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Thanks Sean,
So if the mother ship isn't anchored & is
flowing in a current the unit won't pick this up, as the submarine
upon
launching won't be
accelerating.
If the mother ship was anchored in a
current the unit would need turning on prior to the sub being
released into the current to pick up that movement.
There was an additional unit with gyro for $100-
US
Regards Alan
----- Original Message -----
Sent: Sunday, February 13, 2011 2:19
PM
Subject: Re: [PSUBS-MAILIST]
Navigation
Regrettably, you do tend to get what you pay for. The
unit you linked to is intended for things like video game controllers, such as
the Nintendo Wii wireless controller. By itself, a tri-axial
accelerometer does not constitute an IMU. You need turn rate information
in addition to accelerations, and you need a method of combining those signals
into a useful inertial reference, which means sampling them simultaneously and
fusing them in your Kalman filter at a sufficient sampling rate to minimize
the integration error. That particular instrument is a high noise
device, as well as having no temperature compensation. While it
certainly could be of use for obtaining information such as pitch and roll
angle of your vessel (within the instrument repeatability), it is not
sufficiently accurate to derive meaningful navigation information
from.
As far as a sub moving in a current, all accelerometers will
measure zero (+/- their accuracy limits) when in an inertial reference frame
(i.e. your sub) which is traveling at constant velocity. Integrating an
acceleration signal over time gives you the velocity, and integrating once
again gives you displacement. To illustrate, imagine a support ship
keeping station at a particular GPS location. Your sub is on deck, and
while the accelerometer signal is oscillating due to the ship's roll, the
average is zero. Therefore, the velocity is zero, and net displacement
is zero. Now, have the ship drop your sub over the side into a slight
current. As soon as you are disconnected from the crane, the sub begins
to accelerate as the water force starts to overcome the sub's inertia.
At some point, the acceleration reaches a peak value and then decreases, until
the sub is traveling at the same speed as the current, at which point the
acceleration is zero. The velocity, however, is not zero, since
integrating the acceleration over the time interval between setting the sub
free and reaching the speed of the current results in some positive
value. With the acceleration at zero, the velocity is now some constant
value, and the displacement, being an integral of velocity (now a non-zero
value), will continue to increase over time. Now, actuate your thrusters
to "put on the brakes", with respect to the ground below. You accelerate
in the other direction, slowing from the water current speed to zero speed
with respect to ground. Again, the acceleration increases from zero,
peaks, and drops to zero again (albeit in the negative direction this
time). Integrating that signal over time, the velocity reduces from its
previous constant value to zero, and the displacement, being the integral of
velocity, stops changing. The displacement now has a constant value
equal to the distance you have traveled since you left the ship - in essence,
dead reckoning (distance = velocity * time). Your absolute position is
simply the last known good position (GPS reading at the ship), plus the
accumulated displacement estimate. The quality of this estimate depends
on the quality of the instrumentation, as well as the time over which the
error has been accumulating. If you come to a stop over ground, but the
integration error is such that the resultant velocity is not exactly zero,
then the displacement will continue to increase over time, despite the fact
that you are, in fact, motionless with respect to ground. To correct
this with an external signal, you could surface to obtain a GPS position and
velocity (i.e. eliminating the errors), or similarly, determine this on the
bottom with sonar. The higher the quality of your IMU instrumentation,
the longer you can rely on the dead-reckoning position estimate before the
error becomes unmanageable.
-Sean
On 12/02/2011 4:21 PM,
Alan James wrote:
Hi Sean,
There's a triple axis accelerometer on the
Cytron Robotics site. Needs additional analogue to digital
converter.
Cost RM $109, that's probably less than $40-
US. Have bought stuff off them & it's been good quality.
Will these units cope when your sub is moving
in a current?
Regards Alan
----- Original Message -----
Sent: Sunday, February 13, 2011 9:59
AM
Subject: Re: [PSUBS-MAILIST]
Navigation
A few years ago I experimented with an inertial navigation
system I created using a 3DM-GX1 sensor from Microstrain. I think
the newest model is the 3DM-GX3 now - would have to experiment to see what
accuracy gain there is in the new model. In any case, this is a
three axis accelerometer which incorporates 3 magnetometers and 3 rate
gyros. The magnetometers are supposed to be used to measure the
ambient magnetic field and use this as a quasi-constant input to correct
the gyro bias. Unfortunately, the magnetometers are affected by
external magnetic influences, such as large steel shipwrecks, so the
instrument is least accurate when you tend to need it. The
instrument measures acceleration directly. Integrating this signal
over time gives you your present velocity, and integrating over time once
again gives you your displacement (position) in xyz space. In my
experiment (conducted on a surface vessel), I started with a known
position obtained from GPS, then shut off the GPS signal and simply added
the position variations as calculated from the 3DM-GX1 to determine my
current position. This is, in fact, exactly how military submarines
do it, only their inertial navigation units comprise extremely accurate
(and consequently, extremely expensive) hardware to minimize the
integration error. This is the crux of the inertial navigation
problem - you are essentially determining your position through
dead-reckoning, using the last known good position, and applying
corrections from your IMU instrument. The problem is that error
creeps into the integration, and since you have to integrate twice, the
error starts to get significant. In my experiment, as soon as the
GPS was shut down, the error started to accumulate, so that the
uncertainty in the calculated position grew with time. Eventually,
you reach a point at which the error in your calculated position renders
the position useless for the purpose of navigation. The
solution? Either spend big bucks on a more accurate IMU, or
periodically correct the calculated deviations with another input.
There are several possibilities for this:
1) Doppler sonar -
limited to low speeds at which the sonar reading is accurate, but this is
more accurate than inertial navigation when it is implemented. Doing
this would limit the inertial navigation error to that accumulated during
the descent from the surface to a range from the bottom at which the
doppler sonar becomes effective.
2) Depth transducer - It occurred to
me that since you do know with reasonable accuracy your depth in the water
column (and thus your velocity in the Z direction), you could use
this as a correction input (i.e. do not allow integrated velocity values
in Z direction to exceed this measured velocity, and rein in the X and Y
velocities accordingly). I have no idea what effect this might have
on accuracy without trying it.
3) Acoustic methods - widely used in
industry, but require surface or seafloor based transmitters.
(reference LBL & SBL navigation). If you have no need to operate
independently of surface support, then acoustic navigation alone may meet
your requirements, but this does require some hardware and so may end up
being more expensive than an IMU for small submersible navigation at your
required accuracy - depends on what you need.
I would be inclined
to try and find a low-cost doppler sonar for bottom navigation,
supplemented by an inertial unit that isn't hugely expensive. One
advantage of the IMU is that it will output pitch, roll and yaw angles, so
you could use the output to control, for example, a trim tank system to
keep a level keel.
As I recall, the 3DM-GX1 cost somewhere in the
neighborhood of $1400.00. I would be happy to look into developing a
turnkey PSub inertial navigation solution, but I'd need a 3DM-GX3 (or
similar) IMU to play with, as well as data acquisition hardware that runs
at an appropriate frequency to capture the IMU output with minimal
error. At present, I can't afford to buy these things for a hobby
R&D project, although I might reexamine this at a later date when my
situation changes.
-Sean
On 12/02/2011 10:43 AM, Recon1st@aol.com wrote:
Jim I think navigation would be a good topic for
this
group to discuss. I for one am at a loss for a solution.
I so like my gps system on my surface support boat I want
something decent under water.
How does the military do it? Lots of money I am sure
but seems something better than a compass could be
done.
I am leaning towards a tracking beacon on the sub and
get nav directions from support boat.
Dean
In a message dated 2/12/2011 11:42:17 A.M. Central Standard Time,
kocpnt@tds.net writes:
Hi All,
I am beginning rebuilding Bionic Guppies electronics/electrical
systems. I am planning on again using an aircraft directional gyro for
navigation.
Before I go down this road does anyone have a better/different
idea?
Also, Dan Lance, I believe that you were quite pleased with OTS
communication system.
Can you confirm this, and if so provide contact info for a good
supplier.
Best Regards,
Jim
K
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