Guibas, L., Halperin, D., Hirukawa, H., Latombe, J.C., and Wilson, R.H., A Simple and Efficient Procedure for Polyhedral Assembly Partitioning under Infinitesimal Motions, Proc. IEEE Int. Conf. on Robotics and Automation, Nagoya, 2553-2560, 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... presented algorithms to partition assemblies of polyhedra, where the separating motions are either infinite translations or infinitesimal rigid motions (the latter identifying a superset of the removable subassemblies for general separating motions) Infinitesimal rigid motions are also treated in [3]. Snoeyink and Stolfi [12] present an assembly of convex polyhedra that cannot be partitioned. Other related geometric separation problems are studied in [4, 9, 10, 13] In [6, 7, 16] it was shown that the partitioning problem for polygons in the plane is NP complete. Let us remark here that the ....

L.J. Guibas, D. Halperin, H. Hirukawa, J,C, Latombe and R. Wilson, "A Simple and Efficient Procedure for Polyhedral Assembly Partitioning under Infinitesimal Motions", Proc. IEEE Internat. Conf. Robotics and Automation, Nagoya, Japan, 1995, to appear. 10

....but avoids enumerating the entire set of possible subassemblies. This simple approach allows for several extensions (see e.g. 37] but inherently requires that all moving parts perform the same motion. Wilson et al. 72] describe extensions of the basic techniques. Guibas and Halperin et al. [18] consider infinitesimal translations and rotations for partitioning three dimensional sets. Such infinitesimal motions can indicate directions for removing parts in a single step. However, it cannot be guaranteed that the corresponding extended motion will be collision free. Pollack, Sharir and ....

L. Guibas, D. Halperin, H. Hirukawa, J.-C. Latombe, and R.H. Wilson. A simple and efficient procedure for polyhedral assembly partitioning under infinitesimal motions. In Proc. of the IEEE Intl. Conf. on Robotics and Automation, pages 2553--2560. IEEE, 1995.

.... presented algorithms to partition assemblies of polyhedra, where the separating motions are either infinite translations or infinitesimal rigid motions (the latter identifying a superset of the removable subassemblies for general separating motions) Infinitesimal rigid motions are also treated in [3]. Snoeyink and Stolfi [12] present an assembly of convex polyhedra that cannot be partitioned. Other related geometric separation problems are studied in [4, 9, 10, 13] In [6, 7, 16] it was shown that the partitioning problem for polygons in the plane is NP complete. Let us remark here that the ....

L.J. Guibas, D. Halperin, H. Hirukawa, J,C, Latombe and R. Wilson, "A Simple and Efficient Procedure for Polyhedral Assembly Partitioning under Infinitesimal Motions", Proc. IEEE Internat. Conf. Robotics and Automation, Nagoya, Japan, 1995, to appear.

....in its most general form, is NP complete [27, 30, 36, 47] and thus many researchers began considering restricted, yet still interesting, versions of the problem. For many of these restricted settings, polynomial algorithms have been designed which find an assembly sequence if one exists [1, 19, 22, 43, 45]. There are also algorithms which enumerate all possible assembly sequences [12] however there may be exponentially many such sequences for a product. A logical continuation to this success is to use automated reasoning to find the best assembly sequence under certain complexity measures. In ....

L. Guibas, D. Halperin, H. Hirukawa, and J.-C. L. R. Wilson. A simple and efficient procedure for polyhedral assembly partitioning under infinitesimal motions. In Proc IEEE Int. Conf. on Robotics and Automation, pages 2553--2560, 1995.

.... operation generates a final subassembly, and two handed sequences, where every operation merges exactly two subassemblies) For many classes of motions, described by a constant number of degrees of freedom, polynomial algorithms were developed which will find an assembly sequence if one exists [22, 24, 50, 52]. Most of this success can be achieved within the framework of nondirectional blocking graphs [50, 52] and as our work is intricately related to this approach, we review these approaches in more detail in Section 3.1. It is also possible to enumerate all possible assembly sequences [16] although ....

.... from computational geometry allow for the construction of the NDBG for a variety of motion classes, including infinitesimal translations [52] extended translations (i.e. to infinity) 52] multiple step translations [24] and infinitesimal generalized motions (i.e. rigid body motions) [22, 52]. For each of these families of motions, the NDBG framework immediately provides a polynomial time algorithm for constructing a feasible assembly sequence, if one exists. After constructing the set of DBG s, an arbitrary assembly sequence is found by taking any legal separation using any of the ....

L. Guibas, D. Halperin, H. Hirukawa, and J.-C. Latombe R. Wilson. A simple and efficient procedure for polyhedral assembly partitioning under infinitesimal motions. In Proc IEEE Int. Conf. on Robotics and Automation, pages 2553--2560, 1995.

....generates a final subassembly, two handed sequences, where every operation merges exactly two subassemblies. For many classes of motions parameterized by a constant number of degrees of freedom, polynomial algorithms were then developed to find a binary, monotone assembly sequence when one exists [30, 33, 74, 76]. A good deal of this success was achieved within the framework of non directional blocking graphs [32, 74, 76] As our work is intricately related to this approach, in the following section, we will review in greater detail the concept of non directional blocking graphs and the subsequent ....

.... algorithms have been developed and improved for building the ndbg when the motion class allowed includes, infinitesimal translations [76] extended translations (i.e. to infinity) 76] multiple step translations in the plane [33] and infinitesimal generalized motions (i.e. rigid body motions) [30, 76]. As a general rule, it seems that a family of motions with a constant number of degrees of freedom leads to a polynomial number of distinct equivalence classes. A more recent survey presents a unified framework for understanding the collection of work surrounding the non directional blocking ....

[Article contains additional citation context not shown here]

L. Guibas, D. Halperin, H. Hirukawa, and J.-C. Latombe R. Wilson. A simple and efficient procedure for polyhedral assembly partitioning under infinitesimal motions. In Proc IEEE Int. Conf. on Robotics and Automation, pages 2553--2560, 1995.

....in its most general form, is intractable [27,31,32,37,46] and thus many researchers began considering restricted, yet still interesting, versions of the problem. For many of these restricted settings, polynomial algorithms have been designed which find an assembly sequence if one exists [1,19,22,43,45]. There are also algorithms which enumerate all possible assembly sequences [11] however there may be exponentially many such sequences for a product. A logical continuation to this success is to use automated reasoning to find the best assembly sequence under certain complexity measures. In ....

L. Guibas, D. Halperin, H. Hirukawa, and J.-C. L. R. Wilson. A simple and efficient procedure for polyhedral assembly partitioning under infinitesimal motions. In Proc IEEE Int. Conf. on Robotics and Automation, pages 2553--2560, 1995.

....of motions as well, including one step translations with rotations, and n step translations. Work is presently underway on applying this more advanced reasoning to a practical system (and, in fact, a new but related procedure to handle translations with rotations has just recently been developed (Guibas et al. 1995)) Nonetheless, within the context of assembly plans using one step translations, STAAT represents a significant advance in speed and efficiency over previous work. Our motivation for this system is threefold: to build a useful prototype for industry, to find new and useful algorithms in ....

....for single step translations has been implemented, but the theoretical foundation for this structure extends to other classes of motion, as well. As noted earlier, work is presently underway on finding useful algorithms to apply this theory in a practical system, with some promising early results (Guibas et al. 1995). Even within the realm of NDBGs for single step translations, there are two types of NDBGs available: one for infinitesimal translations and one for extended translations. In this paper we shall focus primarily on the infinitesimal version (complemented by sweeping operations for global ....

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Guibas L. J., Halperin, D., Hirukawa, H., Latombe, J.-C., and Wilson, R. H., 1995, "A simple and efficient procedure for polyhedral assembly partitioning under infinitesimal motions", Proceedings, IEEE International Conference on Robotics and Automation, (Nagoya, Japan), (to appear).

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Guibas, L., Halperin, D., Hirukawa, H., Latombe, J.C., and Wilson, R.H., A Simple and Efficient Procedure for Polyhedral Assembly Partitioning under Infinitesimal Motions, Proc. IEEE Int. Conf. on Robotics and Automation, Nagoya, 2553-2560, 1995.

....however, the number of these sequences is exponential in N . Remark: The above presentation has focused on planar assemblies and infinite translations. However, ndbgs have been successfully extended both to deal with 3D assemblies and to generate more complicated motions (e.g. rotational motions [14, 42] and multiple extended translations [17, 43] This requires adapting the definition of a feasible motion of P i relative to P j . Another planning approach, based on monotone paths, has been proposed to avoid the combinatorial trap of generate and test for assemblies of polygons in the plane ....

Guibas, L., Halperin, D., Hirukawa, H., Latombe, J.C., and Wilson, R.H., A Simple and Efficient Procedure for Polyhedral Assembly Partitioning under Infinitesimal Motions, Proc. IEEE Int. Conf. on Robotics and Automation, Nagoya, 2553-2560, 1995.

....hyperplanes, determined by the vertices of the convex hulls of the planar contacts, induces an arrangement of cells of dimensions 0; 1; 5 on S 5 . The dbg is fixed over each such region. From this point on applying the general scheme is fairly straightforward (see [46] for details) In [17] we show that for the purpose of infinitesimal partitioning it is not necessary to build the entire ndbg, and this observation yields big savings in computation time; see also Section 4.3.2 below. 4.2 The Case of Multi Step Motions We present two ways to cope with multi step motions. First, in ....

....j . The key concept of the improvement is that of a maximally covered cell. Informally, a cell is maximally covered if it is covered by (or contained in) more Q regions than any of its immediate neighbors. Being maximally covered implies that the set of dbg arcs of the cell is locally minimal. In [17] we show that it suffices to test the dbgs of maximally covered cells for strong connectivity in order to solve the partitioning problem. Note that if some Q regions touch one another without overlapping, the maximally covered cell may not be full dimensional. The discussion of maximally covered ....

[Article contains additional citation context not shown here]

L. J. Guibas, D. Halperin, H. Hirukawa, J.-C. Latombe, and R. H. Wilson. A simple and efficient procedure for polyhedral assembly partitioning under infinitesimal motions. In Proc. IEEE Intl. Conf. on Robotics and Automation, pages 2553--2560, 1995.

....and rotations or (b) infinite translations. In the infinitesimal case, a subassembly is identified that can move a very small distance, which is only a necessary condition on a removal path. A more efficient and more practical algorithm for partitioning with infinitesimal motions is given in [8]. Wilson et al. 21] extend the framework of [22] to arbitrary removal motions. However, Kavraki and Kolountzakis [12] show that for assemblies of polygons in the plane the problem of partitioning for arbitrary removal motions is NP complete. This paper addresses an intermediate case for ....

L. J. Guibas, D. Halperin, H. Hirukawa, J.-C. Latombe, and R. H. Wilson. A simple and efficient procedure for polyhedral assembly partitioning under infinitesimal motions. In Proc. IEEE Intl. Conf. on Robotics and Automation, pages 2553--2560, 1995.

....the time for ndbgs induced by infinitesimal motions (see Subsection 4.3) We first exemplify the idea for infinitesimal translations in 3 D, and then discuss it in the context of infinitesimal translations and rotations. Full details of this approach as well as experimental results can be found in [16]. Let A be an assembly of polyhedral parts P 1 ; P n , and let Gamma(A) denote the ndbg of A for infinitesimal translations. We represent the motion space as the unit sphere S 2 in 3 . The M region P ij for every ordered pair of polyhedral parts (P i ; P j ) in A is a spherical ....

....the unit sphere S 2 in 3 . The M region P ij for every ordered pair of polyhedral parts (P i ; P j ) in A is a spherical polygon on S 2 , i.e. a region bounded by arcs of great circles (see Subsection 4. 3) For the rest of this section, and to keep our notations compatible with those in [16], we define Q ij as the complement of P ij in M space. Hence, Q ij is the set of all directions such that an infinitesimal translation of P i is possible without overlap with P j . It is convenient to project the arrangement induced by the boundaries of the regions Q ij onto a plane Pi tangent ....

[Article contains additional citation context not shown here]

L. J. Guibas, D. Halperin, H. Hirukawa, J. C. Latombe, and R. H. Wilson. A simple and efficient procedure for polyhedral assembly partitioning under infinitesimal motions. In Proc. IEEE Int. Conf. on Robotics and Automation, pages 2553--2560, 1995. To appear in Int. J. of Computational Geometry and Applications.

.... Computational geometry techniques allow for the construction of the NDBG for a wide range of motion classes, including infinitesimal translations [20] extended translations (i.e. to infinity) 20] multiple step translations [7] and infinitesimal generalized motions (i.e. rigid body motions) [6, 20]. For each of these families of motion, the NDBG framework immediately provides a polynomial time algorithm for constructing an assembly sequence. After constructing the set of DBG s, an arbitrary assembly sequence can be found by taking any legal separation in any direction, and recursing on ....

L. J. Guibas, D. Halperin, H. Hirukawa, and J.-C. Latombe R. H. Wilson. A simple and efficient procedure for polyhedral assembly partitioning under infinitesimal motions. In IEEE Inter. Conf. of Robotics and Automation, pages 2553--2560, 1995.

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L. Guibas, D. Halperin, H. Hirukawa, J.C. Latombe, and R.H. Wilson. A simple and efficient procedure for polyhedral assembly partitioning under infinitesimal motions. In Proc. IEEE Int. Conf. on Rob. and Autom., pages 2553--2560, 1995.

....specify axes of rotation for the motions. For this case, the running time of our algorithm becomes O(m 8=5 ) for any 0. Prior to our work, most of the study of separability problems deals with translational separation; rotations are often handled by resorting to infinitesimal rotations [10, 19]. Garc ia L opez and Ramos Alonzo [9] study true rotational motions, but in a very limited setting: They consider separating a single point from a polygon. Another recent paper dealing with rotations is by Schomer and Thiel [14] Given a stationary polyhedron and a rotating polyhedron, they can ....

L.J. Guibas, D. Halperin, H. Hirukawa, J.-C. Latombe and R.H. Wilson, A simple and efficient procedure for polyhedral assembly partitioning under infinitesimal motions, Proc. IEEE International Conference on Robotics and Automation, 1995, pp. 2553--2560.

.... Computational geometry techniques allow for the construction of the NDBG for a wide range of motion classes, including infinitesimal translations [22] extended translations (i.e. to infinity) 22] multiple step translations [9] and infinitesimal generalized motions (i.e. rigid body motions) [8, 22]. For each of these families of motion, the NDBG framework immediately provides a polynomial time algorithm for constructing an assembly sequence. After constructing the set of DBG s, an arbitrary assembly sequence can be found by taking any legal separation in any direction, and recursing on the ....

L. J. Guibas, D. Halperin, H. Hirukawa, and J.-C. Latombe R. H. Wilson. A simple and efficient procedure for polyhedral assembly partitioning under infinitesimal motions. In Proc IEEE Int. Conf. on Robotics and Automation, pages 2553--2560, 1995.

No context found.

L. Guibas, D. Halperin, H. Hirukawa, J.-C. Latombe, and R.H. Wilson. A simple and efficient procedure for polyhedral assembly partitioning under infinitesimal motions. In Proc. of the IEEE Intl. Conf. on Robotics and Automation, pages 2553--2560, 1995. 9

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