Reconstruction of Riser Profiles by an Underwater Robot Using Inertial Navigation

<table>Position external measurements <svg height="14.7125" id="M238" style="vertical-align:-3.2316pt" version="1.1" viewbox="0 0 30.0625 14.7125" width="30.0625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.7125)">
<g transform="translate(72,-60.23)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐙</tspan>
</text>
<text transform="matrix(1,0,0,-1,-63.61,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑘</tspan>
<tspan style="font-size: 8.75px; " x="4.7435842" y="0">−</tspan>
<tspan style="font-size: 8.75px; " x="10.738704" y="0">1</tspan>
</text>
</g>
</g>
</svg> and <svg height="14.7125" id="M239" style="vertical-align:-3.2316pt" version="1.1" viewbox="0 0 17.1 14.7125" width="17.1" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.7125)">
<g transform="translate(72,-60.23)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐙</tspan>
</text>
<text transform="matrix(1,0,0,-1,-63.61,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑘</tspan>
</text>
</g>
</g>
</svg> and the corresponding local reference frames (<svg height="14.6" id="M240" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 15.075 14.6" width="15.075" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.6)">
<g transform="translate(72,-60.32)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐗</tspan>
</text>
<text transform="matrix(1,0,0,-1,-62.92,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝐥</tspan>
</text>
</g>
</g>
</svg>, <svg height="14.6" id="M241" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 15.075 14.6" width="15.075" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.6)">
<g transform="translate(72,-60.32)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐘</tspan>
</text>
<text transform="matrix(1,0,0,-1,-62.92,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝐥</tspan>
</text>
</g>
</g>
</svg>, <svg height="14.6" id="M242" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 14.2125 14.6" width="14.2125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.6)">
<g transform="translate(72,-60.32)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐙</tspan>
</text>
<text transform="matrix(1,0,0,-1,-63.61,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝐥</tspan>
</text>
</g>
</g>
</svg>). <svg height="10.325" id="M243" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 11.1875 10.325" width="11.1875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐿</tspan>
</text>
</g>
</g>
</svg> is the scalar displacement between the two positions.</table>

Journal of Robotics

fig10

Figure 10

Figure 10: Reconstruction of Riser Profiles by an Underwater Robot Using Inertial Navigation 