How can a deep-space spacecraft determine in real time the direction of delta-v?

Question

My spacecraft knows it wants to add a certain delta-v in a certain direction to its motion, relative to the stars. It will calculate current mass based on propellant usage history, which hasn't been much so far, and it knows the engine's well-characterized thrust, so taken together, it knows that it needs to burn for a time T in order to produce the correct magnitude of delta-v.

Its internal contents tend to shift, so that the precise location of the spacecraft's center of mass is unpredictable. Luckily the engine is gimbaled, and it can adjust the gimbals continuously during the maneuver to make sure it keeps the center of mass directly on the thrust axis. It does this by detecting rotation with the star cameras and/or gyros and gimbaling to null the rotation.

How does my spacecraft know if the thrust is actually pointing in the right direction? The stars are very far away and there are no handy planets or asteroids nearby, so while it knows attitude, how can it determine that the direction of the delta-v vector is correct?

I suppose internal accelerometers (inertial guidance) that have been cross-calibrated with the star cameras would be one solution, and exchange of radio communication and doppler information with Earth would be another.

Is that it? Inertial sensors and doppler, or is there any other currently used deep-space spacecraft technology that can measure the direction of delta-v in real time?

Related: http://space.stackexchange.com/questions/18184/how-did-the-attitude-system-of-the-uncrewed-soyuz-7k-ok-no-1-fail-on-the-launch — Russell Borogove, Nov 29 '16 at 19:13
"It does this by detecting rotation with the star cameras and gyros and gimbaling to null the rotation." I don't think they use star trackers for gimbal control. That's probably all gyros. The star trackers serve only to periodically correct for drift in the gyros... — , Aug 19 '20 at 06:24
@Alex ya I'll change that to "and/or", thanks! I don't mean to propose it to be a practical solution, just that it is possible to measure rotation somehow. — uhoh, Aug 19 '20 at 07:08

score 4 · Answer 1 · answered Nov 30 '16 at 05:53

How does my spacecraft know if the thrust is actually pointing in the right direction? The stars are very far away and there are no handy planets or asteroids nearby.

That the stars are very far away is a huge advantage. Parallax will not be an issue for a star tracker that looks for distant bright stars, at least not within the solar system. The inherent errors in even state-of-the-art star trackers are significantly larger than the errors induced by parallax. Parallax might become an issue in the distant future, but by then our children's children's spacecraft will be using quasar trackers.

So while it knows attitude, how can it determine that the direction of the delta-v vector is correct?

In many cases, the spacecraft does not know that the direction of the delta-v vector is correct. Their flight software is rather primitive. Deep space probes typically receive delta-V commands from Earth. These spacecraft have rather limited autonomy and intelligence, and simply execute the commands transmitted to them. Suppose the Applied Physics Lab had mistaken commanded the New Horizons spacecraft to perform a maneuver that would have made that spacecraft smack into Pluto. The spacecraft would have done exactly what it had been commanded to do.

Making a spacecraft truly autonomous is a task for the next generation of rocket scientists. For now, autonomy is limited to those phases of flight where intervention from Earth is impossible. This includes automated rendezvous; automated entry, descent and landing; and autonomous pointing (e.g., New Horizons pointing towards Pluto). In all of these cases, the vehicle will have more than the standard set of navigation sensors, and the flight software will be rather complex.

I'm asking how it can measure it's velocity or change in velocity. Stars give attitude. Unless It passes something that's close enough to give substantial parallax and for which It has an ephemeris, cameras won't give any information relating to velocity. — uhoh, Nov 30 '16 at 06:41
@uhoh -- That is not what you asked in either the title or the body of the question. Your question asks about the direction. Now you are asking about the magnitude. Which is it? — David Hammen, Nov 30 '16 at 23:22
OK you are right, I only am asking about the normal of the change in velocity. "direction of delta-v". Thanks. If it's in deep space and executes a burn, but the spacecraft has a center of mass that is uncertain, how can it determine the direction of the change in the velocity vector - "the direction of delta-v"? — uhoh, Dec 01 '16 at 00:56
Actually this is a good and interesting answer for a question about present and future spacecraft autonomy - if it hasn't been asked before I can ask about that explicitly in another question. It may be of greater general interest than this question! — uhoh, Dec 01 '16 at 21:59
David this answer is really interesting, I've asked a spacecraft autonomy question that needs some perspective. — uhoh, Dec 03 '16 at 00:28

score 1 · Answer 2 · edited Dec 20 '16 at 20:38

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Generally a spacecraft will use a gyroscopic inertial platform — a set of powered gyroscopes holding a fixed orientation in space, mounted in nested gimbals allowing the spacecraft to rotate around it. The relative rotation of the gimbals is measured several times a second to determine the direction the craft is pointing and how fast the direction is changing, which lets the guidance system adjust the engine gimbal to keep the craft on course in a continuous feedback loop.

edited Dec 20 '16 at 20:38

Nathan Tuggy

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answered Nov 29 '16 at 19:19

Russell Borogove

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And just to explicitly answer "How does my spacecraft know if the thrust is actually pointing in the right direction", a burn attitude will be computed prior to the burn and fed into the guidance system as the target attitude. The attitude control system as described by @Russell Borogove will then keep the craft pointed in that direction. – Organic Marble Nov 29 '16 at 23:27
@OrganicMarble is that just wrapping my question with the phrase "calculate a burn attitude"? For a spacecraft with a gimbaled engine and uncertain center of mass due to movement of mass internal to the rigid structure, how exactly would the burn attitude be calculated ahead of time without knowledge of the exact center of mass? – uhoh Nov 30 '16 at 00:59
I do not think the burn targets have anything at all to do with the center of mass. Just the direction the craft should be pointing in. Then the control system should correct for your moving masses during the burn to hold the proper attitude. – Organic Marble Nov 30 '16 at 01:04
@RussellBorogove A gyroscopic inertial platform gives essentially the same information as star cameras, except for details of update rates and estimation of rates of change. If I had arbitrarily good star cameras the gyroscopically stabilized platform wouldn't be needed at all. But this doesn't answer the question. Both give spacecraft attitude information, but neither give acceleration vectors, am I wrong here? – uhoh Nov 30 '16 at 01:04
IMUs are used to measure acceleration. – Organic Marble Nov 30 '16 at 01:05
@OrganicMarble I think you are assuming that the direction of acceleration will be the same as the direction the spacecraft is pointing, but that's not a given. – uhoh Nov 30 '16 at 01:06
That doesn't matter. All that is needed is the desired orientation of the craft. – Organic Marble Nov 30 '16 at 01:08
@OrganicMarble the powered gyroscopes of the "gyroscopic inertial platform" serve the same function mathematically as really good star cameras. Really good star cameras + body-fixed accelerometers + math $\approx$ gyroscopically-mounted accelerometers. – uhoh Nov 30 '16 at 01:33
Star cameras are used to get an initial reference orientation for the inertial platform; while in theory you could use them continuously, in practice you'd need a lot of image processing power to do so, and it's much easier to read angles off the gyro gimbals. (On Apollo, for instance, the astronauts had to do the star sightings, taking several minutes to do so.) – Russell Borogove Nov 30 '16 at 01:57
Fixed inertial reference + knowing what your gimbal angle commands are + knowing that you're thrusting through center of mass because you aren't rotating + math = knowing what direction you're thrusting. After the burn you update your position from ground tracking to see how you did, and correct the residuals with your smaller attitude thrusters if necessary. – Russell Borogove Nov 30 '16 at 02:08
@RussellBorogove I've asked "Is that it - inertial sensors and doppler?" - is the answer simply "yes, that's it?" – uhoh Nov 30 '16 at 02:12
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If I understand you, yes. – Russell Borogove Nov 30 '16 at 02:13
@RussellBorogove if you can add a little something like that to the answer somehow, let's clean up all these comments and I can accept. – uhoh Nov 30 '16 at 02:15
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Inertial platforms are so last millennium. That's what the Apollo program used. Too expensive, and not that accurate. There are more modern alternatives, all of which were developed in the previous millennium (but post Apollo). – David Hammen Nov 30 '16 at 04:21
What's the modern standard? – Russell Borogove Nov 30 '16 at 05:25
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@RussellBorogove -- Strapdown systems. – David Hammen Nov 30 '16 at 23:19
@David Hammen: Nonsense. Inertial platforms are fine technology. They are prone to drift which needs to be periodically corrected, but hey---did you know that your strapdown systems themselves include gyros and linear accelerometers that are themselves prone to drift that needs correcting? Yeah, your modern technology has the exact same fundamental drawbacks as "last millenium" inertial platforms. If we're going to beat our chests about our marvelous modern technology, at least let's be sure that it's marvelous. What ailed inertial platforms also ails strapdown systems. – Aug 20 '20 at 02:27
@Alex - Inertial platforms are not just "last millennium" technology. They are an early space age technology that has rightfully been tossed. Fiber optic gyros with no moving parts ofter a much lower drift rate than does even the best mechanical inertial platform. It's hard to beat cheaper, better, faster. It's particularly hard when cheaper, better, faster is accompanied with more accurate and less noise. – David Hammen Aug 20 '20 at 05:33
@David, fiber optic gyros suffer from drift which must be corrected for just like mechanical gyros. They're cheaper and more compact, but the mathematics of navigation is the same: you get your attitude from gyros, which must be carefully set at launch and which must be regularly corrected in orbit using star trackers or equivalent devices. The basic operating principles are the same, which, if anything, speaks volumes for the pedigree of the inertial platforms that preceeded them. Strapdown systems are not a revolution in IMUs---they're just a more refined version of them. – Aug 20 '20 at 07:08
@Alex, I did not say they were perfect. The imperfections are known and since these are commodity items, they're in the spec. If inertial platforms are fine technology, why aren't they used anymore? If the core rope memory used on the Apollo flight computers was fine technology, why aren't they used anymore? Inertial platforms, core rope memory, and many other technologies of the early space age, were very fine technology -- for that time. – David Hammen Aug 20 '20 at 11:24
@David_Hammen: The core technology behind strapdown systems is exactly the same as that of inertial platforms. Gyros and linear accelerometers and mathematics get you attitude and position for GNC. The switch from mechanical to optical gyros is a simple refinement. Fact is our modern spacecraft navigate using mostly the principles developed in the Apollo years. All we've done since is polish the knives they crafted---and now here you are, scoffing at those very knives, as though our polishing them even came close to the work that went into creating them. – Aug 20 '20 at 17:47
To make my point clearer, this "last millenium" technology, has not been "rightfully tossed." It's routinely used in spacecraft today, even if with minor differences in design, which nevertheless use gyros and linear accelerometers and computer algorithms to calculate attitude and position. – Aug 20 '20 at 17:52

score 1 · Accepted Answer · answered Dec 21 '16 at 10:51

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I see the caveat of your question... and simultaneosly, I don't.

The problem: randomly, non-deterministically shifting center of mass.

Solution: as craft tries to turn, this is detected and compensated by engine gimbal, so that the thrust vector always points through CoM, unless it's compensating for the tilt right now.

Side effect: discrepancy between heading and bearing; thrust misaligned with ship's geometrical axis (which is misaligned with the misplaced CoM), propelling it in a different direction than originally intended.

Resulting problem: how to determine the value of the error - shift in velocity vs intended?

Solution: using exactly the same software that is used to drive the gimbal.

You know the value of thrust (force), you have a very good idea about mass (fuel mass flow and ship's total mass), and you know the direction of thrust at any point of time, along with direction of the exhaust-CoM vector (calculated from shift vs stars, necessary to drive the gimbal operation.)

Split the thrust vector into component vectors along the exhaust-COM axis and perpendicular. Integrate force $\rightarrow$ acceleration resultant from the parallel component over time to get the velocity change; integrate (2nd degree) displacement from the perpendicular component (perpendicular component of velocity afterwards will be near zero since the rotation is extinguished, and never allowed to grow significantly).

answered Dec 21 '16 at 10:51

SF.

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How can I know the direction of the thrust? With respect to what? Is it a perfect engine and a perfect nozzle and there's a star cam pointing out the nozzle getting a fix? I understand the gimbal control should mostly prevent the spacecraft from spinning out of control, but even if I wanted to target Alpha Centauri and I could see it, how do I know that I'm accelerating in that (essentially) exact direction? Do I need a star/navigation camera that has been previously aligned with respect to a set of accelerometers? Or instructions from Earth based on doppler? Or is there any other option? – uhoh Dec 21 '16 at 14:07
I'm not questioning your answer, I am just thoroughly flummoxed by my own question. These are the only two things I can think of. 1) Accelerometers pre-aligned to star cameras, or 2) regular updates from Earth (or some proxy) based on doppler measurements relative to a known body for which a good ephemeris exits (e.g. Earth). – uhoh Dec 21 '16 at 14:10
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@Uhoh: The thrust goes according to thrust profile, which is very well known, or your engine would blow up (combustion stability and thrust profile are inexplicably bound; you provide X fuel, Y oxidizer, get Z thrust in void.). As for direction: you drive the gimbal motors! If you tell the gimbal motor to turn by 2.3 degree starboard, your thrust goes 2.3 degree starboard! – SF. Dec 21 '16 at 16:41
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Also: this is to immediately obtain delta-V. To obtain precise locaction and velocity vectors, you use ground contact and get the reply when the signal completes the round-trip. But to get the change in current velocity, you can simply calculate using the thrust from the burn (thrust is very precise as function of fuel dosage - matters of combustion stability) and direction (the gimbals have a very precise feedback on positioning of the nozzle.) – SF. Dec 21 '16 at 16:47
OK got it! If there are pre-calibrated absolute encoders measuring the 2D angles of the engine/nozzle with respect to the spacecraft frame, and star cameras pre-calibrated with respect to the spacecraft frame, then I have a good estimate of the direction of the thrust with respect to the stars. It's not quite the same as an actual measurement of the direction of the delta-v, but it's going to be quite close. Great! A third method beyond accelerometers and doppler data reported from Earth. Thank you!! – uhoh Dec 22 '16 at 00:56
Wouldn't you just integrate the output of your linear accelerometers to obtain the x, y, and z velocity components? You could calculate acceleration from thrust, but you would need an extra sensor to accurately sense thrust direction, even if you had a good model of the engine characteristics. The linear accelerometers come for free with the IMU, so that seems the simpler option. No? – Aug 19 '20 at 06:28
@Alex: Accelerometers are inherently noisy. Determining position through integration of acceleration is a doomed endeavor as measurement error accumulates and grows in quadratic ratio over time. Determining speed - merely linear, so not that horrible. Determining inertia/mass is actually viable though. – SF. Aug 19 '20 at 07:33
@SF: But then you need to convert your thrust and mass to acceleration in order to... integrate twice to obtain position... so you gain nothing. No? Besides, noise in measurement is routinely handled with Kalman filters, and errors in measurement are corrected for using star tracker measurements... Seems to me you only lose by measuring thrust/mass instead of going directly with accelerometer measurements (corrected to include gravity, which would normally not register in accelerometer readings). – Aug 19 '20 at 08:17
@Alex No. Do Not Use Accelerometers To Determine Position. Directly, indirectly, very indirectly or even anywhere close. They are Bad. You can determine the mass to estimate the amount of fuel remaining and thus delta-V remaining. If you absolutely necessarily need to use accelerometers to determine the speed and position, then estimating current speed as initial delta-V minus delta-V remaining ballparked from mass/acceleration, will yield better results than integrating the accelerometers. They are this bad. – SF. Aug 19 '20 at 09:59
@SF, Come on. Linear accelerometers are routinely used in inertial navigation for spacecraft. Your delta V is just a scalar and you need a vector to tell you where you are. You could get that vector by doing F/m to get acceleration and integrating it twice to get position, but then you're better off just measuring acceleration directly, filtering out the noise, and correcting periodically for errors using star trackers. How exactly do you turn a scalar Delta V into a vector? Because the rocket equation that gets you Delta V takes all scalars as input and therefore gives all scalars as output. – Aug 19 '20 at 18:16
@Alex: Any sources on that? Accelerometers are okay for determining spin, and can be used to ballpark the change of velocity but if you start filtering the output, you lose precision; you have a certain sample rate and lose data in between samples, can't distinguish momentary spikes of acceleration coming from minor combustion instabilities (actual acceleration) from flexible vibrations of the spacecraft (no acceleration) as matching 'paired' events get lost in between samples; it's a random walk, taking your measured velocity steadily away from actual. – SF. Aug 19 '20 at 18:32
Additionally, they are completely blind to gravitational disturbances, minuscule steady influences like light pressure are completely drowned in random noise and below their sensitivity threshold, and any even tiny error in speed measurement early on will convert into hundreds of kilometers of location error after a year into the mission. And after a 1km/s burn that error won't be tiny. If the error is 0.1% (which would be awesome accuracy for accelerometers, they are usually closer to 3%) on a 1km/s burn, a year later it will be over 30 thousand kilometers. – SF. Aug 19 '20 at 18:45
(as for how to use the delta-v: poorly. Calculate the velocity changes, plug into simulation as point burn maneuvers, calculate location. At least it will be able to account for gravitational disturbances.) – SF. Aug 19 '20 at 18:49
The NASA papers on the Apollo spacecraft and Saturn rocket are public. Look them up. This is standard knowledge. All the papers on spacecraft navigation I've gone through mention the gyros and integrating accelerometers one way or another. I frankly have better things to do than entertain this discussion any more. It seems to me you're just peddling assumptions without bothering to do your research. I'm not wasting my time. – Aug 19 '20 at 20:06
@SF, what you describe is not how things are done. It's how you imagine them to be done. And on your procedure to determine position vector from thrust: thrust is only one of many forces you have to account for. Knowing which way your engine is pointing doesn't tell you which way you'll accelerate, because you have 1) fuel sloshing , 2) bending modes, 3) solar radiation forces, 4) magnetic field forces to account for. Your net acceleration depends on all of these, not just on the direction of thrust. – Aug 19 '20 at 20:12
I mean, just google the topic. Look it up on Wikipedia. Here's a paragraph on the wiki for Inertial Navigation System:
"Linear accelerometers measure non-gravitational accelerations of the vehicle. Since it can move in three axes, there is a linear accelerometer for each axis.

A computer continually calculates the vehicle's current position. First, for each of the six degrees of freedom, it integrates over time the sensed acceleration, together with an estimate of gravity, to calculate the current velocity. Then it integrates the velocity to calculate the current position."
– Aug 19 '20 at 20:35
And on the earlier question of gravity. It's true, linear accelerometers don't measure the acceleration due to gravity. This term is instead calculated using mathematical models and added to the accelerometers' output. – Aug 19 '20 at 20:46

score 1 · Answer 4 · answered May 28 '20 at 03:18

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I understand your question can be summarised into, how exactly one knows in Inertial frame where one is moving. I understand there are subtle caveats here.

So suppose I know in Inertial frame where I need to fire and onboard can be aligned to this frame using Inertial sensors. Now question is how does one know exact alignment of star sensor to body? and gyro to body? and accelerometer to body? These small misalignments which can be slightly different from ground measurements can not be measured but only statistically corrected such as by rotating spacecraft and comparing values of star sensor and gyro for example.

So once this calibration is done. We only have to see, whether by giving delta-v spacecraft is in ground calculated state vectors or not. Otherwise one can keep the variable which accumulates inertial acceleration and downlinks to ground.

For such inertial navigation integrator one needs a gravity model and any other forces if present.

answered May 28 '20 at 03:18

zephyr0110

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Calibrating gyros to stars I understand, but my question is about linear acceleration. How does one recalibrate that in deep space? I think you have use "breadcrumbs"; actually leave a tiny object next to you, accelerate, check the accelerometers, then look back to where it is against the stars. – uhoh May 28 '20 at 04:42
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the offset part can be estimated as when not firing, it should show zero. The scale factor part, you rotate the spacecraft you know exact rotation speed you know the mounting location of accelerometer calibrate with centrifugal force. – zephyr0110 May 28 '20 at 05:03
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Using rotation to calibrate a linear accelerometer requires an accurate distance to the center of rotation. The question text and drawing highlight that we don't know how the center of mass shifts as we use propellant for example. – uhoh May 28 '20 at 08:12
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Do it before you use propellant, rotate by reaction wheels.. now hopefuly the scale factor and offset are not function of time. – zephyr0110 May 28 '20 at 08:25
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Now I am thinking, since doppler shift are very accurate we can estimate CG accurately by having a transmitter on one arm, so via rotation maybe we can capture max and min doppler. Wondering if gravity gradient can estimate scale factor for highly sensitive accelerometer – zephyr0110 May 28 '20 at 08:31
Well everything changes over time, including ion engine or thruster characteristics, nozzle behavior etc. What if accelerometers are mounted in pairs? For example an X/Y pair can be mounted at +Z and -Z, and the Z accelerometer at +Z and -Z. As long as you know the distance between them $d$ and that stays fixed, then when the spacecraft rotates you can solve for the center of mass. Since the question is about maneuvering in deep space, millions of km from any particular gravitational body, the only acceleration gradient will be due to rotation, which is measured from the stars. – uhoh May 28 '20 at 08:54
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I actually thought about it, but then scale factor will be different for both accelerometer adding one more variable into equation – zephyr0110 May 28 '20 at 09:05

How can a deep-space spacecraft determine in real time the direction of delta-v?

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