Assembly partitioning along simple paths: the case of multiple translations

We consider the following problem that arises in mechanical assembly planning: given an assembly, identify a subassembly that can be removed as a rigid object without disturbing the rest of the assembly. This is the assembly partitioning problem. Specifically, we consider planar assemblies of simple polygons and subassembly removal paths consisting of a single finite translation followed by a translation to infinity. Such paths are typical of the capabilities of simple actuators in fixed automation and other high-volume assembly machines. We present a polynomial-time algorithm to identify such a subassembly and removal path or report that none exists. In addition, we extend this algorithm and analysis to removal paths consisting of a small number k > 2 of translations. We discuss extending the algorithm to three dimensions and to other types of motions typical in non-robotic automated assembly.

[1]  Richard A. Volz,et al.  On the automatic generation of plans for mechanical assembly , 1988 .

[2]  D. Halperin,et al.  Assembly partitioning with a constant number of translations , 1994 .

[3]  Leonidas J. Guibas,et al.  Combinatorics and Algorithms of Arrangements , 1993 .

[4]  J. Latombe,et al.  A Simple and E cient Procedure for Polyhedral Assembly Partitioning under In nitesimal Motions , 1995 .

[5]  Leonidas J. Guibas,et al.  Vertical decompositions for triangles in 3-space , 1994, SCG '94.

[6]  Tomás Lozano-Pérez,et al.  Assembly sequencing for arbitrary motions , 1993, [1993] Proceedings IEEE International Conference on Robotics and Automation.

[7]  Rajeev Motwani,et al.  On certificates and lookahead in dynamic graph problems , 1996, SODA 1996.

[8]  Herbert Edelsbrunner,et al.  Algorithms in Combinatorial Geometry , 1987, EATCS Monographs in Theoretical Computer Science.

[9]  Leonidas J. Guibas,et al.  Vertical decompositions for triangles in 3-space , 1994, SCG '94.

[10]  Jean-Claude Latombe,et al.  Geometric Reasoning About Mechanical Assembly , 1994, Artif. Intell..

[11]  Lydia E. Kavraki,et al.  Two-Handed Assembly Sequencing , 1995, Int. J. Robotics Res..

[12]  Gert Vegter,et al.  In handbook of discrete and computational geometry , 1997 .

[13]  Micha Sharir,et al.  Separating two simple polygons by a sequence of translations , 2015, Discret. Comput. Geom..

[14]  Lydia E. Kavraki,et al.  On the Complexity of Assembly Partitioning , 1993, CCCG.

[15]  Micha Sharir,et al.  Davenport-Schinzel sequences and their geometric applications , 1995, Handbook of Computational Geometry.

[16]  Rajeev Motwani,et al.  Graph certificates, lookahead in dynamic graph problems, and assembly planning in robotics , 1994 .

[17]  Lydia E. Kavraki,et al.  Partitioning a Planar Assembly Into Two Connected Parts is NP-Complete , 1995, Inf. Process. Lett..

[18]  Balas K. Natarajan,et al.  On planning assemblies , 1988, SCG '88.

[19]  Godfried T. Toussaint,et al.  Movable Separability of Sets , 1985 .

[20]  Esther M. Arkin,et al.  On monotone paths among obstacles with applications to planning assemblies , 1989, SCG '89.