What we need now: Guidance system and other issues

[DaveHein]

Thom,

I had a NAR Level 1 certification, but I've let my NAR membership lapse. I had planned on going for level 2. It just seems like other things have taken higher priority in my life. I would encourage you to go through the certification process. It's fun and rewarding.

Dave

[pyramids]

Dave,

I see your point about having less than 9 full dof from a useable navigational information point-of-view. Thanks. I guess I was looking on it too one-sidedly, only considering that there are 9 sensors each measuring something different. Yet it is more than the usual 6 dof, because the magnetometer gives, as you pointed out, at least 2 dof information for correcting the gyro drift (in low-level conditions, i.e. below ionosphere).

Sorry if that was nit picking.
I do agree going after HPR licenses sounds more relevant and like it will be more fun!

[DaveHein]

If a degree of freedom is equivalent to a dimension, then there are only 6 degrees of freedom possible. However, a degree of freedom could be defined as a dimension and a derivative level. Each dimension could have a displacement, velocity and acceleration component, which would yield a total of 18 possible degrees of freedom. Under this definition, the SparkFun "9DOF" sensor would still be only 8DOF since the 3 magetometer measurements contain only 2 independent dimesions of information.

[pauldear]

Wow. This has got complex fast!

One of the things I love about this is that there are so many people out there - in all walks of life - with so much expertise and knowledge. I love listening to people who really know stuff, even when it's way outside my own field (biology!).

My posts on this topic from now on will pale into infantility compared to some of the more technical perspectives! But, on the topic of sun-seeking sensors, I'm assuming that simple is best, and that (for speed of response) you want as little processing as possible. What would happen if you had two very simple sun-sensors, one aligned for the first phase of the launch, and the other for the second? What would it do to the efficiency of the trajectory if the rocket basically tried to describe two straight lines rather than an arc? And, regarding the need for a "double exposure" to get full orientational information, could you do the same if each of the sensors had two apertures and two sets of photocells?

I just have this gut feeling that it would be nice to build a really, really simple fixed-angle sensor with no moving parts and no processing. On the other hand, this is rocket science!

Maybe we could ask a buddy on the ISS to shine a laser pointer for us to follow on the way up... (I was half-thinking of laser guidance from the ground, especially since the ground components wouldn't count towards budget. But then again no...)

[pyramids]

Dave,

your way of looking at degrees-of-freedom as dimensions is very interesting; I have never heard of it seen like this before! Thanks.

Being prejudiced with how physics textbooks understand "degrees-of-freedom," I absolutely agree with your 8 dof assessment, however. Your description of dimension and derivative hits pretty close to the heart of the matter, because the kind of mathematical equations that usually come up in mechanics (whenever inertial effects matter, really) need both of these for a solution, hence typically (but not always) both would seem independent and hence degrees of freedom.

********

Paul,

your questions make me think of how some insects navigate, always keeping a fixed angle between lunar light and their flight path (which makes them spiral into lights if they mistake them for the moon). Having a tracking ground telescope send up a laser beam would almost be sufficient to follow a spiral-like, at least vaguely reasonable looking trajectory into orbit, but we need a second source (a second tracking telescope?) because of the problem that was now mentioned both as 2-angles-only (me) or 8-rather-than-9-dof (Dave).

[pauldear]

I wonder how much laser power you'd need in order to make it followable. Also, you'd have to contend with atmospheric distortion, which means you'd need some pretty schnazzy adaptive optics. Also, I'd imagine that tracking a laser beam is all-or-none: if you lose it, you have no idea where you are.

Am I right in assuming that we're dealing with two semi-independent issues here? On the one hand, there's stability (ie, how the rocket senses minor deviations from its heading, and corrects them before they become major deviations or wild oscillations); on the other, there's trajectory. The former needs very high sensitivity and rapid responses, but in a "relative" sense (ie, the rocket needs to know it's yawing, but doesn't need to know which way it's pointing). The latter presumably needs lower sensitivity and slower responses, but in an "absolute" sense (ie, the rocket doesn't need to know that it's yawing at this precise instant, but it does need to know which way it's going over a timescale of seconds).

Is this a reasonable partitioning of the problem? Does it mean that one system will struggle to do both jobs?

[pyramids]

The power you need in the lasers can (in principle) be made ridiculously low, because lasers can be made to have extremely low bandwidths and extremely high stability (I did my PhD in an experiment about getting both below 1 Hz, that is a fraction of less than 3 * 10^-15 of the visible spectrum). So it is not like you have to worry at all about someone else's laser pointer or city illumination confusing your sensor --- except for constraints of budget and making similarly involved equipment suitable for operation on a rocket.

Even in practice, however, you can buy filters that allow only one thousands of the visible spectrum to pass through off the shelf, and other equipment, etalons, too, which can further narrow that tremendously. So the only question is focusing enough of your laser light on the rocket, which would work well with a telscope of reasonable aperture, say 8in. Atmospheric distortion is not a problem, because in the reverse direction, it is at most comparable to the aperture based optical resolution limit of such a telescope.

The argument that tracking is more or less all-or-nothing is true. But with retro-reflectors on the rocket, it could be automated, excluding human operator error. We are not aiming for the full 97% reliability as I believe they do in unmanned commercial space flight, and as the track record of Apollo and the Space Shuttle would suggest of having achieved but not greatly exceeded in manned space operations, are we?

Paul, your partition of the problem is formally correct, but the trouble is that the long-term "absolute" accuracy needed from the trajectory-following aspect of the INS implies that it correctly follows all the fast and short-term fluctuations. Because turning first and accelerating later or doing it vice versa leads to different results, you cannot just integrate individual gyro and acceleration measurements to get accuracy on the slow timescale. I think I read somewhere that military grade strap-down INS tend to require <= millisecond time scale measurement update intervals to, well, "struggle" sufficiently well with this issue.

[pauldear]

Wow - I didn't realize the criteria for manned flight were so poor - only 97%? However, I presume that most of the 3% is non-catastrophic failure?

Anyway, good to hear that laser guidance isn't completely unfeasible. And your point about the atmospheric distortion nulling itself out (if I understood correctly) is well-taken, as is that about short-term and long-term stability being interwoven.

I always think (naively, perhaps) that there ought to be simple solutions to what are simple (ie, easily-stated!) problems. Some of the most elegant solutions I've seen, to all sorts of problems, seem to just sneak around the problems - a bit like the point you made about the atmospheric distortion being effectively self-nulling.

[DaveHein]

If the launch is at sunrise the rocket just needs to point straight at the Sun. Of course, you want to do this only for the orbital insertion burn, and the direction will be off a bit if it's not done on an equinox. In general, the vertical direction can be determined by a horizon detector, and the compass direction from the location of the Sun, along with knowledge of the longitude, latitude, time of the day and day of the year.

The launch would need to be done shortly after sunrise to have the greatest seperation between vertical and the Sun's position. Compass accuracy would be degraded around noon when the Sun is close to the local zenith. The elevation of the Sun also provides information about the direction of the zenith. The combination of the Sun and the horizon gives 4 independent measurements to determine the 3 dimensions of space.

Dave

[pyramids]

Paul,

the space shuttle program has had two fatal accidents in 132 launches. So it has proven a 98.5 % rate of non-fatal flights, almost as good as the design goal for any kind (fatal or non-fatal) of disaster, which was 1 in 75 (numbers taken from wikipedia). I admit, it is better than 97%, but not significantly so, I'd say. Marketing goal for human fatalities was much, much better, though (something like "necessarily" 1 in 100.000 is the language Feynman complained about when investigating the first fatality).

The Apollo program had no flight fatalities, but in a ground simulator run, all participating astronauts were consumed by fire, and several flights encountered nonfatal problems.


Dave,

could you elaborate on horizontal sensor? That expression always makes me think of the gravity-detecting kind, which obviously does not work for a guidance system (gravitational and inertial forces are indistinguishable). One would need something else, like optical detection, which will be harder than the sun sensor we discussed.