Distance along an ellipse arc (nD Nonlinear System Solver (VI).vi)

I'm hoping to get some help solving an issue I've come up against. I appreciate that what I'm asking requires some of your time, so I've tried hard to do my due diligence before posting here. I'll really appreciate any help I can get. I'm using LabVIEW 2014 Professional on Windows 7.
I've stripped away all the details of the specific application I'm working on and tried hard to isolate just the issue that is causing me difficulties.
I've posed the problem below and I attached some investigation code (sorry, there is quite a bit) that represents my current solution (with the issue).
Problem: Given an ellipse (with a major and a minor axis and a frame of reference), a distance to travel and any point on the ellipse, calculate the end point on the ellipse where the elliptical arc length between the two points equals the given distance to travel.
I'll restate the problem, but with physical values. Given an ellipse, centered on the origin, with axes of 10mm and 8mm, and a starting point (5mm, 0mm); what is the end point on the ellipse after travelling 1 mm along the ellipse?
This initially seemed like a simple calculation (and it is for a circle), but for an ellipse, the math turns out to be somewhat more complicated and requires numerical computation.
Issue: I was given some python code that solves this problem and embarked on a LabVIEW solution. The python code uses the function optimize.fsolve from the scipy library to solve one aspect of the problem. I'm not too familiar with the LabVIEW VIs available to do the equivalent, but settled on "LabVIEW 2014\vi.lib\gmath\zero.llb\nD Nonlinear System Solver (VI).vi" (my code still has other options disabled in the code). When I use this solver VI, I do not always get the same answer from this VI. Sometimes it finds one root and sometimes two. For points separated by less than half the circumference of the ellipse, there should always be 2 roots (one in the clock-wise and one in the counter clock-wise direction). Any ideas why the solver does not always return 2 roots?
Current Solution: My investigation VI takes two points on an ellipse (defined by a start angle and end angle) and calculates the distance between them along the ellipse. Then, I take the start point and the distance and try to calculate the end angle (which I can use to find the end point). Run once, it usually finds the right answer, but run 100 times it often returns the answer 19. I should mention that I'm not 100% positive there are no issues with the code used to support this calculation and I'm open to any suggested changes or improvements, but the issue currently causing problems is the inconsistent operation of the solver VI.
Again, I appreciate this is long and thank you for reading this far; I hope you find this as fun a problem as I do!
Chris
Solved!
Go to Solution.
Attachments:
NI Forums.zip ‏265 KB

Hello Mark,
Thanks for your reply, I was concerned that I had sent up an air ball on this one! And thank you for taking the time to review the code.
You are correct, I am having an issue with the results of the nD Nonlinear System Solver (VI).vi. And that is a good poiint you raise, regarding the choice of the starting points. I'm not intending to use random values, I think I'm using a number very close to the start angle (in this case 20.001 degrees) as a start and 2pi (or 360 degrees) as the end. When I read the description of the start and end from the documentation:
Start is an array describing the left corner of the n-dimension interval. The randomly chosen start points of the zero-finding algorithm can be found in the n-dimensional rectangle spanned by Start and End.
End is an array describing the right corner of the n-dimension interval. The randomly chosen start points of the zero-finding algorithm can be found in the n-dimensional rectangle spanned by Start and End.
I have to admit I don't *understand* what this means and I am currently guessing for the choices of start and end. I will think on this some more and review your links.
As far as my final goal, I'm going to use this code I shared for generating an ellipitical motion profile on the PC to send to a cRIO and have executed on a FPGA.
I'll report back after I work on this some more, but if you have some more insights, please share.
Chris
(BTW, I have an open support item for this #7444649 and it was suggested I also post on the forums)

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Sorry to repeat, but excuse my poor English
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Attachments:
Nonlinear Equation.vi ‏11 KB

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Ps2: sorry for my bad english. it is not my real lenguage
Reason of edit: added the swap partition. I forgot it
Last edited by Thalskarth (2008-12-21 20:11:00)

thanks everybody for the help,
kaola_linux wrote:@Thalskarth - it's better to have /var especially if you're using ext3 or other filesystems which was designed for larger files as your partition for /home and /. Having a seperate partition for /var would be nice (backup purposes and reinstalling without downloading the entire package whole over again). 5gb would be sufficient for your /var, anyway you can always resize it to your needs.
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Inxsible wrote:
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[2010-09-29 15:28] upgraded qt (4.6.3-1 -> 4.7.0-2)
[2010-09-29 15:28] upgraded xf86-input-evdev (2.4.0-2 -> 2.5.0-1)
[2010-09-29 15:28] upgraded xf86-input-keyboard (1.4.0-2 -> 1.4.0-3)
[2010-09-29 15:28] upgraded xf86-input-mouse (1.5.0-2 -> 1.6.0-1)
[2010-09-29 15:28] upgraded xf86-video-ati (6.13.1-1 -> 6.13.2-1)
[2010-09-29 15:28] upgraded xf86-video-vesa (2.3.0-2 -> 2.3.0-3)
[2010-09-29 15:28] upgraded xkeyboard-config (1.8-1 -> 1.9-1)
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Good day,
The challenge of the day is to provide a calibration for an accelerometer output, expressed as a binary value.
I have an accelerometer whose operating range can be set (±2g, ±4g, ±8g). The accelerometer itself then generates a binary value at 16bit resolution. Hence, that 2^16 value (0-65535) represents an acceleration whose value depends on the ranges we set.
So, we make the asumption that the response is linear, allowing us to claim:
Acceleration = Scale x Binary Value + Offset
I have three axes worth of data, accelerometer A, B and C. If I hold the accelerometer stationary, the only thing I should be reading is the accleration due to gravity, g. This gets me the relationship
(A)^2 + (B)^2 + (C)^2 = g^2
since, in any orientation, the magnitude of the combination of all three acceleration readings should be the acceleration due to gravity (and that shouldn't change no matter which way you happen to be pointing the accelerometer).
What this gives me, then, is a nonlinear relationship of 6 variables (three scale factors and three offsets). I should be able to take six measurements in arbitrary orientations, which will give me six output values of each acclerometer. I should then be able to pull out the scale factors and offsets for each accelerometer, either in terms of g or relating to what I think g is.
My question, then, is how can I get Labview to do this? I'm see that there's a Solve Linear Equations tool, but I'm not seeing one appropriate for the nonlinear case. I'm also quite comfortable believing I'm just missing it :-)
Thanks!
Solved!
Go to Solution.

OK, so I've dug a bit deeper and believe that the Nonlinear System Solver is the appropriate starting point, as found in the example file Equation Explorer.vi.
In that example, I can define a system of nonlinear equations and the vi should spit out the solutions (zeros) of the variables. I got it to work with some arbitrary test data generated through excel.
Now, I'm moving on to the next level of complexity in the model, and have derailed m'self again..
The simulated device:
a three axis accelerometer, each of which would generate an output of the form Voltage = Scale * Acceleration + Offset.
In a perfect world, the only accleration I'll be seeing is gravity (9.8 m/s^2), and I set that gravity in a random direction (indicating the accelerometer is at an arbitrary orientation). Knowing that orientation, I then calculated what the components of the acceleration would be along all three axes, and then applied values for Scale and Offet to deterine what the equivalent voltage reading off the accelerometers would be.
So now I start the long way home again. From a Labview perspective, I know that I have three voltage outputs which would feed into a known relationship
((Vx - OffsetX)/ScaleX)^2 + ((Vy - OffsetY)/ScaleY)^2 + ((Vz - OffsetZ)/ScaleZ)^2 - 96.04 = 0
where the 96.04 comes from g^2. This is my nonlinear equation with six unknowns in it and three constants.
Since I have six unknowns, I need six equations, which I can get by rerunning my simulation, right?
I put six generated "voltages" (Vx, Vy, Vz) into this form using my expected values for Scale and Offset, and run the vi. However, the vi returns nothing. I know there should be a solution vecotr, because that's what I used to created the simulated data. Is there something I'm overlooking?
Attachments:
Calibration.png ‏74 KB

System Calibration vs Device Calibration

Hi Guys,
Looking for some experiences/opinions on an approach we are looking to take on a measurement system.
We are using compactRIOs which are buit into a system which is installed in a quite restrictive environment and we are concerned will calibration. To retrieve the measurement cards and replace them will be a costly exercise.
We are considering a concept of using a portable calibration unit to perform a system calibration on site. This would involve putting in known values and notifying the software which can calculate new scaling coefficients to use going foward.
I believe this should account for everything that calibrating the devices would (and more). Assuming this is done at regular intervals and the devices calibration drift is roughly linear there should be no need to calibrate them seperately.
Have you had experience of this method? Would you be confident in this for new systems?
Cheers,
James

OK, so I've dug a bit deeper and believe that the Nonlinear System Solver is the appropriate starting point, as found in the example file Equation Explorer.vi.
In that example, I can define a system of nonlinear equations and the vi should spit out the solutions (zeros) of the variables. I got it to work with some arbitrary test data generated through excel.
Now, I'm moving on to the next level of complexity in the model, and have derailed m'self again..
The simulated device:
a three axis accelerometer, each of which would generate an output of the form Voltage = Scale * Acceleration + Offset.
In a perfect world, the only accleration I'll be seeing is gravity (9.8 m/s^2), and I set that gravity in a random direction (indicating the accelerometer is at an arbitrary orientation). Knowing that orientation, I then calculated what the components of the acceleration would be along all three axes, and then applied values for Scale and Offet to deterine what the equivalent voltage reading off the accelerometers would be.
So now I start the long way home again. From a Labview perspective, I know that I have three voltage outputs which would feed into a known relationship
((Vx - OffsetX)/ScaleX)^2 + ((Vy - OffsetY)/ScaleY)^2 + ((Vz - OffsetZ)/ScaleZ)^2 - 96.04 = 0
where the 96.04 comes from g^2. This is my nonlinear equation with six unknowns in it and three constants.
Since I have six unknowns, I need six equations, which I can get by rerunning my simulation, right?
I put six generated "voltages" (Vx, Vy, Vz) into this form using my expected values for Scale and Offset, and run the vi. However, the vi returns nothing. I know there should be a solution vecotr, because that's what I used to created the simulated data. Is there something I'm overlooking?
Attachments:
Calibration.png ‏74 KB

Distance along an ellipse arc (nD Nonlinear System Solver (VI).vi)

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