VISUALIZING THE MOTION OF A UNICYCLE ON A SPHERE

M.P. Hennessey

References

  1. [1] S.V. Sreenivasan & K.J. Waldron, Displacement analysis of an articulated wheeled configuration on uneven terrain, 23rd Bi78 ennial Mechanisms Conf., ASME Design Engineering Division, 72, Pt. 3, Minneapolis, MN, 1994, 393–402.
  2. [2] D.C. Brogran, R.A. Metoyer, & J.K. Hodgins, Dynamically simulated characters in virtual environments, IEEE Computer Graphics and Applications, 18(5), September/October 1998, 58–69. doi:10.1109/38.708561
  3. [3] M. Ishikawa & M. Sampei, Classification of nonholonomic systems from mechanical and control-theoretic viewpoints, Proc. 2000 IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, Takamatsu, Japan, October 31–November 5, 2000, 121–126.
  4. [4] D. Tilbury, R.M. Murray, & S.S. Sastry, Trajectory generation for the N-trailer problem using Goursat normal form, Proc. 32nd IEEE Conf. on Decision and Control, San Antonio, TX, December 1993, 971–977. doi:10.1109/CDC.1993.325330
  5. [5] J. Ostrowski, A. Lewis, R. Murray, & J. Burdick, Nonholonomic mechanics and locomotion: The Snakeboard example, Proc. IEEE Conf. on Robotics and Automation, 3, San Diego, CA, 1994, 2391–2397. doi:10.1109/ROBOT.1994.351153
  6. [6] A. Bicchi, A. Balluchi, D. Prattichizzo, & A. Gorelli, Introducing the “SPHERICLE : An experimental testbed for research and teaching in nonholonomy, Proc. IEEE Int. Conf. on Robotics and Automation, 3, Piscataway, NJ, 1997, 2620–2625. doi:10.1109/ROBOT.1997.619356
  7. [7] R.M. Murray, Z. Li, & S.S. Sastry, A mathematical introduction to robotic manipulation (Boca Raton, FL: CRC Press, 1994).
  8. [8] J.C. Latombe, Robot motion planning (Dordrecht: Kluwer, 1991).
  9. [9] Y. Yavin & C. Frangos, Open-loop strategies for the control of a disk rolling on a horizontal plane, Computer Methods in Applied Mechanics & Engineering, 127 (1–4), November 1995, 227–240. doi:10.1016/0045-7825(95)00848-6
  10. [10] W. Leroquais & B. d’Andrea-Novel, Modeling and control of wheeled mobile robots not satisfying ideal velocity constraints: The unicycle case, Proc. IEEE Conf. on Decision and Control, 2, Kobe, Japan, 1996, 1437–1442. doi:10.1109/CDC.1996.572715
  11. [11] D.V. Zenkov, A.M. Bloch, & J.E. Marsden, The LyapunovMaklin theorem and stabilization of the unicycle with rider, Systems & Control Letters, 45(4), 2002, 293–302. doi:10.1016/S0167-6911(01)00187-6
  12. [12] A. Bicchi, G. Casalino, & C. Santilli, Planning shortest bounded-curvature paths for a class of nonholonomic vehicles among obstacles, Journal of Intelligent & Robotic Systems, 16(4), 1996, 387–405. doi:10.1007/BF00270450
  13. [13] Y. Yavin, Modelling and control of the motion of a disk rolling on a spherical dome, Mathematical and Computer Modelling, 35(9–10), 2002, 931–939. doi:10.1016/S0895-7177(02)00060-2
  14. [14] A.M. Block, Nonholonomic mechanics and control (New York: Springer-Verlag, 2003).
  15. [15] SolidWorks Corp., SolidWorks r 2001 plus, Solidworks essentials: Parts, assemblies and drawings (Concord, MA: SolidWorks Corp., 2001).
  16. [16] SolidWorks Corp., SolidWorks r 2001 plus, advanced assembly modeling (Concord, MA: SolidWorks Corp., 2001).
  17. [17] SolidWorks Corp., SolidWorks r 2001 plus, advanced part modeling (Concord, MA: SolidWorks Corp., 2001).
  18. [18] P.J. Rabier & W.C. Rheinboldt, Nonholonomic motion of rigid mechanical systems from a DAE viewpoint (Philadelphia, PA: SIAM, 2000).
  19. [19] W.M. Boothby, An introduction to differentiable manifolds and Riemannian geometry, 2nd ed. (volume 120 in Pure and Applied Mathematics) (New York: Academic Press, 1986).
  20. [20] R.P. Paul, Robot manipulators (Cambridge, MA: MIT Press, 1981).
  21. [21] F. Ayres, Theory and problems of plane and spherical trigonometry: Schaum’s outline series (New York: McGraw-Hill, 1954).
  22. [22] A. Candel & L. Conlon, Foliations I (Providence, RI: AMS, 2000).
  23. [23] D.C. Hanselman & B. Littlefield, Mastering MATLAB r 5: A comprehensive tutorial and reference (Upper Saddle River, NJ: Prentice-Hall, 1998).
  24. [24] J. B. Dabney & T.L. Harmon, Mastering SIMULINK r 2 (Upper Saddle River, NJ: Prentice-Hall, 1998).
  25. [25] N.J. Eggleton & M.P. Hennessey, Unconstrained instantaneous center integration (ICI) algorithms, Proc. IASTED Int. Conf., Intelligent Systems and Control 2000, Honolulu, HI, August 14–16, 2000, 317-012, 1–7.
  26. [26] University of St. Thomas, 2004–2006 undergraduate catalog (St. Paul, MN, 2002).
  27. [27] R.R. Roberts, Applying derived data to animate the motion of a unicycle on a sphere, CAM Summer Projects Meeting, University of St. Thomas, August 20, 2003.
  28. [28] M.P. Hennessey, Visualization of the motion of a unicycle on a sphere and the associated Lie algebra, Seminar on Applied Mathematics and Numerical Analysis, School of Mathematics, University of Minnesota, April 17, 2003.

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