paper: Driving a Robot — Fastest Path from A to B

[Mr. N]

Originally Posted by Jared

A great example of where a line would be much faster:

Ha! Agreed!

Thanks very much for the detailed answer. Great work!

One thing: The acceleration limit you used (10 ft/s/s) may be little low. Based on our speed trials, we were getting something more like 22 ft/s/s (Supershifter, hi-speed gear).

I worked up a similar example using the math from my paper (I probably should have included this in the paper itself). I used a 25x25 foot path with a similarly shaped curve. I set my upper speed at 10ft/s and robot wheel base to 2 ft.

Although I don't take acceleration into account, keep in mind that (a) the path is long enough that the effects of acceleration are minimized, and (b) both the linear and curved path benefit from the "instantaneous" acceleration assumption -- they are both slightly faster than real life, by about the same amount.

Here are my results:

- Turn-Straight-Turn: 3.69 seconds, total arc length = 35.36 feet, total heading adjustment = 90 degrees

- Curve: 4.00 seconds, total arc length = 37.79, total heading adjustment = 126 degrees

The curved path takes 8.3% (or 0.31 seconds) longer to execute.

Although this doesn't sound like a lot, over 6 scoring cycles, that 1.84 seconds --- almost 2 seconds from optimizing just one part of a path.