Output-Based Control of Robots with Variable Stiffness Actuation

<div class="floats-full-page floats-full-page-other"><h2>Table 2</h2><div class="floats-full-page-caption">Parameters of the three-link planar manipulator controller used in the simulations. </div><div class="floats-full-page-content"><table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="3"><hr /></td></tr><tr class="thead"><td align="left"> Symbol</td><td align="center"> Case no. 1</td><td align="center"> Case no. 2, no. 3</td></tr><tr><td class="thead-hr" colspan="3"><hr /></td></tr><tr><td align="left"><span style="width: 33.945px;"><svg height="16.567499" id="M265" style="vertical-align:-3.24037pt" version="1.1" viewbox="0 0 33.945 16.567499" width="33.945" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.5675)">
<text transform="matrix(1,0,0,-1,4.666,8.73)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑤</tspan>
</text>
<text transform="matrix(1,0,0,-1,11.961,3.729)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐾</tspan>
</text>
<text transform="matrix(1,0,0,-1,21.489,0.603)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑑</tspan>
</text>
</g>
</svg></span></td><td align="center"> diag<svg height="14.76375" id="M266" style="vertical-align:-2.26974pt" version="1.1" viewbox="0 0 54.018749 14.76375" width="54.018749" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.76375)">
<text transform="matrix(1,0,0,-1,0.498,2.761)">
<tspan style="font-size: 12.50px; " x="0" y="0">{</tspan>
<tspan style="font-size: 12.50px; " x="6.0014977" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="12.253057" y="0">6</tspan>
<tspan style="font-size: 12.50px; " x="18.504618" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="23.705915" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="29.957476" y="0">6</tspan>
<tspan style="font-size: 12.50px; " x="36.209034" y="0">}</tspan>
</text>
</g>
</svg></td><td align="center"> diag<svg height="14.70125" id="M267" style="vertical-align:-2.26974pt" version="1.1" viewbox="0 0 69.647499 14.70125" width="69.647499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.70125)">
<text transform="matrix(1,0,0,-1,0.498,2.761)">
<tspan style="font-size: 12.50px; " x="0" y="0">{</tspan>
<tspan style="font-size: 12.50px; " x="6.0014977" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="12.253057" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="18.504618" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="24.756178" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="29.957476" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="36.209034" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="42.460594" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="48.712154" y="0">}</tspan>
</text>
</g>
</svg></td></tr><tr><td align="left"><span style="width: 34.3825px;"><svg height="16.567499" id="M268" style="vertical-align:-3.24037pt" version="1.1" viewbox="0 0 34.3825 16.567499" width="34.3825" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.5675)">
<text transform="matrix(1,0,0,-1,4.666,8.73)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑤</tspan>
</text>
<text transform="matrix(1,0,0,-1,11.961,3.729)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐷</tspan>
</text>
<text transform="matrix(1,0,0,-1,21.839,0.603)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑑</tspan>
</text>
</g>
</svg></span></td><td align="center"> diag<svg height="14.76375" id="M269" style="vertical-align:-2.26974pt" version="1.1" viewbox="0 0 38.389999 14.76375" width="38.389999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.76375)">
<text transform="matrix(1,0,0,-1,0.498,2.761)">
<tspan style="font-size: 12.50px; " x="0" y="0">{</tspan>
<tspan style="font-size: 12.50px; " x="6.0014977" y="0">6</tspan>
<tspan style="font-size: 12.50px; " x="12.253057" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="17.454355" y="0">6</tspan>
<tspan style="font-size: 12.50px; " x="23.705915" y="0">}</tspan>
</text>
</g>
</svg></td><td align="center"> diag<svg height="14.70125" id="M270" style="vertical-align:-2.26974pt" version="1.1" viewbox="0 0 54.018749 14.70125" width="54.018749" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.70125)">
<text transform="matrix(1,0,0,-1,0.498,2.761)">
<tspan style="font-size: 12.50px; " x="0" y="0">{</tspan>
<tspan style="font-size: 12.50px; " x="6.0014977" y="0">3</tspan>
<tspan style="font-size: 12.50px; " x="12.253057" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="18.504618" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="23.705915" y="0">3</tspan>
<tspan style="font-size: 12.50px; " x="29.957476" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="36.209034" y="0">}</tspan>
</text>
</g>
</svg></td></tr><tr><td align="left"><span style="width: 37.7425px;"><svg height="16.567499" id="M271" style="vertical-align:-3.24037pt" version="1.1" viewbox="0 0 37.7425 16.567499" width="37.7425" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.5675)">
<text transform="matrix(1,0,0,-1,4.666,8.73)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑤</tspan>
</text>
<text transform="matrix(1,0,0,-1,11.961,3.729)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑀</tspan>
</text>
<text transform="matrix(1,0,0,-1,24.527,0.603)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑑</tspan>
</text>
</g>
</svg></span></td><td align="center"> diag<svg height="14.70125" id="M272" style="vertical-align:-2.26974pt" version="1.1" viewbox="0 0 77.462502 14.70125" width="77.462502" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.70125)">
<text transform="matrix(1,0,0,-1,0.498,2.761)">
<tspan style="font-size: 12.50px; " x="0" y="0">{</tspan>
<tspan style="font-size: 12.50px; " x="6.0014977" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="12.253057" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="15.378838" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="21.630398" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="27.881958" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="33.083256" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="39.334816" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="42.460594" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="48.712154" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="54.963715" y="0">}</tspan>
</text>
</g>
</svg></td><td align="center"> diag<svg height="14.70125" id="M273" style="vertical-align:-2.26974pt" version="1.1" viewbox="0 0 77.462502 14.70125" width="77.462502" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.70125)">
<text transform="matrix(1,0,0,-1,0.498,2.761)">
<tspan style="font-size: 12.50px; " x="0" y="0">{</tspan>
<tspan style="font-size: 12.50px; " x="6.0014977" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="12.253057" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="15.378838" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="21.630398" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="27.881958" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="33.083256" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="39.334816" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="42.460594" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="48.712154" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="54.963715" y="0">}</tspan>
</text>
</g>
</svg></td></tr><tr><td align="left"><span style="width: 19.408751px;"><svg height="23.477501" id="M274" style="vertical-align:-5.39853pt" version="1.1" viewbox="0 0 19.408751 23.477501" width="19.408751" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,23.4775)">
<g transform="translate(0.498,17.046)">
<path d="M 0,0 7.339,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path>
</g>
<text transform="matrix(1,0,0,-1,0.498,5.881)">
<tspan style="font-size: 12.50px; " x="0" y="0">Γ</tspan>
</text>
<text transform="matrix(1,0,0,-1,7.837,2.755)">
<tspan style="font-size: 8.75px; " x="0" y="0">1</tspan>
</text>
<text transform="matrix(1,0,0,-1,12.214,0.567)">
<tspan style="font-size: 6.25px; " x="0" y="0">𝑖</tspan>
</text>
</g>
</svg></span></td><td align="center"> 90</td><td align="center"> 90</td></tr><tr><td align="left"><span style="width: 19.408751px;"><svg height="23.477501" id="M275" style="vertical-align:-5.39853pt" version="1.1" viewbox="0 0 19.408751 23.477501" width="19.408751" xmlns="http://www.w3.org/2000/svg">
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<g transform="translate(0.498,17.046)">
<path d="M 0,0 7.339,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path>
</g>
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<tspan style="font-size: 12.50px; " x="0" y="0">Γ</tspan>
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<text transform="matrix(1,0,0,-1,7.837,2.755)">
<tspan style="font-size: 8.75px; " x="0" y="0">2</tspan>
</text>
<text transform="matrix(1,0,0,-1,12.214,0.567)">
<tspan style="font-size: 6.25px; " x="0" y="0">𝑖</tspan>
</text>
</g>
</svg></span></td><td align="center"> 2.7<i>e</i>3</td><td align="center"> 2.7<i>e</i>3</td></tr><tr><td align="left"><span style="width: 19.408751px;"><svg height="23.477501" id="M276" style="vertical-align:-5.39853pt" version="1.1" viewbox="0 0 19.408751 23.477501" width="19.408751" xmlns="http://www.w3.org/2000/svg">
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<tspan style="font-size: 12.50px; " x="0" y="0">Γ</tspan>
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<text transform="matrix(1,0,0,-1,7.837,2.755)">
<tspan style="font-size: 8.75px; " x="0" y="0">3</tspan>
</text>
<text transform="matrix(1,0,0,-1,12.214,0.567)">
<tspan style="font-size: 6.25px; " x="0" y="0">𝑖</tspan>
</text>
</g>
</svg></span></td><td align="center"> 10</td><td align="center"> 10</td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr" /></td></tr></table></td></tr></table></div></div>

Table 2 | Output-Based Control of Robots with Variable Stiffness Actuation

title

Table 2: Output-Based Control of Robots with Variable Stiffness Actuation

description

Table 2

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