https://murray.cds.caltech.edu/index.php?action=history&feed=atom&title=Invariant_Sets_for_Integrators_and_Quadrotor_Obstacle_Avoidance 2026-09-05T02:09:57Z Revision history for this page on the wiki MediaWiki 1.44.2 https://murray.cds.caltech.edu/index.php?title=Invariant_Sets_for_Integrators_and_Quadrotor_Obstacle_Avoidance&diff=24300&oldid=prev 2021-09-05T02:04:15Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 02:04, 5 September 2021</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l9">Line 9:</td> <td colspan="2" class="diff-lineno">Line 9:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|Tag=dnam20-acc</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|Tag=dnam20-acc</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|Funding=AFOSR T&amp;E</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|Funding=AFOSR T&amp;E</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">|Flags=NCS</ins></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>}}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>}}</div></td></tr> <!-- diff cache key acs_math_mw_144-murraycds_:diff:1.41:old-23672:rev-24300:php=table --> </table>

Murray https://murray.cds.caltech.edu/index.php?title=Invariant_Sets_for_Integrators_and_Quadrotor_Obstacle_Avoidance&diff=23672&oldid=prev 2020-05-26T05:51:51Z

<p>Created page with &quot;{{Paper |Title=Invariant Sets for Integrators and Quadrotor Obstacle Avoidance |Authors=Ludvig Doeser, Petter Nilsson, Aaron D. Ames, and Richard M. Murray |Source=2020 Americ...&quot;</p> <p><b>New page</b></p><div>{{Paper<br /> |Title=Invariant Sets for Integrators and Quadrotor Obstacle Avoidance<br /> |Authors=Ludvig Doeser, Petter Nilsson, Aaron D. Ames, and Richard M. Murray<br /> |Source=2020 American Control Conference (ACC)<br /> |Abstract=Ensuring safety through set invariance has proven a useful method in a variety of applications in robotics and control. However, finding analytical expressions for maximal invariant sets, so as to maximize the operational freedom of the system without compromising safety, is notoriously difficult for high-dimensional systems with input constraints. Here we present a generic method for characterizing invariant sets of nth-order integrator systems, based on analyzing roots of univariate polynomials. Additionally, we obtain analytical expressions for the orders n &lt;= 4. Using differential flatness we subsequently leverage the results for the n = 4 case to the problem of obstacle avoidance for quadrotor UAVs. The resulting controller has a light computational footprint that showcases the power of finding analytical expressions for control-invariant sets.<br /> |URL=https://www.cds.caltech.edu/~murray/preprints/dnam20-acc.pdf<br /> |Type=Conference paper<br /> |ID=2019l<br /> |Tag=dnam20-acc<br /> |Funding=AFOSR T&amp;E<br /> }}</div>

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