Nick and I discussed the relative merits of his solution to the “rotter”. He does occasionally display a surprising degree of pragmatism.

The formula I use is the standard formula for intersecting lines the projective plane (where two distinct lines always intersect in one point). Because I’m working in the projective plane, I am using homogeneous coordinates and so I have three coordinates instead of two (perhaps this may have been confusing). The formula is in fact the result of an elementary piece of linear algebra which corresponds to the fact that two (distinct) 2-dimensional subspaces of a 3-dimensional vector space always intersect in a 1-dimensional subspace.

In any case, this Wikipedia page may help you:
http://en.wikipedia.org/wiki/Line-line_intersection

If you want background on projective geometry, then I would recommend the notes linked here:
http://people.maths.ox.ac.uk/hitchin/hitchinnotes/hitchinnotes.html
(For example, see Proposition 2 on page 7 of Chapter 1)

Best of luck and thanks for your interest,
Oliver.

Congratulations on your success with Lawnbott. A 50W amp seems like a pretty beefy piece of kit to generate what I imagine is a fairly weak signal but the most important thing is it worked. I am particularly interested to hear that your Lawnbott is robust to approximately a 1% change in frequency. Anyway, great work!

Thanks for your comments on my situation. The possible distortion caused by my recording and then playing back the signal through my discman (as well as subsequently amplifying it with the LM386) must surely explain why my recorded signal did not work. Indeed I connected my ‘scope up while running this early experiment and did observe some mild distortion/noise (some of which I mention above).

However the signal I generated using python and played back through the discman+LM386 was extremely clean (again, I looked on the ‘scope while testing in place with the mower). In fact it was a good deal cleaner than the signal which I measured in place for the actual Friendly Robotics perimeter switch. So from that I decided it was likely the mower was calibrated to some of the artefacts/glitches present in FR perimeter switch’s signal and if I was willing to recalibrate with my clean signal, the mower would work. This would also fit with why replaying the recorded signal did not work because the glitches were higher frequency than audio and would have been smeared. Of course the filter in the mower *shouldn’t* be sensitive to these but I’d guess it is a bit.

I never tested recalibrating because I didn’t own the mower and didn’t want to mess with its calibration due to the outside chance of ruining it.

In any case, thanks again for the interesting data and good advice and congratulations on building your own solution.

Funny thing, I first used my laptop to generate the exact frequency, but due to a bit of low frequency noise on the output (as seen on analgue scope), it played havoc with the mower.

Instead I built a sine wave generator from a kit for around 20quid, hooked it up to a 50w car amp, and altered the frequency until the lawn bott took off. This is working perfectly. The lawnbott isnt that sensitive to the actual frequency say+- 100hz works ok as long as it is constant.

Perhaps the distortions created by recording and replaying the signal through the discman are giving you similar issues?

Perhaps a sine wave generator at 8khz with brief off periods will do the trick?

If you’re willing, you should be able to build your own switch using the details here. I’m pretty sure it would work perfectly and reliably if you were willing to recalibrate the mower.

In any case good luck with whatever path you end up taking..