Maintaining Wireless Connectivity Constraints for Robot Swarms in the Presence of Obstacles

<table>Frames depict an example of a combination of <svg height="11.8" id="M77" style="vertical-align:-0.15048pt" version="1.1" viewbox="0 0 18.25 11.8" width="18.25" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.8)">
<g transform="translate(72,-62.56)">
<text transform="matrix(1,0,0,-1,-71.95,62.76)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐺</tspan>
</text>
<text transform="matrix(1,0,0,-1,-62.52,67.83)">
<tspan style="font-size: 8.75px; " x="0" y="0">∗</tspan>
</text>
</g>
</g>
</svg>, <svg height="14.0625" id="M78" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 13.5375 14.0625" width="13.5375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.0625)">
<g transform="translate(72,-60.75)">
<text transform="matrix(1,0,0,-1,-71.95,63.09)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑞</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.72,68.09)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑜</tspan>
</text>
</g>
</g>
</svg>, and <svg height="16.549999" id="M79" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 15.9125 16.549999" width="15.9125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.55)">
<g transform="translate(72,-58.76)">
<text transform="matrix(1,0,0,-1,-71.95,61.1)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑞</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.72,66.1)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑓</tspan>
</text>
</g>
</g>
</svg> which are not feasible. Loops in left and right frames are not in the same homotopic equivalence class.</table>

Journal of Robotics

fig3

Figure 3

Figure 3: Maintaining Wireless Connectivity Constraints for Robot Swarms in the Presence of Obstacles 