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On the motion of a disc rolling on a horizontal plane: Path controllability and feedback control. (English) Zbl 0900.70414

Summary: This work deals with the feedback control and guidance of the motion of a disc rolling, without slipping, on the horizontal \((X, Y)\)-plane. The concept of path controllability is introduced, and is used to establish a condition under which the disc’s motion is path controllable. The derivation of this condition is used to design a robust closed-loop control law for the disc’s motion, such that the disc will roll, during a finite time-interval, \([0, t_f]\), from a point \(A\) to a small neighbourhood of \(B\), where \(A\) and \(B\) are two given points in the \((X, Y)\)-plane.

MSC:

70Q05 Control of mechanical systems
70E15 Free motion of a rigid body
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[1] Whittaker, E. T., A Treatise on the Analytical Dynamics of Particles and Rigid Bodies (1917), Cambridge University Press: Cambridge University Press Cambridge, UK · Zbl 0061.41806
[2] Neimark, Ju. I.; Fufaev, N. A., Dynamics of Nonholonomic Systems (1972), American Mathematical Society: American Mathematical Society Providence, Rhode Island · Zbl 0245.70011
[3] Latombe, J. C., Robot Motion Planning (1991), Kluwer Academic Publishers: Kluwer Academic Publishers Boston, MA
[4] Pontryagin, L. S.; Boltyansky, V. G.; Gamkrelidze, R. V.; Mishchenko, E. F., The Mathematical Theory of Optimal Processes (1962), Interscience Publishers, John Wiley and Sons: Interscience Publishers, John Wiley and Sons New York · Zbl 0102.32001
[5] Bryson, A. E.; Ho, Y. C., Applied Optimal Control (1969), Blaisdell Publishing Company: Blaisdell Publishing Company Waltham, MA
[6] Yavin, Y.; Frangos, C., Open-loop strategies for the control of a disk rolling on a horizontal plane, Comput. Methods Appl. Mech. Engrg., 227-240 (1995) · Zbl 0868.70020
[7] Y. Yavin and C. Frangos, On a horizontal version of the inverse pendulum, Comput. Methods Appl. Mech. Engrg., in press.; Y. Yavin and C. Frangos, On a horizontal version of the inverse pendulum, Comput. Methods Appl. Mech. Engrg., in press. · Zbl 0893.70020
[8] Friedland, B., Control System Design (1987), McGraw-Hill: McGraw-Hill New York
[9] Snyman, J. A., An improved version of the original leapfrog dynamic method for unconstrained minimisation: Lfop1(b), Appl. Math. Model., 7, 3, 216-218 (1983) · Zbl 0548.65046
[10] Yavin, Y.; Frangos, C., Computation of feasible control trajectories for the navigation of a ship around an obstacle in the presence of a sea current, Math. Comput. Model., 21, 3, 99-117 (1995) · Zbl 0825.93579
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