Abstract
This paper presents a thorough discussion of the potential of a new cell-subdivision approach to plan translations of a convex polygon in a cluttered environment, where the focus is on planning simple motions on the basis of a fine-grained description of the workspace. A free path is planned in two main stages. The first stage exploits a plane-sweep paradigm in order to build a cell subdivision holding much relevant topological information on the free space and organizing a set of polygonal chains that approximate the boundaries of the configuration space obstacles. Then, the computations in the second stage are driven by an A* scheme designed to search the cell subdivision. During the search the bounding chains are subject to further refinements, but the cell graph is no longer modified. Among the remarkable features of the proposed technique we can mention: simple interface with the geometric modeler, based on two collision-detection primitives; small number of cells and adjacencies; incremental characterization of the free space. A few numerical results suggest that the new technique should be worth considering for applications, where appropriate; in particular, it seems to perform better than other approaches based on quadtrees. Moreover, it is quite interesting to observe that the cost of finding collision-free paths grows with the number of convex obstacles, whereas it is almost independent of the overall number of sides: we can interpret this result as supporting the choice of representing the obstacles decomposed into convex components. A succinct comparison between algorithmic and human intuitive path planning is also discussed in order to appraise the rate of redundant information processed by the algorithm, but we can also see that human planners behave significantly better only when the solutions are easy to find.
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References
Amézquita Bénitez, M. del C., Gupta, K., and Bhattacharya, B.: 2000, EODM – A novel representation for collision detection, in: Proc. of the IEEE Conf. on Robotics and Automation, San Francisco, CA, pp. 3727–3732.
Aronov, B. and Sharir, M.: 1997, On translationalmotion planning of a convex polyhedron in 3-space, SIAM J. Comput. 26(6), 1785–1803.
Atallah, M. J., Cole, R., and Goodrich, M. T.: 1989, Cascading divide-and-conquer: A technique for designing parallel algorithms, SIAM J. Comput. 18, 499–532.
Barbehenn, M. and Hutchinson, S.: 1995, Efficient search and hierarchical motion planning by dynamically maintaining single-source shortest paths trees, IEEE Trans. Robotics Automat. 11(2), 198–214.
Barbehenn, M. and Hutchinson, S.: 1998, Toward incremental geometric robot motion planning, in: K. Gupta and A. P. del Pobil (eds), Practical Motion Planning in Robotics, Wiley, New York, pp. 133–152.
Bentley, J. L. and Ottmann, T. A.: 1979, Algorithms for reporting and counting geometric intersections, IEEE Trans. Comput. 28, 643–647.
Bonner, S. and Kelley, R. B.: 1990, A novel representation for planning 3-D collision-free paths, IEEE Trans. Systems Man Cybernet. 20(6), 1337–1351.
Cameron, S.: 1990, Collision detection by four-dimensional intersection testing, IEEE Trans. Robotics Automat. 6(3), 291–302.
Cameron, S.: 1998, Dealing with geometric complexity in motion planning, in: K. Gupta and A. P. del Pobil (eds), Practical Motion Planning in Robotics, Wiley, New York, pp. 259–274.
Canny, J.: 1988, The Complexity of Robot Motion Planning, MIT Press, Cambridge.
Canny, J. and Lin, M. C.: 1993, An opportunistic global path planner, Algorithmica 10, 102–120.
Chen, D. Z., Szczerba, R. J., and Uhran, J. J.: 1995, Planning conditional shortest paths through an unknown environment: A framed-quadtree approach, in: Proc. of the IEEE/RSJ Internat. Conf. on Intelligent Robots and Systems, Pittsburgh, PE, pp. 33–38.
Chen, D. Z., Szczerba, R. J., and Uhran, J. J.: 1997, A framed-quadtree approach for determining Euclidean shortest paths in a 2-D environment, IEEE Trans. Robotics Automat. 13(5), 668–681.
Cohen, J. D., Lin, M. C., Manocha, D., and Ponamgi, M. K.: 1995, I-COLLIDE: An interactive and exact collision detection system for large-scale environments, in: Proc. of the ACM Interactive 3D Graphics Conf., pp. 189–196.
Dobkin, D. P. and Kirkpatrick, D. G.: 1990, Determining the separation of preprocessed polyhedra –A unified approach, in: Proc. of the 17th ICALP Internat. Colloq. on Automata Lang. Program., Lecture Notes in Computer. Sciences 443, Springer, New York, pp. 400–413.
Dobkin, D., Hershberger, J., Kirkpatrick, D., and Suri, S.: 1993, Computing the intersection-depth of polyhedra, Algorithmica 9(6), 518–533.
Faverjon, B.: 1984, Obstacle avoidance using an octree in the configuration space of a manipulator, in: Proc. of the IEEE Internat. Conf. on Robotics and Automation, Atlanta, pp. 504–510.
Faverjon, B. and Tournassoud, P.: 1988, Motion planning for manipulators in complex environments, in: J. D. Boissonnat and J. P. Laumond (eds), Geometry and Robotics, Proc. of the Workshop, Toulouse, France, Lecture Notes in Computer Sciences 391, Springer, New York, pp. 87–115.
Fujimura, K. and Samet, H.: 1989, A hierarchical strategy for path planning among moving obstacles, IEEE Trans. Robotics Automat. 5(1), 61–69.
Gilbert, E. G. and Foo, C. P.: 1990, Computing the distance between general convex objects in three-dimensional space, IEEE Trans. Robotics Automat. 6(1), 53–61.
Guibas, L. J., Sharir, M., and Sifrony, S.: 1989, On the general motion planning problem with two degrees of freedom, Discrete Comput. Geom. 4, 491–521.
Gupta, K.: 1998, Practical motion planning: An overview and state of the art, in: K. Gupta and A. P. del Pobil (eds), Practical Motion Planning in Robotics, Wiley, New York, pp. 3–8.
Jiménez, P. and Torras, C.: 1999, Benefits of applicability constraints in decomposition-free interference detection between nonconvex polyhedral models, in: Proc. of the IEEE Internat. Conf. on Robotics and Automation, Detroit, pp. 1856–1862.
Johnson, D. E. and Cohen, E.: 1999, Bound coherence for minimum distance computations, in: Proc. of the IEEE Internat. Conf. on Robotics and Automat., Detroit, pp. 1843–1848.
Jung, D. and Gupta, K.: 1996, Octree-based hierarchical distance maps for collision detection, in: Proc. of the IEEE Conf. on Robotics and Automation, Minneapolis, MI, pp. 454–459.
Kim, Y. J., Lin, M. C., and Manocha, D.: 2002, DEEP: Dual-space expansion for estimating penetration depth between convex polytopes, in: Proc. of the IEEE Internat. Conf. on Robotics and Automation, Washington, DC, pp. 921–926.
Kitamura, Y., Tanaka, T., Kishino, F., and Yachida, M.: 1995, 3-D path planning in a dynamic environment using an octree and an artificial potential field, in: Proc. of the IEEE/RSJ Internat. Conf. on Intelligent Robots and Systems, Pittsburgh, PE, pp. 33–38.
Larsen, E., Gottschalk, S., Lin,M. C., and Manocha, D.: 2000, Fast distance queries with rectangular swept volumes, in: Proc. of the IEEE Internat. Conf. on Robotics and Automation, San Francisco, pp. 3719–3726.
Latombe, J.-C.: 1991, Robot Motion Planning, Kluwer Academic Publishers, Boston.
Leven, D. and Sharir, M.: 1987, Planning a purely translational motion for a convex object in two-dimensional space using generalized Voronoi diagrams, Discrete Comput. Geom. 2, 9–31.
Lin, M. C., Manocha, D., and Canny, J.: 1994, Fast contact determination in dynamic environments, in: Proc. of the IEEE Internat. Conf. on Robotics and Automation, San Diego, pp. 602–608.
Lin, M. C. and Gottschalk, S.: 1998, Collision detection between geometric models: A survey, in: Proc. of the IMA Conf. on Mathematics of Surfaces.
Lozano-Pérez, T.: 1983, Spatial planning: A configuration space approach, IEEE Trans. Comput. 32(2), 108–120.
Lumelsky, V. J.: 1987, Effect of kinematics on motion planning for planar robot arms moving amidst unknown obstacles, IEEE J. Robotics Automat. 3(3), 207–223.
Martínez-Salvador, B., del Pobil, A. P., and Pérez-Francisco, M.: 1998, Very fast collision detection for practical motion planning. Part I: the spatial representation, in: Proc. of the IEEE Internat. Conf. on Robotics and Automation, Leuven, Belgium, pp. 624–629.
Mirolo, C.: 1998, Convex minimization on a grid and applications, J. Algorithms 26(2), 209–237.
Mirolo, C. and Pagello, E.: 1989, A solid modeling system for robot action planning, IEEE Computer Graphics Appl. 9(1), 55–69.
Mirolo, C. and Pagello, E.: 1995, A cell decomposition approach to motion planning based on collision detection, in: Proc. of ICAR'95, Sant Feliu de Guixols, Spain, pp. 481–488.
Mirolo, C. and Pagello, E.: 1997, A practical motion planning strategy based on a plane-sweep approach, in: Proc. of the IEEE Internat. Conf. on Robotics and Automation, Albuquerque, pp. 2705–2712.
Mirolo, C. and Pagello, E.: 2000a, Geometric modeling for robot task planning, in: G. W. Zobrist and C. Y. Ho (eds), Intelligent Systems and Robotics, Gordon and Breach, London, pp. 230–277.
Mirolo, C. and Pagello, E.: 2000b, Fast convex minimization to detect collisions between polyhedra, in: Proc. of the IEEE-RSJ Internat. Conf. on Intelligent Robot Systems, IROS 2000, Takamatsu, November, pp. 1605–1610.
Mirolo, C. and Pagello, E.: 2001, Flexible exploitation of space coherence to detect collisions of convex polyhedra, in: Proc. of the IEEE Internat. Conf. on Robotics and Automation, ICRA 2001, Seoul, May, pp. 3783–3788.
Mirolo, C., Pagello, E., and Qian, W. H.: 1995, Simplified motion planning strategies in flexible manufacturing, in: Proc. of IEEE ISATP'95, Pittsburgh, PE, pp. 394–399.
Mulmuley, K.: 1993, Computational Geometry: An Introduction through Randomized Algorithms, Prentice-Hall, Englewood Cliffs, NJ.
Nilsson, N. J.: 1980, Principles of Artificial Intelligence, Tioga Publ., Palo Alto, CA.
Nussbaum, D. and Sack, J. R.: 1993, Disassembling two-dimensional composite parts via translations, Internat. J. Comput. Geom. Appl. 3(1), 71–84
Pérez-Francisco, M., del Pobil, A. P., and Martínez-Salvador, B.: 1998, Very fast collision detection for practical motion planning. Part II: The parallel algorithm, in: Proc. of the IEEE Internat. Conf. on Robotics and Automation, Leuven, Belgium, pp. 644–649.
Rao, N. S. V.: 1995, On fast planning of suboptimal paths amidst polygonal obstacles in plane, Theoret. Comput. Sci. 140(2), 265–289.
Redon, S., Kheddar, A., and Coquillart, S.: 2000, An algebraic solution to the problem of collision detection for rigid polyhedra objects, in: Proc. of the IEEE Internat. Conf. on Robotics and Automation, San Francisco, pp. 3733–3738.
Reif, J. H.: 1979, Complexity of the mover's problem and generalizations, in: Proc. 20th Annual IEEE Sympos. Found. Comput. Sci., pp. 421–427.
Samet, H.: 1990a, Applications of Spatial Data Structures: Computer Graphics, Image Processing, and GIS, Addison-Wesley, Reading, MA.
Samet, H.: 1990b, The Design and Analysis of Spatial Data Structures, Addison-Wesley, Reading, MA.
Seidel, R.: 1991, A simple and fast incremental randomized algorithm for computing trapezoidal decompositions and for triangulating polygons, Comput. Geom. Theory Appl. 1, 51–64.
Sridharan, K. and Stephanou, H. E.: 1994, Algorithms for rapid computation of some distance functions between objects for path planning, in: Proc. of the IEEE Internat. Conf. on Robotics and Automation, San Diego, pp. 967–972.
Staffetti, E., Ros, L., and Thomas, F.: 1999, A simple characterization of the infinitesimal motions separating general polyhedra in contact, in: Proc. of the IEEE Internat. Conf. on Robotics and Automation, Detroit, pp. 571–577.
Szczerba, R. J., Chen, D. Z., and Uhran, J. J.: 1998, Planning shortest paths among 2D and 3D weighted regions using framed-subspaces, Internat. J. Robotics Res. 17(5), 531–546.
Thomas, F., Turnbull, C., Ros, L., and Cameron, S.: 2000, Computing signed distances between free-form objects, in: Proc. of the IEEE Internat. Conf. on Robotics and Automation, San Francisco, pp. 3713–3718.
Van der Stappen, A. F., Halperin, D., and Overmars, M. H.: 1993, The complexity of the free space for a robot moving amidst fat obstacles, Comput. Geom. Theory Appl. 3(6), 353–373.
Van der Stappen, A. F., Overmars, M. H., de Berg, M., and Vleugels, J.: 1998, Motion planning in environments with low obstacle density, Discrete Comput. Geom. 20(4), 561–587.
Zelinsky, A.: 1992, A mobile robot exploration algorithm, IEEE Trans. Robotics Automat. 8(6), 707–717.
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Mirolo, C., Pagello, E. A New Cell-subdivision Approach to Plan Free Translations in Cluttered Environments. Journal of Intelligent and Robotic Systems 38, 5–30 (2003). https://doi.org/10.1023/A:1026231624387
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DOI: https://doi.org/10.1023/A:1026231624387