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A pair of bodies rolling on each other is an interesting example of nonholonomic systems in control theory. There is a geometric condition equivalent to the rolling constraint which enables us to generalize the rolling motions for any two-dimensional Riemannian manifolds. This system has a five-dimensional phase space. In order to study the controllability of the rolling surfaces, we lift the system to a six-dimensional space and show that the lifted system is controllable unless the two surfaces have isometric universal covering spaces. In the non-controllable case there are some three-dimensional orbits each of which corresponds to an isometry of the universal covering spaces.
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참고문헌 (19)
참고문헌 신청
A. Agrachev / 2007 / Rolling balls and octonions / Proc. Steklov Inst. Math 258(1):13~22
A. Agrachev / 2004 / Control Theory and Optimization II / Springer-Verlag
R. L. Bryant / 1993 / Rigidity of integral curves of rank 2 distributions / Invent. Math 114(2):435~461
A. Chelouah / 2003 / On the motion planning of rolling surfaces / Forum Math 15(5):727~758
Y. Chitour / 2015 / Rolling of manifolds and controllability in dimension three
A. Agrachev / 2004 / Control Theory and Optimization II / Springer-Verlag
R. L. Bryant / 1993 / Rigidity of integral curves of rank 2 distributions / Invent. Math 114(2):435~461
A. Chelouah / 2003 / On the motion planning of rolling surfaces / Forum Math 15(5):727~758
Y. Chitour / 2015 / Rolling of manifolds and controllability in dimension three
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