# How are rockets guided to follow specific trajectory?

For a rocket (and its stages, if it's a multistage rocket) to successfully deploy its payload into the desired orbit, it has to follow a specific trajectory with a specific velocity.

I know rockets alter/maintain their course with gimbaled engines, which can be considered the actuator in a control loop. But what is rocket's reference in the control system loop? From where do gimbals get the information on how they should position themselves?

Is the desired trajectory transmitted to the vehicle during flight? Does the vehicle itself have the trajectory uploaded/computed on board? (this is the crucial piece I'm waiting answer for, some references would be nice)

EDIT:

The possible duplicate question is in many ways similar to mine, but it is more general. Answers there do not address the specifics of feeding desired trajectory (i.e. the reference) in launcher's control loop. That said, answers there are still very informative and the OP apparently got what he needed. Answers (or comments) in other questions do touch the subject, but again not the specifics I would like to know. See discussion in comments with Brian Lynch, it may help clarify.

• This is more generally asking about how a closed-loop control system works. You have a desired trajectory, the system compares the current trajectory to desired, the difference is used to generate a control action that will bring the rocket closer to the desired trajectory. That can also be mixed with open-loop control that sends direct commands to the rocket control system based on the desired trajectory alone. – Brian Lynch Jan 4 '16 at 23:47
• @BrianLynch - My question was not meant to be about control systems generally, though I admit I didn't manage to word it to sound as intended. I am asking about rocket launches specifically. So, a desired trajectory is probably calculated in advance. Now,... how and where from does rocket's control system read that information and pass it on to actuators? – James C Jan 4 '16 at 23:50
• So you are asking about how the desired trajectory is transmitted to the vehicle or if the vehicle itself has the trajectory uploaded/computed on board? – Brian Lynch Jan 4 '16 at 23:57
• Possible duplicate of How does a rocket navigate during launch? – Russell Borogove Jan 5 '16 at 0:37
• @RussellBorogove - Thank you for your effort sir, but that is not the case. I did not get my answer in Bill's question. OP is asking pretty much the same thing and got an answer with a lot of info on the control system. But I don't see the answer to how trajectoy data (i.e. the reference) is fed to launcher's controls. He got his answer, but I did not. Please do not be so quick on closing question before making sure it's fine. OTOH if I failed to express my question properly, then it is my fault and let it be closed :) – James C Jan 5 '16 at 1:11

If a controls engineer was designing a rocket guidance algorithm, he would load a desired trajectory into the algorithm and try to follow it. :) There is a place for that type of algorithm, but ascent rockets don't typically face enough complicated optimization or "path constraints" to need that. They can be both less and more adaptive to events during the mission. Early on while in the atmosphere, they can (e.g.: Saturn V, STS, any number of other systems I'm not familiar with) use fixed tables of attitude vs time, altitude, or velocity. These are pre-calculated on the ground, sometimes using wind estimates only hours old, to fly the rocket through the maximum dynamic pressure zone at very low angles of attack. Once the atmosphere is mostly gone (usually around the time of first stage separation), they can use a closed loop scheme that simulates the rest of the flight, sees where it is expected to end up, and try to make that state match the desired end state. There is a subtle difference here: they aren't trying to follow a particular reference trajectory, but rather find the best trajectory (or at least a feasible one) to get to where they are going at the end. This is like the difference between driving on the shoulder when the main line of the freeway is bogged down and choosing an alternate route entirely if that is better.

The desired trajectory is computed on the ground before launch. The rocket determines how well it is following the planned path, and may make some adjustments if required (Most notably the Falcon 9).

There are two reference points of interest. The first is how position is modeled, the second is how the attitude is modeled. Position references are usually done in a coordinate system called Earth Centered Inertial. This basically calls the center of the Earth 0,0,0 with axis being the poles, 0 and 90 degree longitude equator points. The I comes into effect because while the ECI coordinates are set at a point in time, they adjust based on the rotation of the Earth. So an object on the ground not moving will be moving with the rotational speed of the Earth. This is found either by a high precision accelerometer (Part of a device called an IMU) or GPS. Usually the IMU is used for primary navigation, supported by GPS as a backup in case of serious problem.

As for the orientation, one can use a number of systems. For rockets, I believe the most common is Quaternions with a reference point of the position straight down. This can be measured by a number of methods, usually an IMU is used, which is a device that basically figures the difference in pointing from the start point.

• This answers much of my question, but the crucial bit still remains. You say in 1st part that rocket determines how well it is following the planned path. How does it determine this? Where from does it get the data on planned path during the flight? If you can expand your answer with this it will be just what I am looking for. If this differs between various rockets, or different eras of spaceflight, I will be happy to know it too. Thank you! – James C Jan 5 '16 at 20:39
• Add some information on where the current position data comes from and I'll upvote. – Russell Borogove Jan 5 '16 at 20:41
• Added the current position calculation information. – PearsonArtPhoto Jan 5 '16 at 21:41

But what is rocket's reference in the control system loop? From where do gimbals get the information on how they should position themselves?

This is a collaborative effort split amongst the design of the flight software, pre-launch flight planning, commands from the ground, and the operation of the flight software. The key components of the flight software involved in this process are moding, guidance, navigation, and control.

Moding (which goes by various names) determines overall spacecraft operations. Even ignoring the myriad failure, recovery, and abort modes, launch vehicles switch operating modes a number of times during the course of a launch. The mode dictates which algorithms and magic numbers (e.g., control gains) the guidance, navigation, and control systems use to take the spacecraft to the desired orbit.

The navigation software uses a variety of sensors to keep track of the vehicle's state. This state includes position and velocity, attitude and attitude rate, plus other parameters such as angle of attack and sideslip. The vehicle's inertial measurement unit, which senses acceleration and angular velocity, is one of the key inputs to the navigation system. The Saturn V had a gimbaled IMU, so it reported acceleration with respect to some inertial frame. This was very expensive and prone to error. Modern accelerometers are fixed with respect to the vehicle and this report sensed acceleration in a frame fixed with respect to the vehicle. This sensed acceleration needs to be transformed to some inertial frame to be of use.

The accelerometers sense acceleration to thrust and drag, but not gravity. (Accelerometers cannot sense gravity.) The navigation system needs to augment those sensed accelerations with a model of the Earth's gravitational field. Integrating the computed acceleration to yield velocity, and then integrating that to yield position is called dead reckoning. Without correction, the estimated state would drift from the true state. Modern navigation systems use GPS to provide an alternative estimate of position. Reconciling the conflict between these disparate measurements is the job of the navigation system's Kalman filter.

The navigation system feeds the estimated state to the guidance system. The guidance system uses the flight plan (calculated on the ground, prior to launch) to determine the error between the planned and navigated state. This error might be due to thrusters not behaving quite as planned, a change in the wind, a specifically-planned maneuver such as the roll program initiated shortly after launch, or errors in the navigated state. Whatever the cause, the vehicle's planned and navigated state don't agree with one another.

The guidance system feeds this state error to the control system. The control system uses the state error as a hint to issue commands to various actuators. The error has to be used as just a hint; small errors are best left uncorrected, large errors can't be corrected instantaneously, and some errors just aren't corrected at all. In the case of vehicles with throttleable engines, changing the thrust level can help reduce the errors in velocity and position.

Correcting errors in attitude and attitude rate is the job of the attitude controller. A number of different approaches have been and continue to be used for this. One widely-used approach is a phase plane controller. I'll use roll as an example. Suppose the roll error is negative and the roll rate error is positive. The best thing to do might be well be to do nothing. The positive rate error will eventually result in the vehicle having the correct roll angle. A phase plane controller has dead bands where nothing is done. Outside of these dead bands, the phase plane control indicates that something does need to be done. The controller's gain settings translates this something into commands to the gimbals, if the rocket has gimbaled engines. Some rockets don't have gimbaled engines; they instead use vernier jets or thrust vectoring. Whatever the case, errors outside of the dead band result in actuator commands that move the spacecraft toward the desired attitude / attitude rate.

• @JamesC - i think a second question about guidance systems predating modern computers would be the better solution. The idea here is more to build up a set of questions and answers that can be used to get specific information quickly. That topic is different enough to merit its own question. – kim holder wants Monica back Jan 7 '16 at 2:47
• @kimholder - I get your point and will follow your advice, thank you. However, the main part of the original question is still not answered. Only then will it be justified to accept the answer. – James C Jan 7 '16 at 5:18
• @David - You said: The guidance system uses the flight plan (calculated on the ground, prior to launch). Is this flight plan stored in rocket computer's memory? If you can just expand your answer with info on this, the answer will be complete. Thank you! – James C Jan 7 '16 at 23:09

Folowing the sequence of comments to date, I think the universe of possible answers comes down to just two:

• Measurement

And that's it. I don't think I need to exand on the first, and you can make it as complicated as you like. The latter can be:

• Measurement from the vehicle

• inertial (accelerometer or gyroscope, these days called IMU)
• external (star-tracker, ground based radio navigation, GPS)
• (For completeness) Measurement from the ground and telecommand