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	<id>https://murray.cds.caltech.edu/index.php?action=history&amp;feed=atom&amp;title=Real_Time_Trajectory_Generation_for_Differentially_Flat_Systems</id>
	<title>Real Time Trajectory Generation for Differentially Flat Systems - Revision history</title>
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	<updated>2026-06-28T14:32:22Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=Real_Time_Trajectory_Generation_for_Differentially_Flat_Systems&amp;diff=20021&amp;oldid=prev</id>
		<title>Murray: htdb2wiki: creating page for 1996l_nm96-ijrnc.html</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=Real_Time_Trajectory_Generation_for_Differentially_Flat_Systems&amp;diff=20021&amp;oldid=prev"/>
		<updated>2016-05-15T06:20:13Z</updated>

		<summary type="html">&lt;p&gt;htdb2wiki: creating page for 1996l_nm96-ijrnc.html&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;{{HTDB paper&lt;br /&gt;
| authors = Michiel J. van Nieuwstadt and Richard M. Murray&lt;br /&gt;
| title = Real Time Trajectory Generation for Differentially Flat Systems&lt;br /&gt;
| source = &amp;lt;i&amp;gt;Int&amp;#039;l. J. Robust &amp;amp;amp; Nonlinear Control&amp;lt;/i&amp;gt; 8:(11) 995-1020&lt;br /&gt;
| year = 1998&lt;br /&gt;
| type = CDS Technical&lt;br /&gt;
report (preprint)&lt;br /&gt;
| funding = NSF, AFOSR&lt;br /&gt;
| url = http://www.cds.caltech.edu/~murray/preprints/nm96-ijrnc.pdf&lt;br /&gt;
| abstract =  This paper considers the problem of real time trajectory generation and tracking for&lt;br /&gt;
nonlinear control systems. We employ a two degree of freedom approach that separates the&lt;br /&gt;
nonlinear tracking problem into real time trajectory generation followed by local&lt;br /&gt;
(gain-scheduled) stabilization. The central problem which we consider is how to generate,&lt;br /&gt;
possibly with some delay, a feasible state space and input trajectory in real time from an&lt;br /&gt;
output trajectory that is given online. We propose two algorithms that solve the real time&lt;br /&gt;
trajectory generation problem for differentially flat systems with (possibly non-minimum&lt;br /&gt;
phase) zero dynamics. One is based on receding horizon point to point steering, the other&lt;br /&gt;
allows additional minimization of a cost function. Both algorithms explicitly address the&lt;br /&gt;
tradeoff between stability and performance and we prove convergence of the algorithms for&lt;br /&gt;
a reasonable class of output trajectories. To illustrate the application of these&lt;br /&gt;
techniques to physical systems, we present experimental results using a vectored thrust&lt;br /&gt;
flight control experiment built at Caltech. A brief introduction to differentially flat&lt;br /&gt;
systems and its relationship with feedback linearization is also included. &lt;br /&gt;
| flags = &lt;br /&gt;
| tag = nm96-ijrnc&lt;br /&gt;
| id = 1996l&lt;br /&gt;
}}&lt;/div&gt;</summary>
		<author><name>Murray</name></author>
	</entry>
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