robots, and the manipulation will succeed as long as the friction forces associated with contacts between the robots, the object and its supporting plane are not large enough to cause jamming. Unlike other techniques for manipulation planning (e.g. [1, 4, 5, 6, 7, 9]) this approach does not require that robot object contact be maintained during grasping or manipulation, nor does it rely on any particular model of friction or contact dynamics. A limitation of the methods presented in [3, 10, 14] is that the individual robot motions only have one degree of ....

K.Y. Goldberg. Orienting polygonal parts without sensors. Algorithmica, 10(2):201--225, 1993.

....We also gave an algorithm for grasp planning and reported preliminary results. In this paper, we improve the grasp planning algorithm of [36, 51] and introduce a new approach to in hand manipulation. This approach is related to a number of sensorless pushing and squeezing manipulation algorithms [1, 12, 16, 25, 27, 41, 43], and it is based on an explicit configuration space characterization of the possible range of motions of the manipulated part as contact occurs. 1.2 Second Order Immobility Let us consider a rigid object and the contacts between d pins and this object. We assume frictionless hard finger ....

....space (see [43] for related work in the two dimensional, two finger case) As noted in Section 1, this allows us to generalize the notion of grasp stability to finite size displacements. 21 ICS regions will also allow us to plan in hand object motions as sequences of gripper configurations (see [1, 12, 16, 25, 27, 41, 43] for related work) starting from some immobilizing configuration, we can open the gripper jaws and retract the immobilizing pins, then choose another triple of pins whose ICS region contains the initial gripper configuration, lower these pins, and as the jaws close, move the object to the ....

K.Y. Goldberg. Orienting polygonal parts without sensors. Algorithmica, 10(2):201--225, 1993.

....stemmed from ideas in minimalistic manipulation. Mason and Erdmann [1, 3] provided a radical alternative to standard robotic manipulation by significantly simplifying the robot manipulator and developing manipulation algorithms for these low degree of freedom sensorless 4 mechanisms. Goldberg [4] developed an algorithm which orients an object with a sequence of gripper open, close, and rotation operations without sensor information. This sequence of operations is termed a squeeze. Bohringer, et al. 2] applied this type of sensorless manipulation to an array of micromechanical actuators ....

K.Y. Goldberg. Orienting polygonal parts without sensors. Algorithmica: Special Issue on Computational Robotics, 10:201--225, August 1993.

....is such a large scale actuator array (see Figure 2) The MDMS uses distributed control where each cell communicates only with neighboring cells. The companion paper [6] describes the MDMS in more detail. Typical work in actuator arrays [2, 5] expands on work done in minimalistic manipulation [1, 3, 4], and deals with the task of bringing a single, isolated object to a particular translational position at a particular orientation using sensorless (open loop) manipulation strategies. For a summary of prior work in actuator arrays, see the 1 i cell index n number of cells supporting object ....

K.Y. Goldberg. Orienting polygonal parts without sensors. Algorithmica: Special Issue on Computational Robotics, 10:201-225, August 1993.

.... usually too expensive for industrial use [1, 2, 3, 4] Other papers have addressed the use of more practical hardware, such as parallel jaw grippers; however, this research has generally been limited to approaches which model the objects in 2D, either as smooth contours [5, 6, 7] or as polygons [8, 9, 10]. In such cases, it is often presumed that constraining the object s horizontal planar motion would be sufficient to hold the object securely an assumption which is useful in many cases, but not always justifiable. As an alternative, we seek to explore methods of automatically generating ....

K. Y. Goldberg. "Orienting polygonal parts without sensors," Algorithmica, vol. 10, pp. 201--225, 1993.

....continuing the failed plan. This represents an important use of sensor information, and expands the previous notion of reachability to include failure. Goldberg applied preimage planning ideas to construct manipulation plans that orient an 37 object using a parallel gripper without sensors [74] [75]. Fox and Hutchinson developed methods for computing backprojections that include visual constraint rays that result from the correspondence between edges in the workspace and the image plane [66] Algorithms for computing motion plans in the presence of probabilistic uncertainty for mobile robots ....

....layers that the other decision maker has a mixed strategy. The implications are that many multiple robot planning problems quickly become difficult when there are limitations in communication and information. Part orienting This problem formulation is inspired by the approach considered in [74] [75], 76] Suppose that planar parts appear on a conveyor belt at unknown orienta242 Conveyor Belt Parallel Gripper Oriented Parts Figure 5.4 A parallel gripper that squeezes parts for alignment. tions (see Figure 5.4) The task is to use a parallel gripper to perform squeeze operations that ....

K. Y. Goldberg. Orienting polygonal parts without sensors. Algorithmica, 10:201-- 225, 1993.

....orientation of objects by squeeze grasps is analogous to palmar manipulation of one object with two hands, with gravity perpendicular to the plane. He finds sets of actions which reliably orient a part in the presence of uncertainty in the part s location. Goldberg, and later Rao and Goldberg ([37], 74] found algorithms for determining sequences of squeezes of a parallel jaw gripper which will reliably orient (up to symmetry) frictionless, polygonal or algebraic, planar parts from an arbitrary and unknown initial orientation, without sensors. Mason and Erdmann [34] use gravity to propel ....

K. Y. Goldberg. "Orienting Polygonal Parts without Sensors", Algorithmica, vol. 10, pp. 201-225, 1993.

....similar to our Markov model. Others have used analytical techniques to uniquely orient streams of singulated parts. Goldberg presented a design for a sensorless programmable parts feeder. The work describes an algorithm that finds a sequence of gripper actions for orienting a given polygonal part [11] . Brokowski, Peshkin, and Goldberg described the use of curved fences above a moving conveyor [6] It is very time intensive and costly to build prototypes of feeder designs. Researchers have proposed simulation as a technology for making the designer s job more efficient and effective. Jakiela ....

Kenneth Y. Goldberg. Orienting polygonal parts without sensors. Algorithmica, 10:201--225, August 1993.

....or words, punctuated by a checksum. 3 Prior Work Mason and Erdmann [1, 3] provided a radical alternative to standard robotic manipulation by significantly simplifying the robot manipulator and developing manipulation algorithms for these low degree of freedom sensorless mechanisms. Goldberg [4] developed an algorithm which orients to symmetry a part with a sequence of gripper open, close, and rotation operations without sensor information. This sequence of operations is termed a squeeze. Bohringer, Donald, et al. 2] applied this type of sensorless manipulation to an array of ....

K. Goldberg. Orienting polygonal parts without sensors. Algorithmica: Special Issue on Computational Robotics, 10:201--225, August 1993.

....the parts feeding problem using state transitions. Others have developed analytical methods to uniquely orient singulated parts being fed in a stream. Goldberg described a planning algorithm and automatic programmable parts feeder that can orient parts rapidly by analyzing their geometry [8] . Brokowski, Peshkin, and Goldberg proposed the use of curved fences above a moving conveyor to orient streams of parts [4] Research in the past few years has included the development of sensorless strategies to manipulate parts using vibratory motion. B ohringer, Bhatt, and Goldberg examined ....

Kenneth Y. Goldberg. Orienting polygonal parts without sensors. Algorithmica, 10:201--225, August 1993.

....Manipulation of Pose Distributions 3 (dof) manipulator. Lynch [32] extended this idea to 3D parts on a conveyor belt with a two dof manipulator. Wiegley et al. 43] presented a complete algorithm for designing passive fences to orient parts. Here, the initial orientation is unknown. Goldberg [22] showed that it is possible to orient polygonal parts with a frictionless parallel jaw gripper without sensors. Marigo et al. 34] showed how to orient and position a polyhedral part by rolling it between the two hands of a parallel jaw gripper. Grossman and Blasgen [25] developed a manipulator ....

....[9, 10, 28] The idea is that a kind of force field (implemented using e.g. MEMS actuator arrays) can be used to push the part in a certain orientation. Kavraki [28] presented a vector field that induced two stable configurations for most parts. Bohringer et al. 9, 10] used Goldberg s algorithm [22] to define a sequence of squeeze fields to orient a part. They also gave an example how programmable vector fields can be used to simultaneously sort di#erent parts and orient them. 2.2 Stable Poses To compute the stable poses of an object quasistatic dynamics is often assumed. Furthermore, ....

Kenneth Y. Goldberg. Orienting polygonal parts without sensors. Algorithmica, 10(3):201--225, August 1993.

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Ken Goldberg. Orienting polygonal parts without sensors. Algorithmica, (to appear).

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K. Y. Goldberg. Orienting polygonal parts without sensors. Algorithmica, 10(2):201--225, Aug 1993. (Special issue on Computational Robotics).

....use trapezoidal jaw modules that maximize contact between the jaws and the part by combining analysis of toppling, jamming, liftoff, accessibility and form closure. Berretty et al. [1] describe a method to orient parts by pulling with one cylindrical jaw that generalizes the algorithm described in [7]. The stable positions when pulling with the jaw occur only when the jaw is in a concavity. Sugar and Kumar [27] give an excellent review of grasp quality metrics and propose frame invariant quality metrics based on the grasp stiffness matrix. We define a kinematic metric based on sensitivity of ....

Ken Goldberg, Orienting Polygonal Parts Without Sensors, Algorithmica, v10, 1993

....the part is assumed to be unknown. In sensorless manipulation, parts are positioned and or oriented using passivemechanical compliance. The input is a description of part shape and the output is a sequence of open loop actions that moves a part from an unknown initial pose into a unique final pose [2,6,7,8,9, 10, 11, 16,17, 20]. Goldberg [11] considered the problem of orienting (feeding) polygonal parts using a paralleljaw gripper. A parallel jaw gripper consists of a pair of flat parallel jaws that can close in the direction orthogonal to the jaws, allowing it to squeeze the part. Figure 1 shows a (frictionless) ....

....manipulation, parts are positioned and or oriented using passivemechanical compliance. The input is a description of part shape and the output is a sequence of open loop actions that moves a part from an unknown initial pose into a unique final pose [2,6,7,8,9, 10, 11, 16,17, 20] Goldberg [11] considered the problem of orienting (feeding) polygonal parts using a paralleljaw gripper. A parallel jaw gripper consists of a pair of flat parallel jaws that can close in the direction orthogonal to the jaws, allowing it to squeeze the part. Figure 1 shows a (frictionless) parallel jaw ....

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K.Y. Goldberg, Orienting polygonal parts without sensors, Algorithmica 10 (1993), pp. 201-225.

....that describes the outcome of first pushing and then grasping the part. 1 Introduction In manufacturing, it is often necessary to orient parts prior to packing or assembly. In previous work, we showed that a modified parallel jaw gripper can be used to orient planar parts bounded by linear [10] and algebraic curves [32] See Fig.s 1 and 4. This approach uses mechanical compliance of the part as it is grasped; part rotation can be precisely characterized with a function, I : S x S , that we call the grasp function. Given an initial orientation 0 of the part with respect to the gripper, ....

....but the end points as well, then [20] shows that from 3n 2 projection probings, you can recover the complete shape of the polygon. These results show that recovering shape from diameter is a difficult problem as well; many objects have the same diameter function. However, our results in [10, 32] then imply that all parts having the same diameter function (and hence the same grasp function) have the same oftenting plan. In this paper, our focus is on computing the grasp function from extrema (local maxima and local minima) in the diameter function, the first step towards oftenting parts ....

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K. Y. Goldberg. Orienting polygonal parts without sensors. A!gorithmica, 10(2):201-225, Aug 1993. (Special issue on Computational Robotics). 16

....is a description of the shape of the part and the ouput is a sequence of open loop actions that moves the part from an unknown initial pose into a unique final pose. Among the sensorless part feeders considered in the literature are the traditional bowl feeder [18, 19] the paralleljaw gripper [23, 26], the single pushing jaw [3, 29, 31, 34] the conveyor belt with a sequence of fences rigidly attached to both its sides [20, 35, 39] the conveyor belt with a single rotational fence [2] the tilting tray [25,33] and vibratory plates and programmable vector fields [16, 17] Traditionally, ....

....we will see that it is possible to use the knowledge of the shape of the part to synthesize traps that allow the part to pass in only one orientation [9, 12, 13] The first feeders to which thorough theoretical studies have been devoted were the parallel jaw gripper and pushing jaw. Goldberg [26] showed that these devices can be used for sensorless part feeding or orienting of two dimensional parts. He gave an algorithm for finding the shortest sequence of pushing or squeezing actions that will move the part from an unkown initial orientation to a known final orientation. Chen and Ierardi ....

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K. Y. Goldberg. Orienting polygonal parts without sensors. Algorithmica, 10(2):201-225, 1993.

....of a set of points, the maximizing distance over all pairs of points, is well studied in computational geometry [12, 4] Diameter functions, termed width functions in [18] were applied by Jameson [10] to determine grasp stability for a part grasped in the jaws of a parallel jaw gripper. Goldberg [8] used the diameter function to generate plans, in O(n ) time, to orient n gonal parts. Rao and Goldberg [14, 13] extend these results to curved parts. Our work has some relation to geometric probing which was introduced by Cole and Yap [3] and inspired by work in robotics and tactile sensing ....

K. Y. Goldberg. Orienting polygonal parts without sensors. Algorithmica, 10(2):201--225, Aug 1993. (Special issue on Computational Robotics).

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K. Goldberg. Orienting polygonal parts without sensors. Algorithmica, Vol.10, No. 2, p.201-25, August, 1993. Special Issue on Computational Robotics.

....mechanical compliance. The input is a description of the part shape and the output is a sequence of open loop actions that moves a part from an unknown initial orientation into a unique final orientation. Among the sensorless part feeders considered in literature are the parallel jaw gripper [17, 21], the single pushing jaw [2, 27, 28, 32] the conveyor belt with a sequence of (stationary) fences placed along its sides [10, 14, 33, 36] the conveyor belt with a single rotational fence [1] the tilting tray [20, 31] vibratory plates and programmable vector fields [11] The oldest and still ....

....is attached, which identifies the zero orientation of the part. The track is slightly tilted towards the railing so the part remains in contact with the railing as it moves along the railing. The radius function for the part characterizes the stable orientations of the part against the railing [21]. Definition 2.1 The radius of a part at an angle # is the distance from the centerof mass to the line tangent to the part, and orthogonally intersecting the ray from the center of mass in the direction of #. Each stable orientation of P corresponds to a local minimum in the radius function. ....

K. Y. Goldberg. Orienting polygonal parts without sensors. Algoritmica, 10(2):201--225, 1993.

....using passive mechanical compliance. The input is a description of the part shape and the output is a sequence of open loop actions that moves a part from an unknown initial pose into a unique final pose. Among the sensorless part feeders considered in literature are the paralleljaw gripper [17, 21], the single pushing jaw [3, 26, 27, 32] the Research is supported by NATO Collaborative Research Grant CRG 951224. y Department of Computer Science, Utrecht University, PO Box 80089, 3508 TB Utrecht, The Netherlands. z Berretty s research is supported by the Dutch Organization for Scientific ....

....of the part is restricted to O(n) different, discrete orientations. The track is slightly tilted toward the railing so the part remains in contact with the railing as it moves along the railing. The radius function for the part identifies the stable orientations of the part against the railing [21]. Definition 2.3 The radius of a part at an angle is the distance from the center of mass to the line tangent to the part, and orthogonally intersecting the ray from the center of mass in the direction of . Each stable orientation of P corresponds to a local minimum in the radius function. ....

K. Goldberg. Orienting polygonal parts without sensors. Algorithmica, 10(2):201--225, August 1993.

....Presidential Faculty Fellow Award IRI9553197. input is a description of the part shape and the output is a sequence of open loop actions that moves a part from an unknown initial pose into a unique final pose. Among the sensorless part feeders considered in literature are the paralleljaw gripper [8, 12], a single pushing jaw [3, 14, 15, 19] a conveyor belt with a sequence of (stationary) fences placed along its sides [7, 20, 25] a conveyor belt with a single rotational fence (1JOC) 2] a tilting tray [11, 17] and vibratory plates and programmable vector fields [5, 6] We focus on sensorless ....

....referred to as a push plan. Akella et al. 2] have shown that finding a manipulation plan for the 1JOC part feeder is equivalent to finding a sequence of push actions, so any push plan immediately translates into a solution to the problem of sensorless orientation by the 1JOC part feeder. Goldberg [12] showed that any polygonal part can be oriented by a sequence of pushes. Chen and Ierardi [8] proved that any polygonal part with n vertices can be oriented by O(n) pushes. They showed that this bound is tight by constructing (pathological) n gons that require Omega Gamma n) pushes to be ....

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K. Goldberg. Orienting polygonal parts without sensors. Algoritmica, 10(2):201--225, 1993.

....using passive mechanical compliance. The input is a description of the part shape and the output is a sequence of open loop actions that moves a part from an unknown initial pose into a unique final pose. Among the sensorless part feeders considered in literature are the parallel jaw gripper [6, 9], a single pushing jaw [2, 10, 11, 13] a conveyor belt with a sequence of (stationary) fences placed along its sides [5, 14, 17] a conveyor belt with a single rotational fence (1JOC) 1] a tilting tray [8, 12] and vibratory plates and programmable vector fields [3, 4] The pushing jaw [2, 10, ....

....sequence of pushes and jaw reorientations. The problem of sensorless orientation by a pushing jaw is to find a sequence of push directions that will move the part from an arbitrary initial orientation into a single known final orientation. Such a sequence is referred to as a push plan. Goldberg [9] showed that any polygonal part can be oriented by a sequence of pushes. Chen and Ierardi [6] proved that any polygonal part with n vertices can be oriented by O(n) pushes. They showed that this bound is tight by constructing (pathological) n gons that require Omega Gamma n) pushes to be ....

K. Goldberg. Orienting polygonal parts without sensors. Algoritmica, 10(2):201--225, 1993.

....using passive mechanical compliance. The input is a description of the part shape and the output is a sequence of open loop actions that moves a part from an unknown initial pose into a unique final pose. Among the sensorless part feeders considered in literature are the parallel jaw gripper [9, 13], a single pushing jaw [2, 14, 15, 17] a conveyor belt with a sequence of (stationary) fences placed along its sides [7, 18, 21] a conveyor belt with a single rotational fence (1JOC) 1] a tilting tray [12, 16] and vibratory plates and programmable vector fields [5, 6] The pushing jaw [2, ....

....sequence of pushes and jaw reorientations. The problem of sensorless orientation by a pushing jaw is to find a sequence of push directions that will move the part from an arbitrary initial orientation into a single known final orientation. Such a sequence is referred to as a push plan. Goldberg [13] showed that any polygonal part can be oriented by a sequence of pushes. Chen and Ierardi [9] proved that any polygonal part with n vertices can be oriented by O(n) pushes. 1 Figure 1: Three overhead views of the same conveyor belt and fence design. The traversals for three different initial ....

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K. Goldberg. Orienting polygonal parts without sensors. Algoritmica, 10(2):201--225, 1993. 27

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Kenneth Y. Goldberg. Orienting polygonal parts without sensors. Algorithmica, 8(10):201--225, 1993.

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Goldberg, K. Y. (1993). Orienting polygonal parts without sensors. Algorithmica, 10(3):201--225. Goyal, S., Papadopoulos, J. M., and Sullivan, P. A. (1998a). The dynamics of clattering I: Equation of motion and examples. J. of Dynamic Systems, Measurement, and Control, 120:83--93.

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K. Y. Goldberg. Orienting polygonal parts without sensors. Algorithmica, 10:201-225, 1993.

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K. Y. Goldberg. Orienting polygonal parts without sensors. Algorithmica, 10:201--225, 1993.

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K. Y. Goldberg. Orienting polygonal parts without sensors. Algorithmica, 10:201--225, 1993.

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K. Y. Goldberg. Orienting polygonal parts without sensors. Algorithmica, 10:201--225, 1993.

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K. Y. Goldberg. Orienting polygonal parts without sensors. Algorithmica, 10:201-225, 1993.

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Goldberg, K. Y. 1993. Orienting polygonal parts without sensors. Algorithmica 10(2):201--225.

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K. Y. Goldberg. Orienting polygonal parts without sensors. Algorithmica, 10:201--225, 1993.

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Goldberg, K. Y. 1993. Orienting polygonal parts without sensors. Algorithmica 10(2/3/4):201--225.

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K. Y. Goldberg. Orienting polygonal parts without sensors. Algorithmica, 10:201--225, 1993.

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K. Goldberg. Orienting polygonal parts without sensors. Algorithmica, August 1993.

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K. Y. Goldberg. Orienting polygonal parts without sensors. Algorithmica, 10:201--225, 1993.

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K. Goldberg. Orienting polygonal parts without sensors. Algorithmica, 10:201--225, 1993.

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