Reconstruction of Riser Profiles by an Underwater Robot Using Inertial Navigation

<table>Side and upper views of the FPSO and riser configuration. Global (<svg height="14.8" id="M31" style="vertical-align:-3.30182pt" version="1.1" viewbox="0 0 20.5375 14.8" width="20.5375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.8)">
<g transform="translate(72,-60.16)">
<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">𝐆</tspan>
</text>
</g>
</g>
</svg>, <svg height="14.8" id="M32" style="vertical-align:-3.30182pt" version="1.1" viewbox="0 0 20.5375 14.8" width="20.5375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.8)">
<g transform="translate(72,-60.16)">
<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">𝐆</tspan>
</text>
</g>
</g>
</svg>, <svg height="14.8" id="M33" style="vertical-align:-3.30182pt" version="1.1" viewbox="0 0 19.6875 14.8" width="19.6875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.8)">
<g transform="translate(72,-60.16)">
<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">𝐆</tspan>
</text>
</g>
</g>
</svg>) and local (<svg height="14.6" id="M34" 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="M35" 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="M36" 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>) reference systems position and orientation are shown. The FPSO and riser catenary plane are considered as being aligned with the sea current, forming an angle <svg height="14.5875" id="M37" style="vertical-align:-3.22281pt" version="1.1" viewbox="0 0 23.5875 14.5875" width="23.5875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.5875)">
<g transform="translate(72,-60.33)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜙</tspan>
</text>
<text transform="matrix(1,0,0,-1,-63.89,60.47)">
<tspan style="font-size: 8.75px; " x="0" y="0">c</tspan>
<tspan style="font-size: 8.75px; " x="3.8858881" y="0">a</tspan>
<tspan style="font-size: 8.75px; " x="7.7717762" y="0">t</tspan>
</text>
</g>
</g>
</svg> with the <svg height="14.8" id="M38" style="vertical-align:-3.30182pt" version="1.1" viewbox="0 0 20.5375 14.8" width="20.5375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.8)">
<g transform="translate(72,-60.16)">
<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">𝐆</tspan>
</text>
</g>
</g>
</svg> direction in <svg height="14.375" id="M39" style="vertical-align:-3.24037pt" version="1.1" viewbox="0 0 38.575001 14.375" width="38.575001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.375)">
<g transform="translate(72,-60.5)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑋</tspan>
</text>
<text transform="matrix(1,0,0,-1,-62.07,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝐺</tspan>
</text>
<text transform="matrix(1,0,0,-1,-54.98,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑌</tspan>
</text>
<text transform="matrix(1,0,0,-1,-48.29,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝐺</tspan>
</text>
</g>
</g>
</svg> plane.</table>

Journal of Robotics

fig5

Figure 5

Figure 5: Reconstruction of Riser Profiles by an Underwater Robot Using Inertial Navigation 