Accelerometers

I think you'll find nBot also uses a rate gyro in addition to the
accelerometer. You may want to look at some of the autonomous helicopter
projects that have been done. You should be able to turn them up with a
Google search. The nBot page also provides some links to this research,
and the use of filtering on multiple sensors.

There have been some discussions here by people involved in this, and a
company (Rotomotion) makes boards for this. They're expensive and you
may wish to roll your own, but their design fundamentals may be of help.

-- Gordon


Paul Solomon wrote:

The reason gyros are used is because they greatly simplify the process
of getting the actual angle of the device. With your platform, sure, you
can detect the angle by measuring acceleration and doing some simple
calculations based on the acceleration due to gravity. But as soon as
your platform starts moving, the problem gets a lot more complicated.
Moving up or down will generate an acceleration that throws off your
gravity-based calculation. A rotational acceleration in any direction
will also have an effect. Traveling parallel to the ground will product
more accelerations you need to account for.

If the platform isn't going to move too fast, you might try a three-way
PID loop. Place a linear accelerometer on each line from a motor to the
center of the platform. When a corner of the platform is down, or up,
the accelerometers will deviate from zero. Try to modulate the motor
PWMs to balance the accelerometers so that all three are zero. This
should get you to a horizontal position, without calculating the actual
platform angle, and hopefully without shooting the platform into the
ceiling. Vertical motion should be simple enough by adding an equal
offset to all the motors. Sideways motion is bigger problem, since
you'll have to bank and apply thrust.

basicly, the common technique is to use gyros for the fast response, and the
accelerometer as a low spped, horizon reference for zeroing out integration
errors on the gyro.

The resolution isn't the problem - accuracy is.  Your goal is to keep the
platform at 0 degrees in two axes.  This is an angle constraint.  To get the
angle from an accelerometer requires two integrations.  There is way too
much error and drift in the accelerometers for this to work.  You can test
this out by using a spreadsheet to see how long it takes for the error
specified in the accelerometer data sheet to double sum up to a value that
is unacceptable.  It won't take long (seconds).

Mitch

Yup

Accelerometers output acceleration.
Gyros output rotational velocity.

You must integrate a gyro once to get position.
You must integrate an accelerometer twice to get position.

Gyros suffer from temperature instability as well.

if you want to simultaneously control roll, pitch, yaw, and thrust you
need 4 degrees of control freedom so i assume the ducted fans are going
to be steerable or have control vanes in the exhaust or something.


einstein said it: you can never tell the difference between acceleration
and gravity.  an accelerometer in free fall measures zero.  your robot
is in free fall except for the force on it due to the ducted fans.
accelerometers measure the force due to the fans, not gravity.  sure,
they're both -9.8 m/s2 in a stable hover, but that is a special case.


there are commercially available four rotor electric helicopters.  large
slow propellers are more efficient at low speeds .  i suppose with the
energy density of ducted fans you could build something with
missile-like flight characteristics but don't expect too much battery life.


remember that the faster you sample any sensor the noisier it is going
to be.  the physical time constant of your aircraft's torque/rotational
inertia is probably much slower than 50hz.  that is why many flight
control systems are not terribly high frequency.

good luck, though.  flying robots are awesome.  just get adxrs150s
instead of adxl202s and you'll be all set.

-chris

Hi Chris,

thanks for this response!


At the moment I am happy to have an onboard computer (with
accelerometers) attempt to stabalise roll and pitch. I am happy to let
it yaw out of control for the moment (or alternatively pin it it a way
that it cannot yaw). As for thrust, I will control that by hand for the
moment by either varying the power (bench supply) it actually
controlling the thrust through remote control.


My short term goals are to get this platform to hover tethered so that
power (battery weight is not an issue). Then if I get it stabalised, I
plan to make a bigger model with 3 * 1.7kg thrust fans and 3 kg of
battery. my calcs have suggested that I should get ~20min hover out of
this. Ideally (long term if this actually works) I intend to have an
airframe and the ability to transition to forward flight for endurance.

What do you mean by missile like flight characteristics?


Ok, so, with the ADXL202, I get 2 axis acceleration measurement. If I
mount this chip so that one axis it down (or up) and the other us
pointing out to the left or right of the platform. Then I can measure
gravity on both axis and then take atan2(vert, horiz) to get the roll
angle. If I do the same with another chip but one axis vert and the
other forward/backward. Then the same calculation should result in
pitch angle. If I then feed the difference between these angles and 0
into a PID loop, I was thinking that this should stabalise, with no
gyros.

wrt your comment above, do you know if there is any way to determine
mathematically an approx value for the responce time requirements of
the control system i.e.50Hz or higher or lower given the dimentions, CG
etc.

I could model my design as a rigid body with 3 point masses at a fixed
distance from the origin at 120 deg apart. The point mass I could
determint by weighing the platform and dividing by 3, and the distance
from the center could be obtained by cutting off one of the arms and
finding how far out its CG is from the start of the arm.

Any Ideas or comments?

Regards,

Paul Solomon


--

read that part again

I tried and failed. It had the thrust, but I skimped on sensing. I think
that having the shafts of the props all facing up and in may have been a
mistake as well. perhaps vertical or slightly outward would have been
better.

What I do know is that ducted fans are not the thing for this They are all
about speed, you need thrust. Try GWS motors, IPS series, If you can afford
it, use aon brushless, and 4 castle creations motors. I played a bit with
the C gearbox.

google roswell flyer to get a lead on reverse pitch props. They will also
sell carbon fiber rods. Depron foam may also be a valid technique.
Use 4 props, 4 motors, and use torque to control yaw.


You do not want to leave yaw uncontrolled. You do not want to leave yaw
uncontrolled. Really, I mean it. Tourque will induce spin, and unless you
have vertical stabilizers to counter the rotation, you will be in bad shape
really really quickly.

Alternately, buy an Align TREX helicopter, and the lightest brushless motor
that is adequate, ( i think the ticket here is the NEU motor), and a castle
creations  35A speed control.

Just my $0.02