VISUALIZING THE MOTION OF A UNICYCLE ON A SPHERE

M.P. Hennessey

References

  1. [1] S.V. Sreenivasan & K.J. Waldron, Displacement analysis of anarticulated wheeled configuration on uneven terrain, 23rd Bi-78ennial 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, Dynamicallysimulated characters in virtual environments, IEEE ComputerGraphics and Applications, 18(5), September/October 1998,58–69. doi:10.1109/38.708561
  3. [3] M. Ishikawa & M. Sampei, Classification of nonholonomicsystems from mechanical and control-theoretic viewpoints,Proc. 2000 IEEE/RSJ Int. Conf. on Intelligent Robots andSystems, Takamatsu, Japan, October 31–November 5, 2000,121–126.
  4. [4] D. Tilbury, R.M. Murray, & S.S. Sastry, Trajectory generationfor 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, Nonholonomicmechanics 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, Intro-ducing the “SPHERICLE : An experimental testbed for re-search and teaching in nonholonomy, Proc. IEEE Int. Conf. onRobotics 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 introductionto 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 controlof a disk rolling on a horizontal plane, Computer Methods inApplied 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 ofwheeled 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 Lyapunov-Maklin 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 shortestbounded-curvature paths for a class of nonholonomic vehiclesamong 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 rollingon 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 essen-tials: Parts, assemblies and drawings (Concord, MA: Solid-Works Corp., 2001).
  16. [16] SolidWorks Corp., SolidWorks r 2001 plus, advanced assemblymodeling (Concord, MA: SolidWorks Corp., 2001).
  17. [17] SolidWorks Corp., SolidWorks r 2001 plus, advanced part mod-eling (Concord, MA: SolidWorks Corp., 2001).
  18. [18] P.J. Rabier & W.C. Rheinboldt, Nonholonomic motion of rigidmechanical systems from a DAE viewpoint (Philadelphia, PA:SIAM, 2000).
  19. [19] W.M. Boothby, An introduction to differentiable manifoldsand Riemannian geometry, 2nd ed. (volume 120 in Pure andApplied 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 trigonom-etry: 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 instantaneouscenter integration (ICI) algorithms, Proc. IASTED Int. Conf.,Intelligent Systems and Control 2000, Honolulu, HI, August14–16, 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 motionof 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 ona sphere and the associated Lie algebra, Seminar on AppliedMathematics and Numerical Analysis, School of Mathematics,University of Minnesota, April 17, 2003.

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