## Unmanned Systems: MEMS Inertial Sensors and Vibration

We wanted to have a discussion on MEMS inertial avionics and how improper sensor selection, and integration methods can destroy the validity of the output from such precision devices.  Most small UAVs today have only one IMU (inertial measurement unit typically consisting on a triad of accelerometers and a triad of rate gyros) and if this IMU is not outputting excellent measurements in all axes, your vehicle will not be providing for adequate navigation required for automatic control.  After all, we need to have precise navigation/state estimation in order to control precisely.  To compound the problem, it can be difficult to determine the sensors and circumstances leading to the production of erroneous data.  All too often the controls engineer or the control design itself, be it optimal, robust, adaptive, classical, or some combination thereof is blamed for poor control when in reality, the navigation itself contains the significant errors which lead to poor controller performance.

One of the problems frequently encountered is in the area of vibration rectification.  Vibration rectification is an effect where vibration can cause a bias shift in accelerometer output, typically because of asymmetries in the positive and negative accelerations. What’s that you say?  Accelerometers designed for inertial measurement of aircraft often require excellent bias stability.  This is because we are highly interested in the direction and magnitude of the gravity vector in order to approximate the aircraft Euler angles.  This may assume you are interested in attitude feedback control.  OK, so what’s the problem, I’ll just select an accelerometer with excellent bias stability, right?  Not exactly.  Due to the low power and small form-factor requirements of today’s small UAVs, MEMs accelerometers are often used in small UAV IMU applications.  What’s the problem?  Most of the available MEMs accelerometers are deficient for the purpose of inertial navigation.  This is true even of many accelerometers being used for inertial sensing today.  This is true even for MEMS inertial sensors designed and marketed for the purpose of inertial sensing!  Several capacitive type MEMS accelerometers  have proven themselves worthy of the challenge, but even specialty capacitive MEMS accelerometers designed for inertial measurement have nonlinearity problems which can cause significant error under certain dynamic conditions, specifically certain vibration.

The nonlinearity present can be significant when there is a static term combined with an oscillating term on the acceleration being measured capacitively, ie. vibration.  The good news is that you don’t have to worry about all of this if your vehicle has no vibration.  The bad news is that vibration is everywhere and even small amplitude vibrations can be very problematic at certain frequencies.  In the end, under certain vibration environments, a dc offset signal (which will cause significant errors in the rectified attitude estimations) can be generated from the vibration signal all due to the nonlinearity of the measurement of the MEMS sensor:

$\frac{\Delta^2}{d^2} \approx \frac{\Delta^2 sin^2(\omega t)}{d^2} \approx \frac{\Delta^2(1-cos(\omega t))}{2d^2}$

These nonlinearities may be mitigated by subtract them using various differential capacitor arrangements.  The squared nonlinear terms can then be eliminated and only the cubic terms and higher are consequential and these terms are at least significantly smaller than the squared terms.

Big deal, I’ll just select a sensor that specifies a low vibration rectification coefficient, right?  That’s right! Although as you can imagine, it is difficult to get performance and bias stability data on many of today’s inertial sensors with respect to their performance throughout the vibration environment you are interested.  This is especially true when dealing with today’s advance VTOL unmanned aircraft concepts where every frequency imaginable is present, aliasing other frequencies and making your PSD/FFT plots look like a porcupine.

To prevent erroneous or spurious data from presenting themselves on the inertial avionics, various “rules of thumb” and other experimental methods are common but not necessarily practical.  You may have seen various techniques being used in labs today to mitigate high frequency vibration on IMUs such as wrapping the IMU in foam.  (This technique is a bit silly as you can imagine that it will be nearly impossible to keep the IMU’s reference with respect to the airframe constant.  Furthermore, foam may collect moisture, fuel, dirt, as well as it may wear resulting in changing its “filtering” properties.) Other, more practical techniques include selecting appropriate vibration isolators, of which there are many varieties.

Repeatable integrations of inertial avionics are obviously preferable and design work should be performed to specify a suitable vibration isolation system that at a minimum is: consistently repeatable on multiple airframes, is robust and cannot easily fail, and one that exhibits high attenuation at frequencies beyond those that you are interested in sensing.   It should be clear that there is no such thing as a generic integration design suitable for all inertial avionics and on all UAVs.  It is up to the designer to understand all of the magnitude & frequency content that the inertial sensor will be subject to, and which of this content must be destroyed in order to not offend the sensor you have chosen.

There are numerous validation methods that can be used to verify your vehicles navigation.  The point is this validation needs to be performed prior to testing controllers in flight.  Otherwise, you may discover control problems (poor closed loop damping) and then not know if the problems stem from navigation or control.

-Lance Holly

## Gyro Drift: Why You Can’t Walk in a Straight Line with Your Eyes Closed

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:

$\theta = \int_{T_1}^{T_2} \omega dt = \omega(T_2-T_1)$ for constant $\omega$

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:

$\theta = \int_{T_1}^{T_2} \omega + error dt = \omega(T_2-T_1) + error(T_2-T_1)$ for constant $\omega$ 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.

-Bill Donovan

## How to Optimize an Aircraft Design: Part 1 of Many

The first step in optimizing an aircraft design is to realize that you can’t. This may be a bit disappointing given the title of this post, but what I mean is that there is no such thing as an “optimal” aircraft design in the universal sense. Whenever you are talking about a system with multiple objectives (low cost, high performance, etc.) you must start the optimization process with a question: What am I trying to optimize for? Do I want to optimize the aircraft for manufacturing cost? How about maximizing range instead? The truth is that there are multiple things that we are trying to optimize for all at once. This leads to the concept of a cost function. A cost function defines all of the things that we are trying to optimize in addition to their respective weighting. A simple generic cost function is shown here:

$J=w_{1}C_{1}+w_{2}C_{2}+w_{3}C_{3}+...$

We can give this cost function some meat by putting in actual properties we are tying to optimize, such as weight, lift-to-drag, radar cross-section, etc., but this is where many engineers cause themselves problems. We have a tendency to overcomplicate the problem and add costs that don’t belong in the cost function. If the first question we must ask ourselves when performing an optimization is “What are you trying to optimize?” then the second, and equally important question is “Why?”.

As an example let’s say you want to maximize lift-to-drag. Here’s how a conversation with me would go:

You: I want to optimize L/D of the airplane, helicopter, lawn dart, and/or flying squirrel I’m working on.

Me: Why?

You: Optimizing L/D will give the best cruise performance. I want the best cruise performance possible.

Me: Why?

You: Optimizing cruise performance will result in minimum fuel burn. I want to minimize fuel burn.

Me: Why?

You: Minimizing fuel burn will minimize the operating cost of the airplane.

Me: Oh. Sounds good.

And there you have it. You think that you want to optimize one thing (L/D in this case), but that is just a tool you are using to achieve your overall goal of minimizing operating costs. It is important to understand that you have to get to the root goals of what you are trying to optimize before you start the process. Otherwise you will end up pursuing the wrong designs.

Now that you define what you are optimizing for and why you are optimizing those parameters, you must realize that in any multi-objective optimization there is rarely one optimal point. Rather there is what is called a Pareto set of optimal points. Pareto sets are built around Pareto optimality, which is defined as:

“A Pareto optimal outcome is one such that no-one could be made better off without making someone else worse off.”

In airplane terms we could look at a case where we want to maximize vehicle range while minimizing production cost. We would perform dozens (or hundreds) of preliminary designs of different aircraft (different configurations, engine types, etc.) with various range requirements. For each of these designs, we would determine a production cost estimate. For a given range requirement we would see that different designs have different production costs, but we would also see that there is a limit that no matter how hard we try we cant get the cost below this point. We then change the range requirement and repeat the process until we reach the lower bound of cost. After multiple iterations at different ranges we would have a plot similar to whats shown below. It is clear that the designs are bounded by a barrier. This barrier is referred to as the Pareto Frontier. The designs on the Pareto Frontier are considered in the Pareto Set. With the Pareto Frontier we can now establish a simple relationship between production cost and aircraft range. If we extend this process to all of our goals in our cost function, we can understand that the role of optimization is to clearly define the relationship between all of our goals and how each goal affects the others. So even though it may not be possible to design an “optimal” aircraft, you can design an aircraft that lies in the Pareto Set of optimal designs.

Pareto Set

Now there is just too much information on aircraft design to cover in a short post like this so I will stop here and continue at a later date. In the mean time if you are interested in aircraft optimization, you should start with aircraft design books. Roskam, Raymer, Torenbeek, and Nicholai are obvious must reads. For more info specifically on aircraft optimization I would recommend looking into Ilan Kroo at Stanford (http://aero.stanford.edu/people/kroo.html).

Written by Bill Donovan

Bill Donovan is a managing member of Pulse Aerospace.

## Unmanned Systems: Acronyms and Nomenclature

The commonly used term for unmanned aircraft has morphed over the years from drone to remotely piloted vehicle (RPV) to unmanned aerial vehicle (UAV), and now to unmanned aircraft system (UAS). Recently the US Department of Defense has stated that the currently accepted terms are unmanned aircraft system (UAS) and unmanned aircraft (UA). UAS describes the entire system including the ground station, support equipment, launching equipment, etc. UA is used just for the aircraft itself. The DoD believes this move to UAS is important to indicate that we are dealing with systems here and not just aircraft. I have to say that I agree with this, but the whole thing is a bit annoying.

My main problem with the current nomenclature is the need to drop the term UAV, and instead use UA. This puts people and companies in this industry in an interesting predicament: If you use the term UAV you may seem out-of-the-loop and not with the current times. However, there are still a lot of people that use the term UAV as opposed to UA or UAS. According to the Google Trend plot above , UAS has just started to take over UAV in web search trending. So if you use UAS, for example on your website, you may miss out on search traffic. In the end I think it makes sense to follow the standard of the DoD, but I would much prefer using UAV to refer to the vehicle and UAS to refer to the system. UA just makes me think of Unites Airlines, or Under Armour, or anything not UAS related. Furthermore, I have never been a huge fan of “Unmanned” part of the designation. Not only is this gender specific, but it also suggests that someone isn’t “manning” the system, which is completely untrue of almost any UAS currently in use. I personally prefer Uninhabited as this is more telling of the real scenario. Despite what movies may make us believe, these autonomous systems are far from autonomous and I believe the term unmanned furthers that misconception.

Nonetheless I have given in to the general consensus and I regularly use the Unmanned Aircraft System term when talking about what I do. Still, I can’t force myself to use the UA acronym. In the end though, like all trends, these naming conventions appear to have a certain cyclical repetition. Like Reebok Pumps and acid wash jeans, it appears that the oldest designation, drone, is making a strong comeback (see below). Maybe it’s time to give up and go with the flow.

-Bill Donovan

## Welcome to the Pulse Aerospace Tech Journal

Hello and welcome to the Pulse Aerospace Tech Journal. Pulse Aerospace is a new company built around providing unmanned system products and services that help our customers acquire airborne sensor data more efficiently and more effectively. We achieve this goal through the use of advanced design, analysis, modelling, and control methods including multidisciplinary optimization, multivariable system identification, and multivariable controller design utilizing advanced h-infinity methodologies.

The main contributors to this blog will be Bill Donovan (myself) and Lance Holly. Lance and I have been working together for over 8 years on unmanned systems ranging from small 10lbs fixed wing systems up to 1,200 lbs, 26 foot wingspan vehicles. We have worked on fixed wing systems, helicopter systems, and some things in between. We’ve operated unmanned systems all around the world including Antarctica and Greenland. I also teach a short course at the University of Kansas on the conceptual design of Unmanned Aircraft Systems (http://aeroshortcourses.ku.edu/course.php?aid=12).

The world of unmanned aircraft systems is vast and growing rapidly. It is our belief that in this world of rapid development of multidisciplinary systems, strategic partnerships and open constructive dialogue will be necessary to advance the state of the art to the next levels. In our experiences designing, operating, and training users on unmanned systems, we have fielded a wide variety of questions from people with diverse backgrounds. As the field of UAS grows further into the mainstream, there will be even more users that are new to the technologies involved. It is our goal to provide high-level discussions and links to the resources we find useful in the areas of our expertise.

This is a vast community of people doing some really advanced stuff. The more we share, discuss, and collaborate the more we will be able to advance.

-Bill Donovan