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

[Mr. N]

Thanks for reading the paper --- and for your feedback. You raise some very good points. Here are some additional thoughts in response to these points:

1) Acceleration

Very true, the analysis assumes instantaneous accelerations to make the problem more tractable. However, the assumption is based on models developed from speed trial data using our 2013 robot. In a straight-line test, the robot reached 75% of maximum speed within the following times/distances:

- In lo-speed gear (24:1): within 0.2 seconds/20 cm of travel
- In hi-speed gear (9.4:1): within 0.7 seconds/140 cm of travel

FRC robots, going full throttle from a standing start, do virtually all of their accelerating in a faction of a second.

So, the assumption is reasonable when talking about paths lasting several seconds covering several meters. Conversely, it is a poor assumption for very short, very quick paths.

2) Reversing to Get from A to B

This is a great point. When I developed a game simulator for the 2014 game using the "turn-straight-turn" strategy, I realized that the "delta theta" terms (i.e., the changes in heading) had an ambiguity for angles greater than 180 degrees. For example, you get to the same heading by turning +270 or -90. Clearly the second turn is faster. But it also requires the robot to travel backwards during its straight-line motion.

Although not explicitly mentioned in the paper, this result is entirely consistent with the conclusion. Consider the 2013 game: it is faster to travel in reverse from the shooting position at the pyramid to the feeding station, rather than turning 180 degrees first.

3) Multi-Segmented Paths

Given the qualifiers outline in (1), I would argue it is more efficient to plan a trip around a mid-field obstacle (e.g., a pyramid) as a series of straight segments rather than one curved, sweeping path.

4) Impact on Strategy vs. Tactics

Clearly, the findings are more relevant when planning overall game strategy that involves moving between key locations ("way points" or "way poses"), as opposed to tactical moves on the field when contending with defenders.