# Introduction to Control Moment Gyroscopes

## Key Points

- A Control Moment Gyroscope is just a wheel attached to a motor. The whole thing can be flipped in different directions with different motors to make your spacecraft twist. The wheel is usually heavy and spins at a high speed that does not change.
- Understanding how gryoscopes push back when you push on them can be (very) challenging and even engineers with decades of experience can be seen in meetings grasping air with their right hands to figure out what will happen. If you’re confused, you’re in good company!
- Like Reaction Wheels, Control Moment Gyroscopes make a spacecraft twist and turn about the spacecraft’s center of mass. It doesn’t matter how far away the gyroscopes are from this center or how they are oriented, the spacecraft will always rotate about the center of mass.
- Gyroscopes can be designed to rotate spacecraft in two axes by putting the wheels on special perpendicular mounts called gimbals. This is different than Reaction Wheels, which can only rotate a spacecraft in one axis.

## Introduction

Control Momenet Gyroscopes are often found on the largest spacecraft and in satellites that need to twist around quickly. They provide more torque than Reaction Wheels and they provide that torque for much less power. These benefits come at a cost, though, as they’re heavier and more complex both mechanically and in their control algorithms.

## A Bit More Detail

In some ways, Control Moment Gyroscopes (CMGs) are easier than Reaction Wheels. For instance:

- Gyroscopes almost always spin at the same speed while Reaction Wheels change their speed all the time.
- Since Gyroscopes are designed to operate at a constant high speed, you just need a little bit of power to keep them going whereas Reaction Wheels take power to speed up and slow down.
- Because they’re spinning so fast and they tend to be heavy, they have high angular momentum and they can put much higher torques into your spacecraft than most Reaction Wheels.

Where things get tricky is that gyroscopes are a lot of mechanisms in one package: you’ve got the wheel, its motor, and one motorized gimbal per axis (so two gimbals/motors for a dual-axis version). There may also be lubrication mechanisms so all the bearings stay protected. If any one of those things go wrong, the whole system tends to fail. Gyroscopes also tend to be much heaver than Reaction Wheels. And, maybe most importantly, the math and control laws tend to be more complex.

Gryoscopes are all about “angular momentum”. Forces, torques, moments… whatever you’re applying to the gyroscopes, you convert everything to angular momentum. The spacecraft as a whole will align itself with the new angular momentum vector.

## Different Types of Control Moment Gyroscopes

There are three main variations that are used in spacecraft:

**Single Axis**: This is one wheel on one gimbal. Torquing the gimbal moves the wheel one way and the spacecraft in the opposite direction.**Dual Axis**: This is one wheel on a gimbal and this is all set inside a second gimbal. You can apply torque to either or both gimbals to change the angular momentum vector in three dimensions.**Variable Speed**: It can change its wheel speed to change the magnitude of its angular momentum vector. This can help you avoid singularities where it’s “stuck” pointing in the same axis as the external torque you want to counter.

The control software for these are progressively more complex.

## Singularities

Singularities are configurations of your gyroscope or gyroscopes that make them functionally useless to you. Significant time is spent modeling and testing things to, first, understand the behavior of the versions you build and, second, to show how you’ll avoid the singularities. There are a few singularity phrases you may hear:

**Saturation**: This is a holdover term from reaction wheels which “saturate” when they cannot increase the magnitude of their angular momentum any further. (In other words, they’re already spinning as fast as they can and you can’t speed them up anymore.) But control moment gyroscopes spin at a constant speed. What people mean by saturation in this case is that the angular momentum of the gyroscope is pointing in a direction that cannot help you. For a single gyroscope, this would be when the vector points in precisely the same direction as the angular momentum vector you want to change. Since there’s no difference, there’s no way to pull or push anything.**External Singularity**: This is a subset of the saturation case. In this scenario, the angular momentum of your gyroscope system is aligned with the angular momentum of external torque, so it can’t fight back. For instance, if the atmosphere is constantly trying to roll your spacecraft then your gyroscope’s angular momentum vector will eventually align with that roll angular momentum vector and you will “saturate”.**Internal Singularity**: This is when you have multiple gyroscopes and twisting one negatively affects the performance of the others. The anti-parallel singularity is an example.**Anti-Parallel Singularity**: In this case, the different angular momentum vectors are pointing along the same axis, but some are pointing one way and some are pointing another. If there’s an external torque along that axis, you can’t do anything about it since there’s no difference in angles.**Coordinate System**: In the old days, some parameters and math models would result in mathematical singularities where numbers went to infinity. It wasn’t the mechanism, but the control software that was the problem. Modern control theory doesn’t have this problem, but it’s worth being aware of for historical reasons.**Gimbal stops**: Older versions could not twist all the way around and would literally run into hard stops if you twisted them too far. This created dead zones that made the math and operation even more complex. Modern systems can twist around fully, but you may hear people talk about this still.

## Clusters

Image Credit: NASA

Reaction wheels, which are locked in a specific axis, tend to be more sensitive to how you arrange them than control moment gyroscopes because most gyroscopes can rotate in any direction. For example, the black gyroscopes in the image above are on the ISS and they are all installed the same way. That being said, singularity avoidance and the way angular momentum vectors stack does lead to optimization opportunities.

Two popular layouts are pyramid and rooftop. The second link in the “Curated Papers” section below has a good overview and discussion of these options.

## Design Considerations

The most practical problem you have is that most spacecraft use Reaction Wheels and/or Magnetic Torque Rods so market supply/demand has most vendors focusing on those things. Gryoscopes are also more complex to operate and they couple with your structure in ways that make it hard to buy them off the shelf. This means that it can be tough to find someone to build Control Moment Gyroscopes for you.

If you go this route, consider the following hardware topics:

- Most bearings in these assemblies are angular-contact instead of pure radial or axial. Getting and keeping the bearing preload where you need it through all thermal conditions is a tremendous challenge. Do not overlook the temperature cases!
- Lubrication tends to be supplied by an active system. The ISS uses a refined mineral oil called KG80 that they keep between 15.6 to 26.7 degrees Celsius.
- One of the ways the ISS believes they failed two of their original gyroscopes was by gimbaling (twisting) them too quickly. They originally limited themselves to 3.1 degrees per second and now keep themselves below 0.8 degrees per second.
- When in doubt, choose the hardest possible material you can for the preload washers and any bearing surfaces. The ISS switched from A286 to 51200 for their preload nut material.
- Put sensors everywhere: the ISS has accelerometers, temperature sensors, and current measuring systems to help them deduce what’s happening.
- Pay special attention to cleaning everything thoroughly. This may seem obvious, but the ISS found small, hard particles in their failed assemblies and they now use a more thorough cleaning protocol.

For control algorithms, you get into what may be one of the most complex areas of large spacecraft implementation. Consider:

- You need to know the angular momentum of the spacecraft to a good accuracy. Spacecraft tend to have high sensitivity star trackers, inertial measuring units, and other types of rate sensors to help figure this out.
- Sets of gyroscopes dynamically couple with each other. If you apply a torque to one, you’re really applying it to all of them, so you need to apply that torque in a way that addresses the total angular momentum of the spacecraft, not just that gyroscope.
- The flexibility (stiffness) of your spacecraft matters. If you torque the gyroscopes and your structure deflects, you can get undesirable feedback loops and settling behavior. Most systems take into account the stiffness of the structure.

Three steering algorithms you can look into more detail on are the Moore-Penrose Psuedoinverse, the Singularity Robust Inverse, and the Local Gradient. In the second reference of the Curated Papers section, you can find more details on the math and simulation comparison of their performance.

## Curated Videos:

- https://www.youtube.com/watch?v=XPUuF_dECVI

Great video with demonstrations and math. Have to watch it several times! Starts at 14:05 - https://www.youtube.com/watch?v=HmmbOVfHqcg

Good animated video that helps explain why the gyroscope seems to tilt in the wrong place when you push on it. - https://www.youtube.com/watch?v=n5bKzBZ7XuM

Short video with a practical explanation of gyroscopic precession.

## Curated Papers

- https://ntrs.nasa.gov/api/citations/20150021962/downloads/20150021962.pdf

This talks mostly about how the ISS gyroscopes are simulated, if you make a couple of simplifying assumptions. It’s included in this list because the mathematical part of the paper is a good introduction into some of the cross-coupling math involved. - https://yorkspace.library.yorku.ca/xmlui/bitstream/handle/10315/37483/KrishnaMoorthy_Chitiiran__2019_Masters.pdf?sequence=2&isAllowed=y

How you arrange your control moment gyroscopes matters. This thesis tackles this topic and also provides a good overview of control algorithms. Highly recommended for a medium depth overview. - http://adsabs.harvard.edu/full/1997ESASP.381..523R

This paper is almost 25 years old, but math doesn’t change. It talks about singularity avoidance, stiffness, and the basics of control law. - https://ntrs.nasa.gov/citations/20100021932

This is the Lessons Learned report on the first two control moment gyroscopes on the ISS failed. It’s packed with great information and show how even tiny problems can make things fail.

## Glossary

These are terms you may hear when working with these systems.

**CMG**: The abbreviation for Control Moment Gyroscopes

**Singularity:** There are a few ways you can reduce or zero out the effectiveness of these systems and they all tend to get lumped into the general category of, “how are you avoiding singularities?”

**Stator: **The stator and rotor both are the parts of the electrical motor. The significant difference between the rotor and the stator is that the rotor is the rotating part of the motor whereas the stator is the stationary part of the motor. ← Rewrite in own words

**Torque Equilibrium Attitude (TEA)**: Attitude (orientation) of the spacecraft where the balance of external torques is the lowest. Because, for instance, the atmosphere is a little thicker on the day side of the Earth then the night side, the equilibrium attitude is usually more of range that you try to operate in to prevent overworking your Reaction Wheels or Control Moment Gyroscopes too much.

**Tribology**: The science and engineering of friction and lubrication.

**Variable Speed Control Moment Gyroscope**: A gyroscope that changes the wheel speed to change the magnitude of its angular momentum. This helps the gyroscope avoid singularities where its angular momentum is “stuck” pointing in a direction.