Methods for trajectory generation in a magnetic-levitation system under constraints
Citations
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Cites methods from "Methods for trajectory generation i..."
...To overcome these issues, B-spline functions (De Doná et al., 2009; Suryawan et al., 2010) have been used....
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34 citations
Cites methods from "Methods for trajectory generation i..."
...Using the flatness theory (Fliess et al., 1995), (Van Nieuwstadt and Murray, 1998), (Suryawan et al., 2010), the system is parameterized in terms of a finite set of variables zl(t) and a finite number of their derivatives: xl(t) = ξ(zl(t), żl(t), · · · , zl,(q)(t)), (19) ul(t) = η(zl(t), żl(t), ·…...
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26 citations
Cites background from "Methods for trajectory generation i..."
...ro pursued in this paper, is the generation of a timeparametrized trajectory using differential flatness [12], [13] which takes explicitly into account the nonlinear system dynamics....
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References
10,258 citations
"Methods for trajectory generation i..." refers background in this paper
...The following are some properties of B-Splines [ 14 ], [15]....
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4,552 citations
"Methods for trajectory generation i..." refers background or methods in this paper
...The following are some properties of B-Splines [14], [ 15 ]....
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...Given specified way-points in time, and using standard spline interpolation techniques (see, e.g., [ 15 ]), we can find a suitable reference trajectory y ref for the flat output of a...
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3,025 citations
"Methods for trajectory generation i..." refers background in this paper
...In the case of linear systems, a system is flat if and only if it is controllable [1], [13]....
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...REVIEW OF FLATNESS Differential flatness [13] is a property of some controlled (linear or nonlinear) dynamical systems, often encountered in applications, which allows for a complete parameterisation of all system variables (inputs and states) in terms of a finite number of variables, called flat outputs, and a finite number of their time derivatives....
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717 citations
"Methods for trajectory generation i..." refers background in this paper
...For a class of dynamical systems, one very useful tool is the notion of flatness, where every system’s signal can be characterised as a function of a set of variables (called flat outputs) and their derivatives [ 1 ]....
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...In the case of linear systems, a system is flat if and only if it is controllable [ 1 ], [13]....
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285 citations