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Guidelines in nonholonomic motion planning for mobile robots

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References

  1. R. Alami, “Multi-robot cooperation based on a distributed and incremental plan merging paradigm,” Algorithms for Robotic Motion and Manipulation, WAFR'96, J.P. Laumond and M. Overmars Eds, A.K. Peters, 1997.

    Google Scholar 

  2. P.K. Agarwal, P. Raghavan and H. Tamaki, “Motion planning for a steering-constrained robot through moderate obstacles,” ACM Symp. on Computational Geometry, 1995.

    Google Scholar 

  3. J.M. Ahuactzin, “Le Fil d'Ariane: une méthode de planification générale. Application à la planification automatique de trajectoires,” PhD Thesis, INP, Grenoble, 1994.

    Google Scholar 

  4. F. Avnaim, J. Boissonnat and B. Faverjon, “A practical exact motion planning algorithm for polygonal objects amidst polygonal obstacles,” IEEE Int. Conf. on Robotics and Automation, pp. 1656–1661, Philadelphia, 1988.

    Google Scholar 

  5. J. Barraquand and J.C. Latombe, “Robot motion planning: a distributed representation approach,” International Journal of Robotics Research, 1991.

    Google Scholar 

  6. J. Barraquand and J.-C. Latombe, “On non-holonomic mobile robots and optimal maneuvering,” Revue d'Intelligence Artificielle, Vol. 3 (2), pp. 77–103, 1989.

    Google Scholar 

  7. J. Barraquand and J.C. Latombe, “Nonholonomic multibody mobile robots: controllability and motion planning in the presence of obstacles,” Algorithmica, Springer Verlag, Vol. 10, pp. 121–155, 1993.

    Google Scholar 

  8. J. Barraquand, L. Kavraki, J.C. Latombe, T.Y. Li, R. Motvani and P. Raghavan, “A random sampling scheme for path planning,” Robotics Research, the Seventh International Symposium, G. Giralt and G. Hirzinger Eds, Springer Verlag, 1996.

    Google Scholar 

  9. A. Bellaïche, J.P. Laumond and P. Jacobs, “Controllability of car-like robots and complexity of the motion planning problem,” Int. Symposium on Intelligent Robotics, pp. 322–337, Bangalore, 1991.

    Google Scholar 

  10. A. Bellaïche, J.P. Laumond and J.J. Risler, “Nilpotent infinitesimal approximations to a control Lie algebra,” IFAC Nonlinear Control Systems Design Symposium, pp. 174–181, Bordeaux, 1992.

    Google Scholar 

  11. A. Bellaïche, J.P. Laumond and M. Chyba, “Canonical nilpotent approximation of control systems: application to nonholonomic motion planning,” 32nd IEEE Conf. on Decision and Control, San Antonio, 1993.

    Google Scholar 

  12. P. Bessière, J.M. Ahuactzin, E. Talbi and E. Mazer, “The Ariadne's clew algorithm: global planning with local methods,” Algorithmic Foundations of Robotics, K. Goldberg et al Eds, A.K. Peters, 1995.

    Google Scholar 

  13. J.D. Boissonnat and S. Lazard, “A polynomial-time algorithm for computing a shortest path of bounded curvature amidst moderate obstacle,” ACM Symp. on Computational Geometry, 1996.

    Google Scholar 

  14. R.W. Brockett, “Control theory and singular Riemannian geometry,” New Directions in Applied Mathematics, Springer-Verlag, 1981.

    Google Scholar 

  15. X.N. Bui, P. Souères, J.D. Boissonnat and J.P. Laumond, “The shortest path synthesis for nonholonomic robots moving fordwards,” IEEE Int. Conf. on Robotics and Automation, Atlanta, 1994.

    Google Scholar 

  16. L. Bushnell, D. Tilbury and S. Sastry, “Steering three-input nonholonomic systems: the fire-truck example,” International Journal of Robotics Research, Vol. 14 (4), pp. 366–381, 1995.

    Google Scholar 

  17. G. Campion, G. Bastin and B. d'Andréa-Novel, “Structural properties and classification of kinematic and dynamic models of wheeled mobile robots,” IEEE Trans. on Robotics and Automation, Vol. 12 (1), 1996.

    Google Scholar 

  18. J. Canny, The Complexity of Robot Motion Planning, MIT Press, 1988.

    Google Scholar 

  19. J. Canny, A. Rege and J. Reif, “An exact algorithm for kinodynamic planning in the plane,” Discrete and Computational Geometry, Vol. 6, pp. 461–484, 1991.

    Google Scholar 

  20. B. Donald, P. Xavier, J. Canny and J. Reif, “Kinodynamic motion planning,” J. of the ACM, Vol. 40, pp. 1048–1066, 1993.

    Google Scholar 

  21. B. Donald and P. Xavier, “Provably good approximation algorithms for optimal kinodynamic planning: robots with decoupled dynamic bounds,” Algorithmica, Vol. 14, pp. 443–479, 1995.

    Google Scholar 

  22. L. E. Dubins, “On curves of minimal length with a constraint on average curvature and with prescribed initial and terminal positions and tangents,” American Journal of Mathematics, Vol. 79, pp. 497–516, 1957.

    Google Scholar 

  23. P. Ferbach, “A method of progressive constraints for nonholonomic motion planning,” IEEE Int. Conf. on Robotics and Automation, pp. 2929–2955, Minneapolis, 1996.

    Google Scholar 

  24. C. Fernandes, L. Gurvits and Z.X. Li, “A variational approach to optimal nonholonomic motion planning,” IEEE Int. Conf. on Robotics and Automation, pp. 680–685, Sacramento, 1991.

    Google Scholar 

  25. S. Fleury, P. Souères, J.P. Laumond and R. Chatila, “Primitives for smoothing mobile robot trajectories,” IEEE Transactions on Robotics and Automation, Vol. 11 (3), pp. 441–448, 1995.

    Google Scholar 

  26. M. Fliess, J. Lévine, P. Martin and P. Rouchon, “Flatness and defect of non-linear systems: introductory theory and examples,” Int. Journal of Control, Vol. 61 (6), pp. 1327–1361, 1995.

    Google Scholar 

  27. S.J. Fortune and G.T. Wilfong, “Planning constrained motions,” ACM STOCS, pp. 445–459, Chicago, 1988.

    Google Scholar 

  28. T. Fraichard, “Dynamic trajectory planning with dynamic constraints: a 'state-time space’ approach,” IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, pp. 1393–1400, Yokohama, 1993.

    Google Scholar 

  29. V. Y. Gershkovich, “Two-sided estimates of metrics generated by absolutely nonholonomic distributions on Riemannian manifolds,” Soviet Math. Dokl., Vol. 30 (2), 1984.

    Google Scholar 

  30. G. Giralt, R. Sobek and R. Chatila, “A multi-level planning and navigation system for a mobile robot: a first approach to Hilare,” 6th Int. Joint Conf. on Artificial Intelligence, pp. 335–337, Tokyo, 1979.

    Google Scholar 

  31. H. Hermes, A. Lundell and D. Sullivan, “Nilpotent bases for distributions and control systems,” J. of Differential Equations, Vol. 55, pp. 385–400, 1984.

    Google Scholar 

  32. J. Hopcroft, J.T. Schwartz and M. Sharir, “On the complexity of motion planning for multiple independent objects: PSPACE-hardness of the warehouseman's problem,” International Journal of Robotics Research, Vol. 3, pp. 76–88, 1984.

    Google Scholar 

  33. G. Jacob, “Lyndon discretization and exact motion planning,” European Control Conference, pp. 1507–1512, Grenoble, 1991.

    Google Scholar 

  34. P. Jacobs and J. Canny, “Planning smooth paths for mobile robots,” IEEE Int. Conf. on Robotics and Automation, Scottsdale, 1989.

    Google Scholar 

  35. P. Jacobs, A. Rege and J.P. Laumond, “Non-holonomic motion planning for Hilare-like robots,” Int. Symposium on Intelligent Robotics, pp. 338–347, Bangalore, 1991.

    Google Scholar 

  36. F. Jean, “The car with N trailers: characterization of the singular configurations,” ESAIM: COCV, http://www.emath.fr/cocv/, Vol. 1, pp. 241–266, 1996.

    Google Scholar 

  37. Y. Kanayama and N. Miyake, “Trajectory generation for mobile robots,” Robotics Research, Vol. 3, MIT Press, pp. 333–340, 1986.

    Google Scholar 

  38. M. Khatib, H. Jaouni, R. Chatila and J.P. Laumond, “Dynamic path modification for car-like nonholonomic mobile robots,” IEEE Int. Conf. on Robotics and Automation, Albuquerque, 1997.

    Google Scholar 

  39. G. Lafferriere and H.J. Sussmann, “A differential geometric approach to motion planning,” Nonholonomic Motion Planning, Zexiang Li and J.F. Canny Eds, The Kluwer International Series in Engineering and Computer Science 192, 1992.

    Google Scholar 

  40. F. Lamiraux and J.P. Laumond, “From paths to trajectories for multi-body mobile robots,” Int. Symposium on Experimental Robotics, Lecture Notes on Control and Information Science, Springer-Verlag, (to appear) 1997.

    Google Scholar 

  41. F. Lamiraux and J.P. Laumond, “Flatness and small-time controllability of multibody mobile robots: applications to motion planning,” European Conference on Control, Brussels, 1997.

    Google Scholar 

  42. J.C. Latombe, Robot Motion Planning, Kluwer Academic Publishers, 1991.

    Google Scholar 

  43. J.C. Latombe, “A Fast Path Planner for a Car-Like Indoor Mobile Robot,” Ninth National Conference on Artificial Intelligence, AAAI, pp. 659–665, Anaheim, 1991.

    Google Scholar 

  44. J.P. Laumond, “Feasible trajectories for mobile robots with kinematic and environment constraints,” Intelligent Autonomous Systems, L.O. Hertzberger, F.C.A. Groen Edts, North-Holland, pp. 346–354, 1987.

    Google Scholar 

  45. J.P. Laumond, “Finding collision-free smooth trajectories for a non-holonomic mobile robot,” 10th International Joint Conference on Artificial Intelligence, pp. 1120–1123, Milano, 1987.

    Google Scholar 

  46. J.P. Laumond, “Singularities and topological aspects in nonholonomic motion planning,” Nonholonomic Motion Planning, Zexiang Li and J.F. Canny Eds, The Kluwer International Series in Engineering and Computer Science 192, 1992.

    Google Scholar 

  47. J.P. Laumond, “Controllability of a Multibody Mobile Robot,” IEEE Transactions Robotics and Automation, pp. 755–763, Vol. 9 (6), 1993.

    Google Scholar 

  48. J.P. Laumond, P. Jacobs, M. Taïx and R. Murray, “A motion planner for nonholonomic mobile robot,” IEEE Trans. on Robotics and Automation, Vol. 10, 1994.

    Google Scholar 

  49. J.P. Laumond, S. Sekhavat and M. Vaisset, “Collision-free motion planning for a nonholonomic mobile robot with trailers,” 4th IFAC Symp. on Robot Control, pp. 171–177, Capri, 1994.

    Google Scholar 

  50. J.P. Laumond and J.J. Risler, “Nonholonomic systems: controllability and complexity,” Theoretical Computer Science, Vol. 157, pp. 101–114, 1996.

    Google Scholar 

  51. J.P. Laumond and P. Souères, “Metric induced by the shortest paths for a car-like robot,” IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, Yokoama, 1993.

    Google Scholar 

  52. Z. Li and J.F. Canny Eds, Nonholonomic Motion Planning, Kluwer Academic Publishers, 1992.

    Google Scholar 

  53. T. Lozano-Pérez, “Spatial planning: a configuration space approach,” IEEE Trans. Computers, Vol. 32 (2), 1983.

    Google Scholar 

  54. F. Luca and J.J. Risler, “The maximum of the degree of nonholonomy for the car with n trailers,” in IFAC Symp. on Robot Control, pp. 165–170, Capri, 1994.

    Google Scholar 

  55. B. Mirtich and J. Canny, “Using skeletons for nonholonomic path planning among obstacles,” IEEE Int. Conf. on Robotics and Automation, Nice, 1992.

    Google Scholar 

  56. J. Mitchell, “On Carnot-Carathéodory metrics,” J. Differential Geometry, Vol. 21, pp. 35–45, 1985.

    Google Scholar 

  57. S. Monaco and D. Normand-Cyrot, “An introduction to motion planning under multirate digital control,” IEEE Int. Conf. on Decision and Control, pp. 1780–1785, Tucson, 1992.

    Google Scholar 

  58. R.M. Murray and S. Sastry, “Steering nonholonomic systems using sinusoids,” IEE Int. Conf. on Decision and Control, pp. 2097–2101, 1990.

    Google Scholar 

  59. R.M. Murray, “Robotic Control and Nonholonomic Motion Planning,” PhD Thesis, Memorandum No. UCB/ERL M90/117, University of California, Berkeley, 1990.

    Google Scholar 

  60. R.M. Murray, “Nilpotent bases for a class on nonintegrable distributions with applications to trajectory generation for nonholonomic systems,” Math. Control Signal Syst., Vol. 7, pp. 58–75, 1994.

    Google Scholar 

  61. N.J. Nilsson, “A mobile automaton: an application of artificial intelligence techniques”, 1st Int. Joint Conf. on Artificial Intelligence, pp. 509–520, Washington, 1969.

    Google Scholar 

  62. C. O'Dunlaing, “Motion planning with inertial constraints,” Algorithmica, Vol. 2 (4), 1987.

    Google Scholar 

  63. P. Rouchon, M. Fliess, J. Lévine and P. Martin, “Flatness and motion planning: the car with n trailers,” European Control Conference. pp. 1518–1522, 1993.

    Google Scholar 

  64. P. Rouchon, “Necessary condition and genericity of dynamic feedback linearization,” in J. Math. Systems Estimation Control, Vol. 4 (2), 1994.

    Google Scholar 

  65. J. A. Reeds and R. A. Shepp, “Optimal paths for a car that goes both forward and backwards,” Pacific Journal of Mathematics, 145 (2), pp. 367–393, 1990.

    Google Scholar 

  66. J. Reif and H. Wang, “Non-uniform discretization approximations for kinodynamic motion planning and its applications,” Algorithms for Robotic Motion and Manipulation, WAFR'96, J.P. Laumond and M. Overmars Eds, A.K. Peters, 1997.

    Google Scholar 

  67. M. Renaud and J.Y. Fourquet, “Time-optimal motions of robot manipulators including dynamics,” The Robotics Review 2, O. Khatib, J.J. Craig and T. Lozano-Pérez Eds, MIT Press, 1992.

    Google Scholar 

  68. J.J. Risler, “A bound for the degree of nonholonomy in the plane,” Theoretical Computer Science, Vol. 157, pp. 129–136, 1996.

    Google Scholar 

  69. J.T. Schwartz and M. Sharir, “On the ‘Piano Movers’ problem II: general techniques for computing topological properties of real algebraic manifolds,” Advances in Applied Mathematics, 4, pp. 298–351, 1983.

    Google Scholar 

  70. S. Sekhavat, P. Švestka, J.P. Laumond and M. H. Overmars, “Multi-level path planning for nonholonomic robots using semi-holonomic subsystems,” Algorithms for Robotic Motion and Manipulation, WAFR'96, J.P. Laumond and M. Overmars Eds, A.K. Peters, 1997.

    Google Scholar 

  71. S. Sekhavat, “Planification de mouvements sans collisions pour systèmes non holonomes,” PhD Thesis 1240, INPT, LAAS-CNRS, Toulouse, 1996.

    Google Scholar 

  72. S. Sekhavat and J-P. Laumond, “Topological Property of Trajectories Computed from Sinusoidal Inputs for Chained Form Systems,” IEEE Int. Conf. on Robotics and Automation, Mineapollis, 1996.

    Google Scholar 

  73. S. Sekhavat and J-P. Laumond, “Topological property for collision-free nonholonomic motion planning: the case of sinusoidal inputs for chained form systems,” IEEE Transaction on Robotics and Automation (to appear).

    Google Scholar 

  74. S. Sekhavat, F. Lamiraux, J-P. Laumond, G. Bauzil and A. Ferrand, “Motion planning and control for Hilare pulling a trailer: experimental issues,” in IEEE Int. Conf. on Robotics and Automation, Albuquerque, 1997.

    Google Scholar 

  75. J.J.E. Slotine and H.S. Yang, “Improving the efficiency of time-optimal pathfollowing algorithms,” IEEE Transactions on Robotics and Automation, 5 (1), pp. 118–124, 1989.

    Google Scholar 

  76. P. Souères and J.P. Laumond, “Shortest path synthesis for a car-like robot,” IEEE Trans. on Auromatic Control, Vol. 41 (5), pp. 672–688, 1996.

    Google Scholar 

  77. E.D. Sontag, “Controllability is harder to decide than accessibility,” SIAM J. Control and Optimization, Vol. 26 (5), pp. 1106–1118, 1988.

    Google Scholar 

  78. O.J. Sordalen, “Conversion of a car with n trailers into a chained form,” IEEE Int. Conf. on Robotics and Automation, pp. 382–387, Atlanta, 1993.

    Google Scholar 

  79. S. Sternberg, Lectures on Differential Geometry, Chelsea Pub., 1983.

    Google Scholar 

  80. R. S. Strichartz, “Sub-Riemannian geometry,” Journal of Differential Geometry, Vol. 24, pp. 221–263, 1986.

    Google Scholar 

  81. R. S. Strichartz, “The Campbell-Baker-Hausdorff-Dynkin formula and solutions of differential equations,” Journal of Functional Analysis, Vol. 72, pp. 320–345, 1987.

    Google Scholar 

  82. H.J. Sussmann and V. Jurdjevic, “Controllability of nonlinear systems,” J. of Differential Equations, 12, pp. 95–116, 1972.

    Google Scholar 

  83. H. Sussmann, “Lie brackets, real analyticity and geometric control,” Differential Geometric Control Theory (R. Brockett, R. Millman and H. Sussmann, eds.), Vol. 27 of Progress in Mathematics, pp. 1–116, Michigan Technological University, Birkhauser, 1982.

    Google Scholar 

  84. H. J. Sussmann and W. Liu, “Limits of highly oscillatory controls and the approximation of general paths by admissible trajectories,” Tech. Rep. SYSCON-91-02, Rutgers Center for Systems and Control, 1991.

    Google Scholar 

  85. P. Svestka and M. Overmars, “Coordinated motion planning for multiple car-like robots using probabilistic roadmaps,” IEEE Int. Conf. on Robotics and Automation, Nagoya, Japan, 1995.

    Google Scholar 

  86. D. Tilbury, R. Murray and S. Sastry, “Trajectory generation for the n-trailer problem using Goursat normal form,” IEEE Trans. on Automatic Control, Vol. 40 (5), pp. 802–819, 1995.

    Google Scholar 

  87. D. Tilbury, J.P. Laumond, R. Murray, S. Sastry and G. Walsh, “Steering car-like systems with trailers using sinusoids,” in IEEE Conf. on Robotics and Automation, pp. 1993–1998, Nice, 1992.

    Google Scholar 

  88. A. Thompson, “The navigation system of the JPL robot,” 5th Int. Joint Conf. on Artificial Intelligence, pp. 749–757, Cambridge, 1977.

    Google Scholar 

  89. P. Tournassoud, “Motion planning for a mobile robot with a kinematic constraint,” Geometry and Robotics, J.D. Boissonnat and J.P. Laumond Eds, pp. 150–171, Lecture Notes in Computer Science, Vol 391, Springer Verlag, 1989.

    Google Scholar 

  90. V.S. Varadarajan, Lie Groups, Lie Algebra and their Representations, Springer-Verlag, 1984.

    Google Scholar 

  91. M. Vendittelli and J.P. Laumond, “Visible positions for a car-like robot amidst obstacles,” Algorithms for Robotic Motion and Manipulation, J.P. Laumond and M. Overmars Eds, A.K. Peters, 1997.

    Google Scholar 

  92. A.M. Vershik and V.Ya. Gershkovich, “Nonholonomic problems and the theory of distributions,” Acta Applicandae Mathematicae, Vol. 12, pp. 181–209, 1988.

    Google Scholar 

  93. X. Viennot, Algèbres de Lie libres et monoïdes libres. Lecture Notes in Mathematics, 691, Springer Verlag, 1978.

    Google Scholar 

  94. G.T. Wilfong, “Motion planning for an autonomous vehicle,” IEEE Int. Conf. on Robotics and Automation, pp. 529–533, 1988.

    Google Scholar 

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Laumond, J.P., Sekhavat, S., Lamiraux, F. (1998). Guidelines in nonholonomic motion planning for mobile robots. In: Laumond, J.P. (eds) Robot Motion Planning and Control. Lecture Notes in Control and Information Sciences, vol 229. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0036070

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