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cs:hydrophones:start [2016/12/10 19:43] Ryan Summers |
cs:hydrophones:start [2019/02/21 19:50] Christofer Freeberg [Hydrophones] |
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| ====== Hydrophones ====== | ====== Hydrophones ====== | ||
| - | <WRAP info> | + | Our hydrophones are a powerful tool for figuring out where we are in the water. Using 4 hydrophones, we can calculated our bearing to the pinger. For details, see [[cs:hydrophones:pinger_bearing:start|Pinger Bearing]]. |
| - | Before reading this page, make sure to check out the **Problem Setup** section of [[ee:hydrophones:trilateration:start|this page]]. | + | |
| - | </WRAP> | + | |
| - | This page is a summary of how we use the hydrophones to figure out our position. | + | ====== Testing Procedure ====== |
| + | ==Materials:== | ||
| + | * 1 tub of water | ||
| + | * 1 pinger | ||
| + | * Hydrophone Test Rig | ||
| - | Note that | + | ==Test Rig:== |
| - | + | * Pinger at one end of tub | |
| - | + | * Hydrophones at other end of tub | |
| - | The primary results from [[ee:hydrophones:trilateration:start|this derivation]] are equations $\ref{eq:xyz}$ and $\ref{eq:p0_initial}$. | + | * If lots of noise in readings observed, can place towels around tub |
| - | $$ | + | |
| - | \begin{equation} \label{eq:xyz} | + | |
| - | x = \frac{\Delta x (2p_0 - \Delta x) + \delta^2}{2 \delta} \\ | + | |
| - | y = \frac{\Delta y (2p_0 - \Delta y) + \epsilon^2}{2 \epsilon} \\ | + | |
| - | z = \frac{\Delta z (2p_0 - \Delta z) + \zeta^2}{2 \zeta} | + | |
| - | \end{equation}$$ | + | |
| - | + | ||
| - | $$ \begin{equation}\label{eq:p0_initial} | + | |
| - | 0 = p_0^2(a_x + a_y + a_z - 1) + p_0(b_x + b_y + b_z) + (c_x+c_y+c_z) | + | |
| - | \end{equation} | + | |
| - | $$ | + | |
| - | + | ||
| - | With variable definitions given by $\ref{eq:variable_definitions}$. | + | |
| - | + | ||
| - | $$ \begin{equation} \label{eq:variable_definitions} | + | |
| - | a_x = \left(\frac{\Delta x}{\delta}\right)^2 \qquad | + | |
| - | b_x = \frac{\Delta x}{\delta^2}(\delta^2 +\Delta x^2) \qquad | + | |
| - | c_x = \left(\frac{\Delta x^2 - \delta^2}{2 \delta}\right)^2 \\ | + | |
| - | + | ||
| - | + | ||
| - | a_y = \left(\frac{\Delta y}{\epsilon}\right)^2 \qquad | + | |
| - | b_y = \frac{\Delta y}{\epsilon^2}(\epsilon^2 +\Delta y^2) \qquad | + | |
| - | c_y = \left(\frac{\Delta y^2 - \epsilon^2}{2 \epsilon}\right)^2 \\ | + | |
| - | + | ||
| - | a_z = \left(\frac{\Delta z}{\zeta}\right)^2 \qquad | + | |
| - | b_z = \frac{\Delta z}{\zeta^2}(\zeta^2 +\Delta z^2) \qquad | + | |
| - | c_z = \left(\frac{\Delta z^2 - \zeta^2}{2 \zeta}\right)^2 | + | |
| - | \end{equation} | + | |
| - | $$ | + | |
| - | + | ||
| - | $h_0$ is at location $(0,0,0)$ \\ | + | |
| - | $h_x$ is at location $(\delta,0,0)$ \\ | + | |
| - | $h_y$ is at location $(0,\epsilon,0)$ \\ | + | |
| - | $h_z$ is at location $(0,0,\zeta)$ \\ | + | |
| - | + | ||
| - | Let us simplify eq. $\ref{eq:p0_initial}$ using the following substitution: | + | |
| - | $$ | + | |
| - | a = (a_x + a_y + a_z - 1) \\ | + | |
| - | b = (b_x + b_y + b_z) \\ | + | |
| - | c = (c_x+c_y+c_z) | + | |
| - | $$ | + | |
| - | + | ||
| - | This gives us eq. $\ref{eq:p0_initial_simple}$, which is an ordinary quadratic equation. | + | |
| - | $$ \begin{equation}\label{eq:p0_initial_simple} | + | |
| - | 0 = p_0^2 a + p_0 b + c | + | |
| - | \end{equation} | + | |
| - | $$ | + | |
| - | + | ||
| - | Applying the quadratic formula to eq. $\ref{eq:p0_initial_simple}$, we can solve for $p_0$. | + | |
| - | + | ||
| - | $$ \begin{equation}\label{eq:p0_solved} | + | |
| - | p_0 = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} | + | |
| - | \end{equation} | + | |
| - | $$ | + | |
| - | + | ||
| - | This will give us two possible solutions for $p_0$. We can combine this result with eq. $\ref{eq:xyz}$ to solve for $x$, $y$, and $z$. | + | |
| - | + | ||
| - | ====== Reversing the Problem ====== | + | |
| - | Here we describe how the simulator takes the position of the sub and calculates fake hydrophone timing data. <WRAP todo> | + | |
| - | Need figure this part out! | + | |
| - | </WRAP> | + | |
| + | ==Procedure:== | ||
| + | - ssh into the sub | ||
| + | - roslaunch robosub cobalt.launch | ||
| + | - rosrun robosub pinger_bearing | ||
| + | - rostopic echo /hydrophones/bearing | ||
| + | - Manipulate hydrophones & Observe bearing readings | ||
