I am working on a project to measure (approximate) the distance traveled by a football kicked into a training net. The idea that someone kicks a football (foam football stuffed with a bunch of sensors) into a training net and based on the data collected in the first couple of seconds (before the football hits the net), I can approximate footballs path in real life (while making assumptions about wind, etc). This is just for a game application, not for scientific measurements.
Did you really try it or did you read the above and (prematurely) condemn it ? Because integrating drift and offsets leading to large errors in position estimation shouldn't be a problem in your application. There may be other reasons for failure, both sensor and non-sensor related, but there's no reason I can think of that a hobbyist grade IMU can't be used in the fashion I think you're trying to.
Let’s start there and make sure I understand what you’re trying to do. You system is like a golf simulator, where the guy whacks the ball off a tee and into a screen. From the initial data some computer then calculates the trajectory a real ball would have taken and projects that onto the screen. You may not have the fancy visuals but the process is the same, collect some initial data and then do the physics to estimate the trajectory. If I’ve got that right then you see why the double integration problem is (was) not your problem. You’re only using data and propagating errors for the time the foot is in contact w/the ball … a short time. After that it’s all physics where you use the initial data (which will have errors) and assume the forces acting on the ball (vs using error laden measurements).
A good question is whether a hobbyist grade IMU can be used to give a good estimate of the state of the ball just after the foot looses contact. That depends on how accurate you need your estimation to be. The good thing is that once you define that, you can define the max errors associated with the IMU and know if a suitable IMU exists.
As to the physics of a spinning kicked football … you’re on your own. :mrgreen: Those of a baseball or even a golf ball are well known. Those of a football ???
As for alternatives … how about 2 high speed cameras; one to capture the downrange and vertical data (before the ball hits the net) and one to capture the downrange and crossrange data ? I can’t think of any other system that will give you the complete state of the ball and I’d expect spin to factor into the aerodynamics of the kick.
Thanks a lot, that’s a good answer. I feel like I have some errors in my current calculations, so whether drift is a problem is still TBD You are exactly correct on the “golf simulator” aspect, that’s the exact application.
Cameras is a great alternative (or something like MS Kinect), but I would rally want the football to be “self contained” measuring system, so if I can use sensors I would rather do that. Do you think that an IMU is the best way to go? Any thoughts on ultrasonics?
gratner:
Do you think that an IMU is the best way to go? Any thoughts on ultrasonics?
As you've not stated what accuracy you need I can't say which, if any, IMI would work. My guess is that keeping track of the orientation of the ball and thus being able to properly account for gravity will be the biggest error source in an IMU approach. So not only do the components (gyros, accelerometers) need to have the dynamic range, they need to have wide enough bandwidth ... a factor often overlooked.
As a first guesstimate to what’s required for an IMU I would suggest using a simpler item to model than a football. Use a cannon ball, have Iron Man kick it but only as hard as a normal person would a football. This way spin and aerodynamics don’t play a part. See what velocity (magnitude) changes (+/-1%) do for the downrange and crossrange distances. Repeat for small changes in the departure angles. See what’s acceptable to you. Then you can back figure what’s needed for at least the accelerometers. If you already have a model for the football, use that w/o any spin. Then use that w/spin and vary the spin +/- 1%. You should be able to figure out how much error you can tolerate in the gyros.
As for ultrasonics … my guess is you’d need 2 just like the cameras, except they’d be more error prone. Also I think they take a relatively long time to come up with a measurement, all while the distance and velocity (all they could, at best, measure) are changing. And I’m being generous … I don’t know of any that measure Doppler to get range rate, they just measure distance at perhaps a 10 Hz rate (which I think is too slow).
How inaccurate was your “completely inaccurate and useless” ?
Thanks a lot! I might have an error in my calculations, so maybe it won’t be that bad. I am going back to the drawing board in processing the calculations.
Accuracy is not very important, since it will be a game, as long as accuracy can be consistent relative to each other.
Mee_n_Mac:
As for ultrasonics … my guess is you’d need 2 just like the cameras, except they’d be more error prone. Also I think they take a relatively long time to come up with a measurement, all while the distance and velocity (all they could, at best, measure) are changing. And I’m being generous … I don’t know of any that measure Doppler to get range rate, they just measure distance at perhaps a 10 Hz rate (which I think is too slow).
How inaccurate was your “completely inaccurate and useless” ?
There's an idea...
Thinking maybe a gy could you put an ultrasonic 'ducer (or two or three, whatever it takes) in the football, say it’s throwing out a constant 50Khz (and ticking off all the neighbor’s pets at the same time).
Put a few microphones, which are also ultrasonic sensitive, downstream from the ball’s original placement, in the X/Y/Z axis’s’s.s.s, on the ceiling, on the floor, a bit to the left, a bit to the right, etc.
Continuously sample all that with a PC and post-process the waves (eg. doppler) to get angles, velocities, etc. and estimate the downrange? Obviously wouldn’t get any spin rates or anything, but…
I couldn’t tell ya one way or the other. Probably doesn’t even need to be ultrasonic as such. Probably could get away with just really high frequency.
All other things being equal (eg. sensitivity of the sound ‘producer’ / microphones, etc), I would think that a real limitation would be the sampling rate of the microphones, how much of a doppler shift could actually be derived from a kicked football, and so on and so on.
Those clowns on the “Mythbusters” are constantly using high speed cameras with lines in the background to deduce speeds and such from moving objects.
If you had a checkerboard background along with a camera that’ll do a fair amount more than 30FPS, and a PC that could record that, a person could fairly easily figure out angles and velocities, etc… But, there goes the “real-time results” out the window.
skimask:
Continuously sample all that with a PC and post-process the waves (eg. doppler) to get angles, velocities, etc. and estimate the downrange? Obviously wouldn’t get any spin rates or anything, but…
Hmmm ... perhaps if you make the speakers all shout at different frequencies you might be able to get spin by identifying the amplitude modulation of the each tone and their relationship to each other ?? I don't know, might make an interesting question for a physics major.
Given the OP says this is more of a game than a “serious” training tool, perhaps capturing spin isn’t all that necessary. After all that data is only of use if you have a good model for the football aerodynamics that uses it. Then again I’ll opine that a good kick uses spin to both stabilize the ball and extend the flight … and a good kicker knows and uses that (like a baseball pitcher uses spin). It might not be a good game when, even if every same kick is consistently graded, a good “spin” kick is not given it’s proper due.
While an IMU approach might work (it’s worth a few days of calcs and sim to figure it out) you know a camera approach must work. I have to believe that’s how the golf sims do it. And given the vision processing these days (I’m not that familiar with) it might well be very automated to get the needed data from the camera(s). Heck if you don’t care about crossrange motion, you might get away with just 1 “side” cam and skip the overhead cam (given it’s a game) ???
In either case the hardest part (IMO) would be to come up with a good enough physics model for a kicked football. At a minmum you’d have to have a drag model and I have no idea where to begin with that given the shape involved.
gratner:
Thanks a lot! I might have an error in my calculations, so maybe it won’t be that bad. I am going back to the drawing board in processing the calculations.
Recall what I'm advocating; that the IMU or camera be used to track the football only while in contact with the foot. After that it's a pure ballistics problem (albeit with an odd shape) which can be solved just by knowing the velocity vector at that moment (plus the displacement during the kick and the spin if you include aerodynamics). While you could, in theory, continue to use IMU data during the whole flight to estimate the trajectory ... that would be subject to the errors discussed at StackExchange. Once the football leaves the foot you know the only forces acting on the ball are gravity and aero (including wind if you want). The only significant errors will then be those due to errors in the velocity vector (magnitude and/or orientation) and errors in your model.
This sounds an awful lot like the punching bag arcade game but upside down.
Another thought is building the sensors into the frame of the net. If you have an IR gate at the start you could time the ball from that point to a similar series of gates lining the frame of the net. That would give you speed and angle. You could line the top and bottom of the frame with more sensors to get a lateral angle as well.
It would work like this:
IR start gate = free => start timer
IR gate 4 = blocked => stop timer
if IR gate 4 then angle = 25deg
travel_dist/time = velocity
MATH
result = 15ft
PrintF(" wet noodle legged kicker")
edit you could use a few more sensors in the ball to give you some more information for the *MATH section. A gyro or accelerometer.
trueRF:
Another thought is building the sensors into the frame of the net. If you have an IR gate at the start you could time the ball from that point to a similar series of gates lining the frame of the net. That would give you speed and angle. You could line the top and bottom of the frame with more sensors to get a lateral angle as well.
And thinking of the above I'm almost certain of how a golf simulator works. They measure (like above) the time from when the ball leaves the T to when it hits the screen. A camera facing the screen records the X, Y position of the hit and, given the pre-known position of the T relative to the screen, that gives you Az and El angles. Add in the timing and you've got speed. Neglecting any spin effects, that's all you need.
An IR gate is probably a bit specific. A broader term would be photogate. Which is any device that uses a beam of light to detect an interruption. Like the light based trip sensors you see in front of doors. An IR gate would be a photogate that uses an IR light beam.
You could use something like the IR devices below to get the appropriate effect. It might take a little effort to avoid cross talk between multiple emitters and receivers but there are some things that you can do to avoid that digital and mechanical. If you staggered them at 1/2-1 width-of-a-football intervals you could get a pretty good angle measurement.
You are exactly correct on the “golf simulator” aspect, that’s the exact application.