Geodesic
Control of the underactuated mechanical systems using natural motion
Kybernetika, Tome 48 (2012) no. 2, pp. 223-241.

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The paper deals with the control of underactuated mechanical systems between equilibrium positions across the singular positions. The considered mechanical systems are in the gravity field. The goal is to find feasible trajectory connecting the equilibrium positions that can be the basis of the system control. Such trajectory can be stabilized around both equilibrium positions and due to the gravity forces the mechanical system overcomes the singular positions. This altogether constitutes the control between the equilibrium positions. The procedure is demonstrated on the different inverse pendulum mechanisms.
Classification : 70E55, 93B60, 93C10
Keywords: underactuated systems; nonlinear control; mechanical systems 
@article{KYB_2012__48_2_a3,
     author = {Neusser, Zden\v{e}k and Val\'a\v{s}ek, Michael},
     title = {Control of the underactuated mechanical systems using natural motion},
     journal = {Kybernetika},
     pages = {223--241},
     publisher = {mathdoc},
     volume = {48},
     number = {2},
     year = {2012},
     mrnumber = {2954322},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2012__48_2_a3/}
}
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Neusser, Zdeněk; Valášek, Michael. Control of the underactuated mechanical systems using natural motion. Kybernetika, Tome 48 (2012) no. 2, pp. 223-241. http://geodesic.mathdoc.fr/item/KYB_2012__48_2_a3/