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Reason #1 to very carefully design your system. |
Then you too can be on the cutting edge of the "cheaper" and "better" - just not necessarily "faster" - movement in aerospace! Join us in our attempt to build the first (we think!) |
As serious amateur rocket enthusiasts and budding aerospace engineers, we must point out that an INS is a fantastic way to do active rocket stabilization. Heck, NASA does it, ESA does it, NASDA does it, everyone does it. It's just until now the sensors and computing horsepower have been out of reach of the everyday rocket scientist. Finally, the availability of cheap, off the shelf microcontrollers coupled with micromachined inertial sensors is making cheap and, umm, fairly accurate INS an idea who's time has come.
What is an Inertial Navigation System (INS)?
Is this really rocket science?
What is an Inertial Measurement Unit (IMU)?
What problems are there with IMUs?
How can a GPS unit help?
What's all this about absolute attitude sensing?
Now that you know where you are, how do you control the rocket?
Ok, fine, but have you actually accomplished?
What are you working on right now?
What are your future plans?
INS Resources and Links
What is an Inertial Navigation System (INS)?
Every object that is free to move in space has six "degrees of freedom" - or ways it can move. There are three linear degrees of freedom (x,y,z) that specify your position and three rotational degrees of freedom (theta (pitch), psi (yaw), and phi (roll)) that specify your attitude. If you know these six variables, you know where you are and which way you're pointed - a handy thing to know for controlling rockets. If you know them over a period of time, then you can also figure out how fast you're moving, and what your acceleration rate is. It's not quite rocket science, but we're getting there.
The inertial part of the INS is the way we obtain these variables. We essentially go backwards: we use accelerometers (devices that measure acceleration) and rate gyroscopes (devices which measure rotational velocity) to sense how the rocket is accelerating and rotating in space. We then get back to the position and attitude by integrating the accelerometers twice and the rate gyros once. Although you could do the integration by making complicated analog circuits, we've chosen to use cheap, off-the-shelf microcontrollers (computers on a chip) to do it digitally.
So, we have our sensors, we have our microcontroller, and thus we have our position and attitude calculated. Now, the fun begins: we can use control theory - a branch of electrical and mechanical engineering - to control the rocket with thrusters or fins or whatever control mechanism we choose. That's where the navigation system part comes in. We're essentially closing the loop between the rocket, the outside world, and where we want to be.
Is this really Rocket Science?
YES! Heck, anyone can measure the inertial sensors but controlling the rocket is the key. We're talking full blown modern control theory here: fusing data from multiple sources, Kalman filtering, robust control, etc. Actively stabilizing a rocket, while correcting for gravity turning and wind disturbance, is the quintessential control problem of "balancing the broomstick" in three dimensions. It is an unstable system which must be actively controlled to be fully stable
What is an Inertial Measurement Unit (IMU)?
An inertial measurement unit, or IMU, is a "clump" of six inertial sensors. Three linear accelerometers and three rate gyros make up our IMU. Usually, an IMU also contains a computational unit to do the position calculations based off of the sensors.
What problems are there with IMUs?
The catch to IMUs are the error from sensors. Although the error can be small - in the milli'g's for some accelerometers - it is nontrivial. And unfortunately, it gets really nontrivial when you integrate it twice over long periods of time. Basically, you integrate the noise in the system along with the actual signal. This noise starts to accumulate (after all, you're integrating it!) and that shows up as a slow but then very fast drift. For example, if you put your IMU on your test bench and turn it on, it'll know where it is (e.g., 0,0,0 @ 0,0,0). But then the errors drift in. Slowly at first, but they're cumulative. Within no time (10's of minutes to hours) your IMU thinks it's traveling Mach 18 and is somewhere in deep space. This is not a serious problem if your flight is very, very short (less than a minute). However, if you want to push your flight into the minutes regime, you have to start dealing with this serious drift error.
And then there's always more problems in store: for example, since a body rotates around its center of mass, that’s where the linear accelerometers should be, so they don't pick up components of pitch, yaw, and roll. If a horizontal sensor is off-axis (as it usually is, since it's hard to get perfectly aligned) and the rocket has a high spin component, it will pick up a sinusoidal component of horizontal acceleration. This nasty problem is referred to as sensor cross-coupling.
Obviously, one way to minimize error is to build a better, smarter IMU. And trust us, we're trying (you can see below for more info on that).
How can a GPS unit help?
GPS - Global Positioning System - receivers are great because they'll give you an absolute data point on where you are. Granted, they have error, but their error doesn't drift to infinity and beyond - and you can characterize it. With differential GPS (DGPS) you can get your error down to tens of meters instead of hundreds of meters. So we can "null" out the IMU drift error from the GPS data.
So why can't you just use GPS? Usually, GPS receivers give out their position only once a second, and that's obviously far too slow to use on a fast, unstable rocket. And further, the GPS doesn't give you any attitude information - it just gives position.
Joining an INS and a GPS into a single unit, however, is definitely the first step towards a real Inertial Navigation System.
What's all this about absolute attitude sensing?
So we can use GPS to null our position errors, but what about our attitude errors? There are several sensors you can use to determine your attitude (besides a personality assessment): our two favorites are a sun sensor and a 3D magnetic compass.
Sun sensors simply track the sun using optics. It works, just don't do it on a cloudy day. We prefer the magnetic way: using a theoretical model of the Earth's magnetic field, coupled with a 3D magnetometer (a 3D "compass"), can give you a pretty good idea of which way your vehicle is pointed. You can't get position, and local anomalies make it unusable near the ground, but it's another source of data.
So now we have three independent sensors, all with different characteristics, working together: the IMU, the GPS and the electronic compass.
Now we're really cooking.
Now that you know where you are, how do you control the rocket?
Now we know where we, where we are heading, and where we are pointed, and we can calculate where we want to go. At this point, we actually have to control the rocket. This is obviously the hardest part of the whole project. Before we even begin to control the rocket, we need to do a lot of control theory simulation to learn how to get there: what is the "plant" (control theory speak for "system dynamics")? What is the "control plan" (the best way to control it)? How fast does our INS have to be? How fast does the controller have to be?
Once we answer these questions, then we move on to an even bigger problem: how do we actually control the rocket? Fins are easy, but they create drag and don't work once you get out of the atmosphere. Thrust Vector Control (TVC) is great but requires large, heavy actuators which lower the rocket’s center of mass relative to its center of pressure (not a good thing!). And small Reaction Control Systems (RCS, or "thrusters") are good but require a separate fuel supply and could get large and heavy as well. So ask again in about a year!
Ok, fine, but what have you actually accomplished?
We've launch two rockets so far.
Launch Vehicle 0, or LV0, was our first attempt at a rocket. It was, uh, small, and err, simple. It proved a few things: we could launch a rocket with an amateur TV transmitter and broadcast data down. The data was a simple Z-axis accelerometer digitized by a simple 8-bit microcontroller. It was fun, and got us started. Here's the full story.
We moved on to Launch Vehicle 1, or LV1, and upped the complexity. Now we had color video camera, a manual uplink for backup recovery of the rocket, a faster data downlink, a multistage recovery system and the first honest-to-Betsy IMU. Although the IMU design wasn't very pretty, and it simply streamed data down to the ground, it did work and on April 11, 1999, we launched it and gathered data. Here's the full story. And here's the data from the launch.
What are you working on right now?
We're refining what we've already done. We've upped the complexity again, and while we've kept the payload just about the same, we've completely redesigned the flight computer. Dubbed "LV1b", it's got a more advanced IMU coupled to a 33MHz RISC microcontroller. And this time, we'll be doing actual position calculation on board the flight computer in addition to streaming down the raw data in real time. We also have 1MB of SRAM on board to store additional data on the flight so we can start to characterize the dynamics of our rocket. And finally we'll be adding a GPS unit on board. We are planning to launch sometime in spring or summer 2000.
Here's more on LV1b (11/04/99 Warning: may not be up for another week or so).
What are your future plans?
LV2 is just starting the development process. We'll start with a full blown IMU, coupled with a full blown GPS system, coupled with an electronic compass, coupled with a major avionics redesign based around the CANbus, all thrown in a 4m rocket designed to go 16.7km (55,000ft). We'll characterize LV2, and then begin the first of our inertial navigation experiments on it. For more information on LV2, including a kick-butt whitepaper on the CANbus-based avionics system, click here.
In the future, we'll be updating this page more frequently, and adding the resources we use to build our INS. Come back and visit us soon!
PSAS Inertal Navigation Collaboration Page
We're currently using a TWIKI collaboration page for all of the latest work on inertial measurement and navigation.
Please Click here for all of our current work.