Toggle PRM: A Coordinated Mapping of C-Free and C-Obstacle in Arbitrary Dimension

Abstract Motion planning has received much attention over the past 40 years. More than 15 years have passed since the introduction of the successful sampling-based approach known as the Probabilistic RoadMap Method (PRM). PRM and its many variants have demonstrated great success for some high-dimensional problems, but they all have some level of difficulty in the presence of narrow passages. Recently, an approach called Toggle PRM has been introduced whose performance does not degrade for 2-dimensional problems with narrow passages. In Toggle PRM, a si-multaneous, coordinated mapping of both C f ree and Cobst is performed and every connection attempt augments one of the maps – either validating an edge in the cur-rent space or adding a configuration ’witnessing ’ the connection failure to the other space. In this paper, we generalize Toggle PRM to d-dimensions and show that the benefits of mapping both C f ree and Cobst continue to hold in higher dimensions. In particular, we introduce a new narrow passage characterization, α-ε-separable nar-row passages, which describes the types of passages that can be successfully mapped by Toggle PRM. Intuitively, α-ε-separable narrow passages are arbitrarily narrow regions of C f ree that separate regions of Cobst, at least locally, such as hallways in an office building. We experimentally compare Toggle PRM with other methods in a variety of scenarios with different types of narrow passages and robots with up to 16 DOF.

Motion Planning via Manifold Samples

We present a general and modular algorithmic framework for path planning of robots. Our framework combines geometric methods for exact and complete analysis of low-dimensional configuration spaces, together with practical, considerably simpler sampling-based approaches that are appropriate for higher dimensions. In order to facilitate the transfer of advanced geometric algorithms into practical use, we suggest taking samples that are entire low-dimensional manifolds of the configuration space that capture the connectivity of the configuration space much better than isolated point samples. Geometric algorithms for analysis of low-dimensional manifolds then provide powerful primitive operations. The modular design of the framework enables independent optimization of each modular component. Indeed, we have developed, implemented and optimized a primitive operation for complete and exact combinatorial analysis of a certain set of manifolds, using arrangements of curves of rational functions and concepts of generic programming. This in turn enabled us to implement our framework for the concrete case of a polygonal robot translating and rotating amidst polygonal obstacles. We demonstrate that the integration of several carefully engineered components leads to significant speedup over the popular PRM sampling-based algorithm, which represents the more simplistic approach that is prevalent in practice. We foresee possible extensions of our framework to solving high-dimensional problems beyond motion planning.Comment: 18 page

Observation Of Very High Energy Cosmic-ray Families In Emulsion Chambers At High Mountain Altitudes (i)

Characteristics of cosmic-ray hadronic interactions in the 1015 - 1017 eV range are studied by observing a total of 429 cosmic-ray families of visible energy greater than 100 TeV found in emulsion chamber experiments at high mountain altitudes, Chacaltaya (5200 m above sea level) and the Pamirs (4300 m above sea level). Extensive comparisons were made with simulated families based on models so far proposed, concentrating on the relation between the observed family flux and the behaviour of high-energy showers in the families, hadronic and electromagnetic components. It is concluded that there must be global change in characteristics of hadronic interactions at around 1016 eV deviating from thise known in the accelerator energy range, specially in the forwardmost angular region of the collision. A detailed study of a new shower phenomenon of small-pT particle emissions, pT being of the order of 10 MeV/c, is carried out and its relation to the origin of huge "halo" phenomena associated with extremely high energy families is discussed as one of the possibilities. General characteristics of such super-families are surveyed. © 1992.3702365431Borisov, (1981) Nucl. Phys., 191 BBaybrina, (1984) Trudy FIAN 154, p. 1. , [in Russian], Nauka, MoscowLattes, Hadronic interactions of high energy cosmic-ray observed by emulsion chambers (1980) Physics Reports, 65, p. 151Hasegawa, ICR-Report-151-87-5 (1987) presented at FNAL CDF Seminar, , Inst. for Cosmic Ray Research, Univ. of TokyoCHACALTAYA Emulsion Chamber Experiment (1971) Progress of Theoretical Physics Supplement, 47, p. 1Yamashita, Ohsawa, Chinellato, (1984) Proc. 3rd Int. Symp. on Cosmic Rays and Particle Physics, p. 30. , Tokyo, 1984, Inst. for Cosmic Ray Research, Univ. of Tokyo(1984) Proc. 3rd Int. Symp. on Cosmic Rays and Particle Physics, p. 1. , Tokyo, 1984Baradzei, (1984) Proc. 3rd Int. Symp. on Cosmic Rays and Particle Physics, p. 136. , Tokyo, 1984Yamashita, (1985) J. Phys. Soc. Jpn., 54, p. 529Bolisov, (1984) Proc. 3rd Int. Symp. on Cosmic rays and Particle Physics, p. 248. , Tokyo, 1984, Inst. for Cosmic Ray Research, Univ. of TokyoTamada, Tomaszewski, (1988) Proc. 5th Int. Symp. on Very High Energy Cosmic-Ray Interactions, p. 324. , Lodz, 1988, Inst. for Cosmic Ray Research, Univ. of Tokyo, PolandHasegawa, (1989) ICR-Report-197-89-14, , Inst. for Cosmic Ray Research, Univ. of TokyoCHACALTAYA Emulsion Chamber Experiment (1971) Progress of Theoretical Physics Supplement, 47, p. 1Okamoto, Shibata, (1987) Nucl. Instrum. Methods, 257 A, p. 155Zhdanov, (1980) FIAN preprint no. 45, , Lebedev Physical Institute, MoscowSemba, Gross Features of Nuclear Interactions around 1015eV through Observation of Gamma Ray Families (1983) Progress of Theoretical Physics Supplement, 76, p. 111Nikolsky, (1975) Izv. Akad. Nauk. USSR Ser. Fis., 39, p. 1160Burner, Energy spectra of cosmic rays above 1 TeV per nucleon (1990) The Astrophysical Journal, 349, p. 25Takahashi, (1990) 6th Int. Symp. on Very High Energy Cosmic-ray Interactions, , Tarbes, FranceRen, (1988) Phys. Rev., 38 D, p. 1404Alner, The UA5 high energy simulation program (1987) Nuclear Physics B, 291 B, p. 445Bozzo, Measurement of the proton-antiproton total and elastic cross sections at the CERN SPS collider (1984) Physics Letters B, 147 B, p. 392Wrotniak, (1985) Proc. 19th Cosmic-Ray Conf. La Jolla, 1985, 6, p. 56. , NASA Conference Publication, Washington, D.CWrotniak, (1985) Proc. 19th Cosmic-Ray Conf. La Jolla, 1985, 6, p. 328. , NASA Conference Publication, Washington, D.CMukhamedshin, (1984) Trudy FIAN, 154, p. 142. , Nauka, Moscow, [in Russian]Dunaevsky, Pluta, Slavatinsky, (1988) Proc. 5th Int. Symp. on Very High Energy Cosmic-Ray Interactions, p. 143. , Lodz, 1988, Inst. of Physics, Univ. of Lodz, PolandKaidalov, Ter-Martirosyan, (1987) Proc. 20th Int. Cosmic-Ray Conf., Moscow, 1987, 5, p. 141. , Nauka, MoscowShabelsky, (1985) preprints LNPI-1113Shabelsky, (1986) preprints LNPI-1224, , Leningrad [in Russian]Hillas, (1979) Proc. 16th Int. Cosmic-Ray Conf., Kyoto, 6, p. 13. , Inst. for Cosmic Ray Research, Univ. of TokyoBorisov, (1987) Phys. Lett., 190 B, p. 226Hasegawa, Tamada, (1990) 6th Int. Symp. on Very High Energy Cosmic-Ray Interactions, , Tarbes, FranceSemba, Gross Features of Nuclear Interactions around 1015eV through Observation of Gamma Ray Families (1983) Progress of Theoretical Physics Supplement, p. 111Ren, (1988) Phys. Rev., 38 D, p. 1404Dynaevsky, Zimin, (1988) Proc. 5th Int. Symp. on Very High Energy Cosmic-Ray Interaction, p. 93. , Lodz, 1988, Inst. of Physics, Univ. of Lodz, PolandDynaevsky, (1990) Proc. 6th Int. Symp. on Very High Energy Cosmic-Ray Interactions, , Tarbes, France(1989) FIAN preprint no. 208, , Lebedev Physical Institute, Moscow(1990) Proc. 21st Int. Cosmic-Ray Conf., Adelaide, 8, p. 259. , Dept. Physics and Mathematical Physics, Univ. of Adelaide, AustraliaHasegawa, (1990) ICR-Report-216-90-9, , Inst. for Cosmic-Ray Research, Univ. of TokyoTamada, (1990) Proc. 21st Int. Cosmic-Ray Conf., Adelaide, 1990, 8. , Dept. Physics and Mathematical Physics, Univ. of Adelaide, AustraliaTamada, (1990) ICR-Report-216-90-9(1981) Proc. 17th Int. Cosmic-Ray Conf., Paris, 5, p. 291(1990) Proc. Int. Cosmic-Ray Conf., Adelaide, 1990, 8, p. 267. , Dept. Physics and Mathematical Physics, Univ. of Adelaide, Australia(1989) Inst. Nucl. Phys. 89-67/144, , preprint, Inst. Nucl. Phys., Moscow State UnivSmilnova, (1988) Proc. 5th Int. Sym. on Very High Energy Cosmic-Ray Interactions, p. 42. , Lodz, 1988, Inst. of Physics, Univ. of Lodz, PolandGoulianos, (1986) Proc. Workshop of Particle Simulation at High Energies, , University of Wisconsin, Madison, USAIvanenko, (1983) Proc. 18th Int. Cosmic-Ray Conf., Bangalore, 1983, 5, p. 274. , Tata Inst. Fundamental Research, Bombay, IndiaIvanenko, (1984) Proc. Int. Symp. on Cosmic-Rays and Particle Physics, p. 101. , Tokyo, 1984, Inst. for Cosmic Ray Research, Univ. of Tokyo(1988) 5th Int. Symp. on Very High Energy Cosmic-Ray Interactions, p. 180. , Lodz, 1988, Inst. of Physics, Univ. of Lodz, Poland(1990) Proc. 21st Int. Cosmic-Ray Conf., Adelaide, 1990, 8, p. 251. , Dept. Physics and Mathematical Physics, Univ. of Adelaide, Australia(1991) Izv. AN USSR No. 4, , to be publishedNikolsky, Shaulov, Cherdyntseva, (1990) FIAN preprint no. 140, , Lebedev Physical Institute, Moscow, [in Russian](1987) Proc. 20th Int. Cosmic-Ray Conf., Moscow, 1987, 5, p. 326. , Nauka, Mosco

Observation Of A High-energy Cosmic-ray Family Caused By A Centauro-type Nuclear Interaction In The Joint Emulsion Chamber Experiment At The Pamirs

An exotic cosmic-ray family event is observed in the large emulsion chamber exposed by the joint at the Pamirs (4360 m above sea level). The family is composed of 120γ-ray-induced showers and 37 hadron-induced showers with individual visible energy exceeding 1 TeV. The decisive feature of the event is the hadron dominance: ΣEγ, ΣE(γ) h, 〈Eγ, 〈E(γ) h〉, 〈Eγ·Rγ〉 and 〈E(γ)·Rh〉 being 298 TeV, 476 TeV, 2.5 TeV, 12.9 TeV, 28.6 GeV m and 173 GeV m, respectively. Most probably the event is due to a Centauro interaction, which occured in the atmosphere at ∼700 m above the chamber. The event will constitute the second beautiful candidate for a Centauro observed at the Pamirs. © 1987.1901-2226233Bayburina, (1981) Nucl. Phys. B, 191, p. 1Lattes, Fujimoto, Hasegawa, Hadronic interactions of high energy cosmic-ray observed by emulsion chambers (1980) Physics Reports, 65, p. 151(1984) Trudy FIAN, 154, p. 1Borisov, (1984) Proc. Intern. Symp. on Cosmic rays and particle physics, p. 3. , TokyoRen, (1985) 19th Intern. Cosmic ray Conf., 6, p. 317. , La JollaYamashita, (1985) 19th Intern. Cosmic ray Conf., 6, p. 364. , La JollaTamada, (1977) Nuovo Cimento, 41 B, p. 245T. Shibata et al., to be publishedHillas, (1979) 16th Intern. Cosmic ray Conf., 6, p. 13. , KyotoBattiston, Measurement of the proton-antiproton elastic and total cross section at a centre-of-mass energy of 540 GeV (1982) Physics Letters B, 117, p. 126UA5 Collab., G.J. Alner et al., preprint CERN-EP/85-62Taylor, (1976) Phys. Rev. D, 14, p. 1217Burnett, (1984) Proc. Intern. Symp. on Cosmic rays and particle physics, p. 468. , Toky

Nuclear Interactions Of Super High Energy Cosmic-rays Observed In Mountain Emulsion Chambers

Here we present a summary of joint discussions on the results of three mountain experiments with large-scale emulsion chambers, at Pamir, Mt. Fuji and Chacaltaya. Observations cover gamma quanta, hadrons and their clusters (called "families"). The following topics are covered, concerning the characteristics of nuclear interactions the energy region 1014-1016 eV: (i) rapid dissipation seen in atmospheric diffusion of high-energy cosmic-rays; (ii) multiplicity and Pt increase in produced pi-mesons in the fragmentation region; (iii) existence of large-Pt jets, (iv) extremely hadron-rich family of the Centauro type; (v) exotic phenomena in the extremely high energy region beyond 1016 eV. © 1981.1911125(1977) Acta Univ. Lodz ser. II, (60)(1973) 13th Int. Cosmic-ray Conf., 3, p. 2228(1975) 14th Int. Cosmic-Ray Conf., 7, p. 2365(1979) AIP Conf. Proc. no. 49, p. 334(1979) 16th Int. Cosmic-ray Conf., 6, p. 344(1979) 16th Int. Cosmic-ray Conf., 7, p. 6816th Int. Cosmic-ray Conf. (1979) 16th Int. Cosmic-ray Conf., 7, p. 284(1979) 16th Int. Cosmic-ray Conf., 7, p. 294(1979) 16th Int. Cosmic-ray Conf., 13, p. 87(1979) 16th Int. Cosmic-ray Conf., 13, p. 92(1979) 16th Int. Cosmic-ray Conf., 13, p. 98(1979) AIP Conf. Proc. no. 49, p. 94(1979) AIP Conf. Proc. no. 49, p. 145(1979) AIP Conf. Proc. no. 49, p. 317(1979) 16th Int. Cosmic-ray Conf., 6, p. 350(1979) 16th Int. Cosmic-ray Conf., 6, p. 356(1979) 16th Int. Cosmic-ray Conf., 6, p. 362Nikolsky, Proc. 9th Int. High-energy Symp. (1978) CSSR, 21. , ToborMiyake, (1978) Proc. 19th Int. Conf. on High-energy physics, p. 433Vernov, (1977) Physica, 3, p. 1601Khristiansen, (1978) JETP Lett., 28, p. 124(1973) 13th Int. Cosmic-ray Conf., 3, p. 2219Izv. Acad. Nauk USSR, ser Phys. (1974) Izv. Acad. Nauk USSR, ser Phys., 38, p. 918(1975) 14th Int. Cosmic-ray Conf., 7, p. 2365(1979) 16th Int. Cosmic-ray Conf., 7, p. 68Dunaevsky, Urysson, Emelyanov, Shorin, Tashimov, (1975) FIAN preprint no. 150Dunaevsky, Urysson, Emelyanov, Shorin, Tashinov, (1979) Acta Univ. Lodz ser. II, (60), p. 199Ivanenko, Kanevskya, Roganova, (1978) JETP Lett., 40, p. 704Ivanenko, Kanevsky, Roganova, (1979) 16th Int. Cosmic-ray Conf., 7, p. 101Ivanenko, Kanevsky, Roganova, (1979) 16th Int. Cosmic-ray Conf., 7, p. 198Wrotniak, (1977) Acta Univ. Lodz ser. II, (60), p. 165Krys, Tomaszevski, Wrotniak, (1979) 16th Int. Cosmic-ray Conf., 7, p. 182Krys, Tomaszevski, Wrotniak, (1979) 16th Int. Cosmic-ray Conf., 7, p. 186Fomin, Kempa, Khristiansen, Levina, Piotrowska, Wdowczyk, (1977) 15th Int. Cosmic-ray Conf., 7, p. 248Fomin, Kempa, Khristiansen, Levina, Piotrowska, Wdowczyk, (1979) 16th Int. Cosmic-ray Conf., 13, p. 82Azimov, Mullazhanov, Yuldashbayev, (1979) 16th Int. Cosmic-ray Conf., 7, p. 262Azimov, Mullazhanov, Yuldashbayev, (1977) Acta Univ. Lodz ser. II, (60), p. 275Kasahara, Torri, Yuda, (1979) 16th Int. Cosmic-ray Conf., 13, p. 70Kasahara, Torii, Yuda, (1979) 16th Int. Cosmic-ray Conf., 13, p. 79Shibata, (1979) 16th Int. Cosmic-ray Conf., 7, p. 176H. Semba, T. Shibata and T. Tabuki, Suppl. Prog. Theor. Phys., to be publishedZhdanov, Roinishvilli, Smorodin, Tomaszevski, (1975) FIAN preprint no. 163Lattes, Fujimoto, Hasegawa, Hadronic interactions of high energy cosmic-ray observed by emulsion chambers (1980) Physics Reports, 65, p. 152Ellsworth, Gaisser, Yodh, (1981) Phys. Rev., 23 D, p. 764Baradzei, Smorodin, (1974) FIAN preprint nos. 103, 104Baradzei, Smorodin, (1977) Acta Univ. Lodz ser. II, (60), p. 51Zhdanov, (1980) FIAN preprint no. 140H. Semba, T. Shibata and T. Tabuki, Suppl. Prog. Theor. Phys., to be publishedShibata, (1980) Phys. Rev., 22 D, p. 100Slavatinsky, (1980) Proc. 7th European Symp. on Cosmic rays, , Leningrad, to be published(1979) AIP Conference Proc. no. 49, p. 145Azimov, Abduzhamilov, Chudakov, (1963) JETP (Sov. Phys.), 45, p. 40713th Int. Cosmic-ray Conf. (1973) 13th Int. Cosmic-ray Conf., 5, p. 326Acharya, Rao, Sivaprasad, Rao, (1979) 16th Int. Cosmic-ray Conf., 6, p. 289Ellsworth, Goodman, Yodh, Gaisser, Stanev, (1981) Phys. Rev., 23 D, p. 771Bariburina, Guseva, Denisova, (1980) Acta Univ. Lodz, 1, p. 9415th Int. Cosmic-ray Conf. (1977) 15th Int. Cosmic-ray Conf., 7, p. 184(1979) AIP Conf. Proc. no. 49, p. 33

Track A Basic Science

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/138319/1/jia218438.pd

Efficient multi-robot motion planning for unlabeled discs in simple polygons

We consider the following motion-planning problem: we are given m unit discs in a simple polygon with n vertices, each at their own start position, and we want to move the discs to a given set of m target positions. Contrary to the standard (labeled) version of the problem, each disc is allowed to be moved to any target position, as long as in the end every target position is occupied. We show that this unlabeled version of the problem can be solved in O (n log n + mn + m2) time, assuming that the start and target positions are at least some minimal distance from each other. This is in sharp contrast to the standard (labeled) and more general multirobot motion planning problem for discs moving in a simple polygon, which is known to be strongly np-hard