R.H. Wilson and T. Matsui, Partitioning an assembly for infinitesimal motions in translation and rotation, Proc. IEEE International Conference on Intelligent Robots and Systems, 1992, pp. 1311--1318. 8  Home/Search   Document Not in Database   Summary   Related Articles   Check

....7 illustrates three of the twelve bodies that are generated by the group action of A 4 . Stationary contact points on moving faces will rule out certain isometries; we determine which ones using an analysis technique that is common to closure grasps [11, 14] and assembly sequence planning [10, 17] in robotics. Any infinitesimal rigid motion can be expressed as translational force and a rotational torque applied to the origin and can be represented as a force torque vector with six coordinates. If we apply a force at a point p, pushing into a face with normal n, then the force and torque ....

....Within each cell one can define a unique blocking graph, with a directed edge from object A to B if contact with A prevents B from moving according to force torque vectors in the cell. No subset can move infinitesimally iff all blocking graphs are strongly connected. See Wilson and Matsui [17] for more detail. In our case, however, the 150 hyperplanes form an arrangement with 2 34 cells, and further reductions require tricky programming. 7 Conclusion The constructions in this paper are further evidence, if any were needed, that favorite techniques and tools of computational ....

R. H. Wilson and T. Matsui. Partitioning an assembly for infinitesimal motions in translation and rotation. In IEEE International Conference on Intellegent Robots and Systems, pages 1311--1318, 1992. 17

....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 ....

R. H. Wilson and T. Matsui, Partitioning an assembly for infinitesimal motions in translation and rotation, Proceedings of the IEEE International Conference on Intelligent Robots and Systems (1992), pp. 1311--1318.

....available paths and the fact that the environment may not be as cluttered to allow only a smaller number of paths to exist. A similarity exists between what assembly planning offers and what maintainability expects. Research in assembly planning has produced useful results (e.g. Wilson92a] [Wilson92b ], and [Lozano93] A close examination reveals, however, significant differences: In assembly planning, focuses are to capture the (de)assembly sequencing information Figure 1. Search resolution in C space. The circled configurations are attainable at the grid resolution. The triangle ones are ....

Wilson, R. and Matsui, T. "Partitioning an Assembly for Infinitesimal Motions in Translation and Rotation, " Proc. IEEE Int'l Conf. on Intelligent Robotics and Systems, 1992.

....only infinitesimally, there is still more checking to be done in order to produce a full disassembly step, if one exists. In spite of its limitations, infinitesimal motion is attractive in assembly planning because its analysis translates to handling linear constraints, even when allowing rotation [16]. Fore more information on assembly planning see, e.g. 6] 15] In 1988, in his paper On Planning Assemblies [11] Natarajan conjectured that two hands suffice to assemble any composite comprised of convex polyhedra in 3 space . In a surprising result, Snoeyink and Stolfi [13] have recently ....

.... that the work by Snoeyink and Stolfi continues a long line of research, whose objective was to construct composites that are interlocked under various types of motions (see, e.g. 3] 4] 11] An efficient procedure for the infinitesimal partitioning problem was proposed by Wilson and Matsui [16] who devised a polynomial time algorithm to solve this problem. Their solution is based on the nondirectional blocking graph (NDBG) concept [14] see also Section 2 below. In this paper we take a similar approach to that of Wilson and Matsui, but we derive a considerably more efficient ....

[Article contains additional citation context not shown here]

R.H. Wilson and T. Matsui, Partitioning an assembly for infinitesimal motions in translation and rotation, Proc. IEEE International Conference on Intelligent Robots and Systems, 1992, pp. 1311--1318. 8

.... face F i of P i and a face F j of P j intersect at a piece of planar surface (plane plane contact) The set of motions dX allowed by this contact is the intersection of all the closed half spaces n F j J V k dX 0 computed for the vertices V k of the convex hull of the intersection of F i and F j [18, 49]. For example, in Fig. 6, the vertices V k are circled. We make the same simplifying assumptions about contacts as in Subsection 5.1. For each vertex V k of the convex hull of the intersection of two parts, the equation n F J V k dX = 0 defines a 5D hyperplane in the 6D space of infinitesimal ....

Wilson, R.H. and Matsui, T. 1992. Partitioning an Assembly for Infinitesimal Motions in Translation and Rotation. IEEE Int. Conf. on Intelligent Robots and Systems, Raleigh, NC, 1311--1318.

.... that a face F i of P i and a face F j of P j intersect in a piece of planar surface (see Figure 3) The set of motions dX allowed by this contact is the intersection of all the closed half spaces nF j JV k dX 0 computed for the vertices Vk of the convex hull of the intersection of F i and F j [20, 46]. For each vertex Vk of the convex hull of the intersection of two parts, the equation nF JV k dX = 0 defines a 5 D hyperplane in the 6 D space of infinitesimal motions, which partitions S 5 into two open half spheres and a great circle. The set of all such hyperplanes, determined by the ....

....The set of all such 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 ....

[Article contains additional citation context not shown here]

R. H. Wilson and T. Matsui. Partitioning an assembly for infinitesimal motions in translation and rotation. In Proc. Intl. Conf. on Intelligent Robots and Systems, pages 1311--1318, 1992.

.... F i of P i and a face F j of P j intersect at a piece of planar surface (plane plane contact) The set of motions dX allowed by this contact is the intersection of all the closed half spaces n F j J V k dX 0 computed for the vertices V k of the convex hull of the intersection of F i and F j [19, 44]. For example, in Figure 4, the vertices V k are circled. For each vertex V k of the convex hull of the intersection of two parts, the equation n F J V k dX = 0 defines a 5 D hyperplane in the 6 D space of infinitesimal motions, which partitions S 5 into two open half spheres and a great ....

....k) where k denotes (as in Subsection 4.3) the number of equivalent point plane contacts in the assembly. For infinitesimal motions in 3 D, the dimension of the motion space is 5. The maximally covered cells approach leads to significant savings over the best previously known algorithm [44] to solve this partitioning problem. In addition, the algorithm is based on linear programming techniques and hence simpler to implement robustly than the arrangement computations required by most ndbgs. In particular, we have implemented an algorithm based on this approach and have been able to ....

R. H. Wilson and T. Matsui. Partitioning an assembly for infinitesimal motions in translation and rotation. In Proc. Intl. Conf. on Intelligent Robots and Systems, pages 1311--1318, 1992.

....thus there is still more checking to be done in order to produce such a motion, if one exists. In spite of this shortcoming, infinitesimal motions are attractive in assembly planning because their analysis translates to handling linear constraints, even when allowing rotation (see, e.g. 5] 9] [17]) Fore more information on assembly planning see, e.g. 6] 16] 18] In 1988, in his paper On Planning Assemblies [12] Natarajan conjectured that two hands suffice to assemble any composite comprised of convex polyhedra in 3 space . In a surprising result, Snoeyink and Stolfi [14] have ....

.... that the work by Snoeyink and Stolfi continues a long line of research, whose objective was to construct composites that are interlocked under various types of motions (see, e.g. 3] 4] 12] An efficient procedure for the infinitesimal partitioning problem was proposed by Wilson and Matsui [17] who devised a polynomial time algorithm to solve this problem. Their solution is based on the nondirectional blocking graph (NDBG) concept [15] See Section 2 below. In this paper we take a similar approach to that of Wilson and Matsui, but we derive a considerably more efficient algorithm. Our ....

[Article contains additional citation context not shown here]

R.H. Wilson and T. Matsui, Partitioning an assembly for infinitesimal motions in translation and rotation, Proc. IEEE International Conference on Intelligent Robots and Systems, 1992, pp. 1311--1318.

.... the constraints[7] The authors also investigated the motion of polyhedra in contact in the tangent space of the moving polyhedron and developed an algorithm for determining their possible velocity and applicable force from their geometric models[8] The result was applied to mechanical assembly[9]. Considering the above results, we can summarize the open problems in the motion planning of polyhedra in contact as follows. We don t have an algorithm to de1 termine a sequence of the topological contact states, each of which is defined by the combination of the features of the polyhedra in ....

R.H.Wilson and T.Matsui, "Partitioning an assembly for infinitesimal motions in translation and rotation", IEEE Int. Conf. Intel. Robot and Systems, 1311/1318, 1992.

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Wilson, R. H. and Matsui, T. "Partitioning an Assembly for Infinitesimal Motions in Translation and Rotation". Proceedings of the 1992 IEEE International Conference on Intelligent Robots and Systems. Vol. 2, pages 1311-1318, Raleigh, NC, July 1992.

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Wilson, R.H. and Matsui, T. Partitioning an Assembly for Infinitesimal Motions in Translation and Rotation. Proc. of the 1992 IEEE Int. Conf. on Intelligent Robots and Systems. Raleigh, NC, July 1992.

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