1. 1 MONALISA Compact Straightness Monitor Simulation and Calibration Week 5 Report By Patrick Gloster

2. 2 Tidying up last week’s work Last week we saw a comparison between my calculated values for the observer coordinates and the true values What about comparing our initial approximations with the calculated values? It turned out that the initial values were just as good as the calculated values Errors on my errors!

3. 3 Constraints and the fmincon function Fmincon – one of Matlab’s inbuilt minimizers Can apply constraints, but I dismissed it because the function it minimizes has to return a scalar value, while ours returns a vector However, we can use this function by minimizing the sum of the square of the residuals

4. 4 Further success (or rather, parallel success) I have also got my own function to apply constraints Tested successfully – constraints are applied Again, my function and Matlab’s function give the same answers… and again my function is much slower  We decided to continue to work with the Matlab function fmincon

5. 5 The bow tie problem Having successfully developed a minimization function which can apply constraints, I moved on to a new set up y x z

6. 6 The bow tie problem In this problem, which is a 2D version of the real thing, we hold one plate fixed and move the second plate all over the place, measuring the distances marked in the diagram The second plate can move up/down, left/right and rotate about the z-axis y x z

7. 7 The bow tie problem Again, we define an origin and a direction We then write our objective function This function is then minimized subject to the constraint that the distance between the two points on plate 2 is constant

8. 8 Results The program successfully applies the constraint that the distance between the two points on plate 2 is always the same However, depending on the error on the initial approximations, the program converges to the wrong point Examining the results further, the distribution is not what we expected

9. 9 Disaster Having more target points (N) does not improve the accuracy of the results; it appears to change arbitrarily with N The results are generally accurate to about 0.0001 Even increasing the accuracy of the laser doesn’t help (although this may just be converging further to an incorrect point)

10. 10 The spread of the results 10 points2050100150 X010.00027620.00026030.002140.0015780.001039 Y010.031840.00026810.00038190.00034380.0002062 X020.00038180.00079680.0018980.0016460.001332 Y02error9.478e-0050.00035720.00026460.0003025 Table showing c1 from the equation a1*exp(-((x-b1)/c1)^2)

11. 11 What to do now? Examine an identical problem with my own program and see what results we get At least we know how my program works Perhaps I’m not giving the fmincon all of the information