The other day I was watching Mythbusters and saw something that comes up often when discussing flight control systems. The show, which aired on October 12, was named “Walk a Straight Line.” The premise of the myth is that people cannot walk in a straight line when they don’t have a point of reference, such as when they are blindfolded. I think everyone has some experience with this as we have all tried walking through a dark room inevitably bumping into any number of shin-height objects.
The show went on to prove that, indeed, it is difficult, if not impossible to navigate with your eyes closed. The first thing that piqued my interest in the myth is that the reason for our navigational difficulty when blindfolded is similar to what happens to an unmanned aircraft when you try to navigate with rate gyros alone. Essentially, when we close our eyes, we now rely on our internal sensors, which can detect movement, but not position. For example, if you sit in a chair, close your eyes, then let someone spin you slowly. You will be able to tell which direction you are spinning, and roughly how fast you are spinning. If you combine these two pieces of information with the amount of time you were spinning you can arrive at an estimate of how far you have been rotated. For the mathematically inclined you just integrated your rotational rate through time to estimate the angle you rotated as is shown here:
This is essentially what we are doing when trying to blindly walk in a straight line: constantly use our “rate sensor” to estimate how far we have turned off course. The problem is that our internal rate sensor, much like the rate gyros in a UAV, have some bias error. When we introduce this bias error into the above equation we get:
for constant and constant error
So when we introduce an error in the rate measurement and integrate through time, we see that the error in our attitude estimate grows with time. This is why Jamie and Adam diverged more and more the further they walked. You might be asking, “Is the error really constant?” The answer is no, but it is typically biased in one direction. This explains why Adam constantly veered to the left.
So how do we deal with this rate bias? You can improve the sensor to minimize the bias as is done in fiber-optic gyros and ring-laser gyros, or you can add another sensor that corrects for the bias. In people this second sensor is our eyes. In aircraft this sensor can be a magnetometer for heading corrections, or accelerometers for pitch and roll attitude correction. Getting these sensors to work together can be a trick, which is where the wonderful Kalman filter comes into play. I won’t get into any details of Kalman filtering, except to say that it is a method of combining multiple measurements to arrive at the best guess of a systems current state.
There was one more part to the myth that was really interesting. At the end of the show, Jamie and Adam linked themselves together with a ladder while they walked. The concept was that they would cancel the error of the other person and walk in a straighter line. The results weren’t great, but the concept does hold promise. If you build an inertial measurement unit for a UAV using multiple rate gyros in each axis and average their outputs, you can actually get better results.
The last thing I wanted to mention is that at one point in the show Jamie and Adam put buckets on their head to simulate poor visibility. I have been through survival training in Antarctica and this is definitely part of the course. They call it the bucket-head excercise. It is meant to simulate white-out conditions. It is shocking how disoriented you can get when you can’t see your surroundings. There are multiple methods people use to navigate in these scenarios, but the most interesting is what the New Zealand teams do. They use the wind as a type of compass. If you turn until the wind is at your back (or your side or face, etc), then you can use this information to get some amount of orientation information assuming the wind isn’t changing directions. Pretty interesting.