Stable and unstable quasiperiodic oscillations in robot dynamics
G. Stépán, G. Haller
Delays in robot control may result in unexpectedly sophisticated nonlinear dynamical behavior. Experiments on force controlled robots frequently show periodic and quasiperiodic oscillations which cannot be explained without including the time lag and/or the sampling time of the system in our models. Delayed systems, even of low degree of freedom, can produce phenomena which are already well understood in the theory of nonlinear dynamical systems but hardly ever occur in simple mechanical models. To illustrate this, we analyze the delayed positioning of a single degree of freedom robot arm. The analytical results show typical nonlinear behavior in the system which may go through a codimension two Hopf bifurcation for an infinite set of parameter values, leading to the creation of two-tori in the phase space. These results give a qualitative explanation for the existence of self-excited quasiperiodic oscillations in the dynamics of force controlled robots.
American Society of Mechanical Engineers, Design Engineering Division (Publication) DE
Mo Shahinpoor, H.S. Tzou
Publ by ASME
14th Biennial Conference on Mechanical Vibration and Noise - Albuquerque, NM, USA
Duration: Sep 19 1993 → Sep 22 1993
14th Biennial Conference on Mechanical Vibration and Noise
Nonlinear dynamical systems
Hopf bifurcation
Stépán, G., & Haller, G. (1993). Stable and unstable quasiperiodic oscillations in robot dynamics. In M. Shahinpoor, & H. S. Tzou (Eds.), American Society of Mechanical Engineers, Design Engineering Division (Publication) DE (Vol. 56, pp. 279-286). Publ by ASME.
Stable and unstable quasiperiodic oscillations in robot dynamics. / Stépán, G.; Haller, G.
American Society of Mechanical Engineers, Design Engineering Division (Publication) DE. ed. / Mo Shahinpoor; H.S. Tzou. Vol. 56 Publ by ASME, 1993. p. 279-286.
Stépán, G & Haller, G 1993, Stable and unstable quasiperiodic oscillations in robot dynamics. in M Shahinpoor & HS Tzou (eds), American Society of Mechanical Engineers, Design Engineering Division (Publication) DE. vol. 56, Publ by ASME, pp. 279-286, 14th Biennial Conference on Mechanical Vibration and Noise, Albuquerque, NM, USA, 9/19/93.
Stépán G, Haller G. Stable and unstable quasiperiodic oscillations in robot dynamics. In Shahinpoor M, Tzou HS, editors, American Society of Mechanical Engineers, Design Engineering Division (Publication) DE. Vol. 56. Publ by ASME. 1993. p. 279-286
Stépán, G. ; Haller, G. / Stable and unstable quasiperiodic oscillations in robot dynamics. American Society of Mechanical Engineers, Design Engineering Division (Publication) DE. editor / Mo Shahinpoor ; H.S. Tzou. Vol. 56 Publ by ASME, 1993. pp. 279-286
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title = "Stable and unstable quasiperiodic oscillations in robot dynamics",
abstract = "Delays in robot control may result in unexpectedly sophisticated nonlinear dynamical behavior. Experiments on force controlled robots frequently show periodic and quasiperiodic oscillations which cannot be explained without including the time lag and/or the sampling time of the system in our models. Delayed systems, even of low degree of freedom, can produce phenomena which are already well understood in the theory of nonlinear dynamical systems but hardly ever occur in simple mechanical models. To illustrate this, we analyze the delayed positioning of a single degree of freedom robot arm. The analytical results show typical nonlinear behavior in the system which may go through a codimension two Hopf bifurcation for an infinite set of parameter values, leading to the creation of two-tori in the phase space. These results give a qualitative explanation for the existence of self-excited quasiperiodic oscillations in the dynamics of force controlled robots.",
author = "G. St{\'e}p{\'a}n and G. Haller",
editor = "Mo Shahinpoor and H.S. Tzou",
booktitle = "American Society of Mechanical Engineers, Design Engineering Division (Publication) DE",
publisher = "Publ by ASME",
T1 - Stable and unstable quasiperiodic oscillations in robot dynamics
AU - Stépán, G.
AU - Haller, G.
N2 - Delays in robot control may result in unexpectedly sophisticated nonlinear dynamical behavior. Experiments on force controlled robots frequently show periodic and quasiperiodic oscillations which cannot be explained without including the time lag and/or the sampling time of the system in our models. Delayed systems, even of low degree of freedom, can produce phenomena which are already well understood in the theory of nonlinear dynamical systems but hardly ever occur in simple mechanical models. To illustrate this, we analyze the delayed positioning of a single degree of freedom robot arm. The analytical results show typical nonlinear behavior in the system which may go through a codimension two Hopf bifurcation for an infinite set of parameter values, leading to the creation of two-tori in the phase space. These results give a qualitative explanation for the existence of self-excited quasiperiodic oscillations in the dynamics of force controlled robots.
AB - Delays in robot control may result in unexpectedly sophisticated nonlinear dynamical behavior. Experiments on force controlled robots frequently show periodic and quasiperiodic oscillations which cannot be explained without including the time lag and/or the sampling time of the system in our models. Delayed systems, even of low degree of freedom, can produce phenomena which are already well understood in the theory of nonlinear dynamical systems but hardly ever occur in simple mechanical models. To illustrate this, we analyze the delayed positioning of a single degree of freedom robot arm. The analytical results show typical nonlinear behavior in the system which may go through a codimension two Hopf bifurcation for an infinite set of parameter values, leading to the creation of two-tori in the phase space. These results give a qualitative explanation for the existence of self-excited quasiperiodic oscillations in the dynamics of force controlled robots.
BT - American Society of Mechanical Engineers, Design Engineering Division (Publication) DE
A2 - Shahinpoor, Mo
A2 - Tzou, H.S.
PB - Publ by ASME