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Robot arm problem (TACO) - Revision history
2024-03-29T15:53:59Z
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JonasSchulze: Text replacement - "\<bibref\>(.*)\<\/bibref\>" to "<bib id="$1" />"
2015-12-30T20:32:09Z
<p>Text replacement - "\<bibref\>(.*)\<\/bibref\>" to "<bib id="$1" />"</p>
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<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 20:32, 30 December 2015</td>
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<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>This page contains a model of the [[Robot arm problem]] in [http://www.ampl.org AMPL] format, making use of the TACO toolkit for AMPL control optimization extensions. This problem is due to <<del class="diffchange diffchange-inline">bibref></del>Moessner1995<del class="diffchange diffchange-inline"><</del>/<del class="diffchange diffchange-inline">bibref</del>>. The original model using a collocation formulation can be found in the [http://www.mcs.anl.gov/~more/cops/ COPS library].</div></td><td class='diff-marker'>+</td><td style="color:black; 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>This page contains a model of the [[Robot arm problem]] in [http://www.ampl.org AMPL] format, making use of the TACO toolkit for AMPL control optimization extensions. This problem is due to <<ins class="diffchange diffchange-inline">bib id="</ins>Moessner1995<ins class="diffchange diffchange-inline">" </ins>/>. The original model using a collocation formulation can be found in the [http://www.mcs.anl.gov/~more/cops/ COPS library].</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Note that you will need to include a generic [[support AMPL files|AMPL/TACO support file]], OptimalControl.mod.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Note that you will need to include a generic [[support AMPL files|AMPL/TACO support file]], OptimalControl.mod.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>To solve this model, you require an optimal control or NLP code that uses the TACO toolkit to support the AMPL optimal control extensions.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>To solve this model, you require an optimal control or NLP code that uses the TACO toolkit to support the AMPL optimal control extensions.</div></td></tr>
</table>
JonasSchulze
https://mintoc.de/index.php?title=Robot_arm_problem_(TACO)&diff=1102&oldid=prev
JonasSchulze: Text replacement - "<bibreferences/>" to "<biblist />"
2015-12-30T20:28:26Z
<p>Text replacement - "<bibreferences/>" to "<biblist />"</p>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== References ==</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== References ==</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>[[Category:AMPL/TACO]]</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>[[Category:AMPL/TACO]]</div></td></tr>
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JonasSchulze
https://mintoc.de/index.php?title=Robot_arm_problem_(TACO)&diff=670&oldid=prev
Ckirches: Reference for robotarm problem
2011-09-29T19:46:36Z
<p>Reference for robotarm problem</p>
<table class='diff diff-contentalign-left'>
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<td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 19:46, 29 September 2011</td>
</tr><tr><td colspan="2" class="diff-lineno" id="L1" >Line 1:</td>
<td colspan="2" class="diff-lineno">Line 1:</td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>This page contains a model of the [[Robot arm problem]] in [http://www.ampl.org AMPL] format, making use of the TACO toolkit for AMPL control optimization extensions. The original model using a collocation formulation can be found in the [http://www.mcs.anl.gov/~more/cops/ COPS library].</div></td><td class='diff-marker'>+</td><td style="color:black; 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>This page contains a model of the [[Robot arm problem]] in [http://www.ampl.org AMPL] format, making use of the TACO toolkit for AMPL control optimization extensions<ins class="diffchange diffchange-inline">. This problem is due to <bibref>Moessner1995</bibref></ins>. The original model using a collocation formulation can be found in the [http://www.mcs.anl.gov/~more/cops/ COPS library].</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Note that you will need to include a generic [[support AMPL files|AMPL/TACO support file]], OptimalControl.mod.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Note that you will need to include a generic [[support AMPL files|AMPL/TACO support file]], OptimalControl.mod.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>To solve this model, you require an optimal control or NLP code that uses the TACO toolkit to support the AMPL optimal control extensions.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>To solve this model, you require an optimal control or NLP code that uses the TACO toolkit to support the AMPL optimal control extensions.</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="L119" >Line 119:</td>
<td colspan="2" class="diff-lineno">Line 119:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* Mathematical notation at [[Robot arm problem]]</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* Mathematical notation at [[Robot arm problem]]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* [[:Category:AMPL | AMPL]] (using a fixed discretization) at the [http://www.mcs.anl.gov/~more/cops/ COPS library]</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* [[:Category:AMPL | AMPL]] (using a fixed discretization) at the [http://www.mcs.anl.gov/~more/cops/ COPS library]</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; 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;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; 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;">== References ==</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; 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;"><bibreferences/></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   </div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>   </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>[[Category:AMPL/TACO]]</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>[[Category:AMPL/TACO]]</div></td></tr>
</table>
Ckirches
https://mintoc.de/index.php?title=Robot_arm_problem_(TACO)&diff=664&oldid=prev
Ckirches: Robot arm problem (TACO)
2011-09-29T19:16:16Z
<p>Robot arm problem (TACO)</p>
<p><b>New page</b></p><div>This page contains a model of the [[Robot arm problem]] in [http://www.ampl.org AMPL] format, making use of the TACO toolkit for AMPL control optimization extensions. The original model using a collocation formulation can be found in the [http://www.mcs.anl.gov/~more/cops/ COPS library].<br />
Note that you will need to include a generic [[support AMPL files|AMPL/TACO support file]], OptimalControl.mod.<br />
To solve this model, you require an optimal control or NLP code that uses the TACO toolkit to support the AMPL optimal control extensions.<br />
<br />
=== AMPL ===<br />
<br />
This is the source file robotarm_taco.mod<br />
<source lang="AMPL"><br />
# ----------------------------------------------------------------<br />
# Robot arm problem using AMPL and TACO<br />
# (c) Christian Kirches, Sven Leyffer<br />
#<br />
# Source: COPS 3.1 collocation formulation - March 2004<br />
# David Bortz - Summer 1998 <br />
# ----------------------------------------------------------------<br />
include OptimalControl.mod;<br />
<br />
# Final positions of the length and the angles for the robot arm<br />
<br />
param L; # total length of arm<br />
param pi := 4*atan(1);<br />
<br />
# Upper bounds on the controls<br />
<br />
param max_u_rho;<br />
param max_u_the;<br />
param max_u_phi;<br />
<br />
# Initial positions of the length and the angles for the robot arm<br />
<br />
param rho_0;<br />
param the_0;<br />
param phi_0;<br />
<br />
# Final positions of the length and the angles for the robot arm<br />
<br />
param rho_n;<br />
param the_n;<br />
param phi_n;<br />
<br />
# The length and the angles theta and phi for the robot arm.<br />
<br />
var rho >=0, <= L; <br />
var the >= -pi, <= pi; <br />
var phi >=0, <= pi;<br />
<br />
# The derivatives of the length and the angles.<br />
<br />
var rho_dot;<br />
var the_dot;<br />
var phi_dot;<br />
<br />
# The controls.<br />
<br />
var u_rho >= -max_u_rho, <= max_u_rho, suffix type "u0";<br />
var u_the >= -max_u_the, <= max_u_the, suffix type "u0";<br />
var u_phi >= -max_u_phi, <= max_u_phi, suffix type "u0";<br />
<br />
# The independent time and the final time.<br />
<br />
var t;<br />
var tf := 1.0, >= 0.1, <= 12 suffix scale 10.0;<br />
<br />
# The moments of inertia.<br />
<br />
var I_the = ((L-rho)^3+rho^3)*(sin(phi))^2/3.0;<br />
var I_phi = ((L-rho)^3+rho^3)/3.0;<br />
<br />
# The robot arm problem.<br />
<br />
minimize time: eval(t,tf) suffix scale 1e+2;<br />
<br />
subject to rho_eqn:<br />
diff(rho, t) = rho_dot;<br />
<br />
subject to the_eqn:<br />
diff(the, t) = the_dot;<br />
<br />
subject to phi_eqn:<br />
diff (phi, t) = phi_dot;<br />
<br />
subject to u_rho_eqn:<br />
diff (rho_dot, t) = u_rho/L;<br />
<br />
subject to u_the_eqn:<br />
diff (the_dot, t) = u_the/I_the;<br />
<br />
subject to u_phi_eqn:<br />
diff (phi_dot, t) = u_phi/I_phi;<br />
<br />
# Boundary Conditions<br />
<br />
subject to rho_0_eqn: eval (rho, 0) = 4.5 suffix type "dpc";<br />
subject to the_0_eqn: eval (the, 0) = 0 suffix type "dpc";<br />
subject to phi_0_eqn: eval (phi, 0) = pi/4 suffix type "dpc";<br />
<br />
subject to rho_f_eqn: eval (rho, tf) = 4.5;<br />
subject to the_f_eqn: eval (the, tf) = 2*pi/3;<br />
subject to phi_f_eqn: eval (phi, tf) = pi/4;<br />
<br />
subject to rho_dot_0_eqn: eval (rho_dot, 0) = 0 suffix type "dpc";<br />
subject to the_dot_0_eqn: eval (the_dot, 0) = 0 suffix type "dpc";<br />
subject to phi_dot_0_eqn: eval (phi_dot, 0) = 0 suffix type "dpc";<br />
<br />
subject to rho_dot_f_eqn: eval (rho_dot, tf) = 0;<br />
subject to the_dot_f_eqn: eval (the_dot, tf) = 0;<br />
subject to phi_dot_f_eqn: eval (phi_dot, tf) = 0;<br />
<br />
option solver ...;<br />
<br />
solve;<br />
<br />
</source><br />
<br />
== Other Descriptions ==<br />
<br />
Other descriptions of this problem are available in<br />
<br />
* Mathematical notation at [[Robot arm problem]]<br />
* [[:Category:AMPL | AMPL]] (using a fixed discretization) at the [http://www.mcs.anl.gov/~more/cops/ COPS library]<br />
<br />
[[Category:AMPL/TACO]]</div>
Ckirches