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References
K. Bekka, Propriétés métriques et topologiques des espaces stratifiés, Thèse, Orsay, 1988.
K. Bekka, C-régularité et trivialité topologique, Warwick Singularity Theory Symposium 1989, to appear.
J. Canny, The complexity of robot motion planning, M.I.T. Thesis, 1986, ACM doctoral dissertation series, MIT Press, Cambridge, Mass. 1988.
J. Canny, A new algebraic method for robot-motion planning and real geometry, Proceedings of the 28th IEEE Symposium on the Foundations of Computer Science, Los Angeles, 1987, pp.39–48.
J. Canny, Some algebraic and geometric computations in PSPACE, 20th Annual ACM Symposium on Theory of Computing, 1988, pp.460–467.
G. E. Collins, Quantifier elimination for real closed fields by cylindrical algebraic decomposition, Lecture Notes in Computer Science, No.33, Springer-Verlag, New York, 1975.
J. H. Davenport and J. Heintz, Real quantifier elimination is doubly exponential, Journal of Symbolic Computation 5 (1988), pp.29–35.
M. Goresky and R. MacPherson, Stratified Morse Theory, Springer, Ergebnisse, 1988.
J. Mather, Notes on topological stability, Harvard University, 1970.
J. Mather, Stability of C∞ Mappings: IV, Classification of stable germs by ℝ-algebras, Publ. Math. I.H.E.S. 37 (1970),pp.223–248.
J. Mather, Generic projections, Annals of Math. 98 (1973), pp.226–245.
J. Mather, How to stratify mappings and jet spaces, Singularités d'Applications Différentiables, Plans-sur-Bex 1975, Lecture Notes in Math. 535, Springer, Berlin-New York, 1976, pp. 128–176.
R. Pignoni, Density and stability of Morse functions on a stratified space, Ann. Scuo. Norm. Sup. Pisa (4) 4, 1979, pp.592–608.
J. T. Schwartz and M. Sharir, Motion planning and related geometric algorithms in robotics, Proceedings of the International Congress of Mathematicians, Berkeley 1986, Vol.2, A. M. S. 1987, pp.1594–1611.
M. Sharir, Algorithmic motion planning in robotics, Computer, March 1989, pp. 9–20.
B. Teissier, Variétés Polaires II. Multiplicités polaires, sections planes et conditions de Whitney, Algebraic Geometry Proceedings, La Rabida 1981, Lecture Notes in Mathematics 961, Springer-Verlag, New York, 1982, pp.314–491.
R. Thom, Ensembles et morphismes stratifiés, Bull. Amer. Math. Soc. 75, 1969, pp.240–284.
D. Trotman, On the canonical Whitney stratification of algebraic hypersurfaces, Séminaire sur la Géometrie Algébrique Réelle (sous la direction de J.-J. Risler), Publications Mathématiques de l'Université Paris VII, No. 24, 1987, pp. 123–152.
Additional references
J. Canny, Constructing roadmaps of semi-algebraic sets I: Completeness, Artificial Intelligence, 37, 1988, pp. 203–222
J. Heintz, M.-F. Roy, P. Salerno, Single exponential path finding in semialgebraic sets, manuscript, 1990.
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Trotman, D. (1991). On Canny's roadmap algorithm: orienteering in semialgebraic sets (an application of singularity theory to theoretical robotics). In: Mond, D., Montaldi, J. (eds) Singularity Theory and its Applications. Lecture Notes in Mathematics, vol 1462. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086391
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DOI: https://doi.org/10.1007/BFb0086391
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