Replies to This Discussion

Permalink Reply by Tom on May 23, 2011 at 12:44am

Thanks for your work and sharing it with others Caleb. BYU's paper's style is always nice to read.

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Permalink Reply by Roy Brewer on May 23, 2011 at 4:45am

Thanks Caleb for your great work and for being willing to share it with us.

 

FYI, Salaun's PhD thesis is also available (its mostly in English - don't be fooled by the first few pages)

http://pastel.archives-ouvertes.fr/docs/00/55/44/37/PDF/PhD_Thesis_...

 

- Roy

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Permalink Reply by Amr Marzouk on September 2, 2011 at 8:05am

Hey,

A friendly quick note: Fig. 7.1 in page 148 says ATMEGA128 and shows an Analog Devices ADIS16355 IMU. I was just skimming through pages :)

 

Best Regards,

Amr

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Permalink Reply by Tom Yochum on May 23, 2011 at 9:28am

Great stuff Caleb! Thanks for sharing.

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DeveloperPermalink Reply by Doug Weibel on May 23, 2011 at 8:15pm

Hi Caleb,

Nice analysis.  Of course there is always more work to be done...    But it looks like a nice step in the right direction.

 

You appear to have an error in formula 5.15.  Fortunately it does not appear to carry forward anywhere.

 

I can follow the math but cannot intuitively see how the LPF filter model corrects the phase lag between the accelerometer estimated and actual angles.  Do you have an intuitive understanding of this that you can put in words?

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Permalink Reply by Caleb Chamberlain on May 23, 2011 at 8:46pm

Hi Doug,

 

The basic idea is that, in the absence of appreciable aerodynamic drag, any deviation in the attitude from zero will cause lateral accelerations that "cancel out" the gravity measurement on the x and y axes.  Gravity can only be measured accurately when the aircraft is no longer accelerating (i.e. when it is moving fast enough that drag prevents it from accelerating more).

 

The low-pass filter model simply accounts for the time it takes for the aircraft to reach that steady-state velocity.

 

You are right that more work remains to be done.  In fact, I would not recommend that anyone use the estimator I present in the thesis.  There are better ways of doing it.  A paper is in the works to provide an overview of possible ways to design a good estimator.

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Permalink Reply by Roy Brewer on May 24, 2011 at 3:14pm

Doug,

 

The way I see it, since the sensed accelerometer model includes a lag, the estimator effectively inverts the lag to compute the angle.

 

- Roy

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DeveloperPermalink Reply by Doug Weibel on May 24, 2011 at 9:03pm

Well, sure, I am just having trouble seeing how it phase shifts it "forward in time"....

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Permalink Reply by Caleb Chamberlain on May 24, 2011 at 10:27pm

It doesn't, really.  It filters the angle estimates, not the accelerometer data.  The accelerometer data is "filtered" by the aircraft dynamics, and the angle estimates on the estimator are filtered to match.

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Permalink Reply by Roy Brewer on June 4, 2011 at 4:47pm

Caleb,

A necessary (but not sufficient) condition for the accelerometer to provide an accurate estimate the pitch/bank angle is for the magnitude of its output vector to be 1 g, Just examining the results holding the sensor in my hand, it seems that the gyro bias changes fairly slowly, hence we should be able to get decent estimates with infrequent accel-based updates. I know DCM exploits this to a certain degree, but I would take it further, using a very high observer gain on the accels when the (filtered) magnitude is close to 1 g, and zero gain otherwise. I haven't tried any of this on a quad yet.

Here are a few papers that use a similar idea:
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.142.4218&a...
http://infolab.ulsan.ac.kr/research/jsmefinal%282006%29.pdf
http://infolab.ulsan.ac.kr/research/orientation/paper.pdf

The downside to your approach is that it may be difficult to experimentally identify the lag dynamics, without access to a wind tunnel or an expensive external orientation measurement system.

- Roy

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Permalink Reply by Caleb Chamberlain on June 4, 2011 at 10:17pm

Hi Roy,

 

Yeah, measuring the aerodynamic drag coefficient could be tricky without truth data.  I actually think it can be done with an optic flow sensor and a clever filter.  On the other hand, the drag coefficient needn't be perfectly accurate to obtain really good results, and for most small quadrotors, there is a reasonable ballpark that will produce more accuracy.

 

Using accelerometers directly, like you suggest, can work.  There is a tradeoff, though.  When accelerometer updates are infrequent, the filter becomes much more sensitive to non-zero gyro biases.  When accelerometer measurements are weighted more heavily, on the other hand, the filter is more sensitive to non-gravity accelerations.  Improving performance in one area necessarily reduces performance in the other.

 

Fully accounting for the dynamics of the aircraft, as described in my thesis, allows the above tradeoff to be circumvented almost altogether.  For a hobbyist who just wants to motor around, it probably isn't important.  But in any application where accurate truth states are required (i.e. geolocation, sensor registration, automated gimbal target tracking, etc.) the performance benefits definitely justify the increased complexity of the filter.  Moreover, if you want a full GPS/INS system, there really isn't an alternative to modeling the aircraft more accurately.

 

This is particularly true if it is desirable to use lower-cost MEMS sensors.  If you were using, say, FOG rate gyros, accelerometer updates would be almost unnecessary in the short term.  An uncalibrated ITG-3200 would be a totally different story.

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Permalink Reply by Roy Brewer on June 11, 2011 at 2:34pm

Caleb,

 

Actually, I think it may be important to the hobbyists - many of the projects seem to be having accelerometer issues with their attitude estimation routines (just look here on DIYDrones and the Aeroquad forums).

 

Also, this paper looks intriguing, but I don't have access to it!

A linear fusion algorithm for attitude determination using low cost MEMS-based sensors
http://www.sciencedirect.com/science/article/pii/S0263224106001072

 

- Roy

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