https://murray.cds.caltech.edu/index.php?action=history&feed=atom&title=Nonholonomic_Motion_Planning%3A_Steering_Using_Sinusoids 2026-09-07T01:09:37Z Revision history for this page on the wiki MediaWiki 1.44.2 https://murray.cds.caltech.edu/index.php?title=Nonholonomic_Motion_Planning:_Steering_Using_Sinusoids&diff=20068&oldid=prev 2016-05-15T06:20:57Z

<p>htdb2wiki: creating page for 1993d_ms93.html</p> <p><b>New page</b></p><div>{{HTDB paper<br /> | authors = Richard M. Murray and S. Shankar Sastry<br /> | title = Nonholonomic Motion Planning: Steering Using Sinusoids<br /> | source = &lt;em&gt;IEEE T. Automatic Control&lt;/em&gt;, 38(5):700-716<br /> | year = 1993<br /> | type = Technical report<br /> | funding = <br /> | url = http://www.cds.caltech.edu/~murray/preprints/erl-M91-45.pdf<br /> | abstract = In this paper we investigate methods for steering systems with nonholonomic<br /> constraints between arbitrary configurations. Early work by Brockett derives the optimal<br /> controls for a set of canonical systems in which the tangent space to the configuration<br /> manifold is spanned by the input vector fields and their first order Lie brackets. Using<br /> Brockett&#039;s result as motivation, we derive suboptimal trajectories for systems which are<br /> not in canonical form and consider systems in which it takes more than one level of<br /> bracketing to achieve controllability. These trajectories use sinusoids at integrally<br /> related frequencies to achieve motion at a given bracketing level. We define a class of<br /> systems which can be steered using sinusoids (chained systems) and give conditions under<br /> which a class of two-input systems can be converted into this form. <br /> | flags = NoRequest<br /> | tag = ms93<br /> | id = 1993d<br /> }}</div>

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