Part 3 of 4: A Winning Strategy
This is Part 3 of a 4-part series investigating how math may help in LEGO Robotics Competitions. Part 1 introduced the past research and the context of the present investigation — a local LEGO robotics competition where investigators conducted interviews about team strategies. Part 2 laid out the range of strategies that were observed, and teased out an interesting result that teams using math-based strategies seemed to have widely varying success in the competition, with math-users both leading the pack and trailing near the rear.
So what was it that the most successful teams did that led to their success? In part 3, we take a look at the winning team's strategy and see how they used math to great effect.
A Focus Team
In addition to short, standardized interviews with teams on the day of the competition, the research team also sat down for more in-depth interviews with four robotics teams outside of the competition, hoping to gain greater insight into their solution strategies. Two of these Focus Teams were composed of middle school aged students and two of elementary school aged students. One of the Focus Teams – codenamed M2 – happened to be the team that won the competition.
Team M2 used a math-based Calculate-Test-Adjust strategy for their first move. They were one of only four teams (out of 16 interviewed) who used a math-based strategy. But Team M2's overall solution was fascinating and worth sharing as there is so much that can be learned from what they did.
Team M2 was a school-based team consisting of 10 students, all from a gifted program in a suburban school. There were one 8th grader, six 7th graders, and three 6th graders. Four of the students had been to a competition before, but the rest were rookies. Their coach, a gifted teacher from the school, had been a coach for five previous robot competitions, so she was very experienced. They reported spending about 17 total hours preparing for the competition, with about 10 of those hours in just the last two weeks. This was, in fact, on the low end of total preparation time compared to other teams that were interviewed. Team M2 met during normal school hours, when the gifted teacher was able to pull the students from their regular classes, which may have constrained the amount of time they could meet.
Team M2's Robots and Game Strategy
Team M2 was large enough and had multiple robots, and so were able to split into two sub-teams. They divided the task into missions, with one sub-team working on the toilet paper tubes and the other sub-team working on the nests. They built one robot according to the Robotics Educator Model (REM) given in the LEGO® instructions, although they adapted it by substituting larger wheels. They also built a second robot entirely from scratch. The REM robot had two different attachments: one for collecting the toilet paper tubes and the other for loading and transporting the ping pong balls to the gutter and the empty tubes to the end zone scoring area. The second robot was used to retrieve the nests. They designed this second robot from scratch because they felt they needed a robot that was heavier than the REM robot design in order to effectively pull the nests back. Below are photos of Team M2's robots and attachments. These robots as a whole were not very complex, but each robot design and attachment was well-tuned to specific parts of the challenge.
Team M2's Winning Round
Team M2 ended up with a high score in the competition of 91 points. See below for a video of their winning round. It is clear from the video of Team M2's robots in action that all of their movements are quick and reliable. They retrieve all three toilet paper tubes very fast and without any fumbling. As mentioned in Part 2, the research team suspects that this is because Team M2 was able to use the Calculate-Test-Adjust strategy to make efficient calculations that got them close to correct motor rotation values very quickly. The time savings allowed them to work on other aspects of the challenge, such as ensuring that both of their robot designs were robust and reliable. This too, shows clearly in the video, as Team M2 uses their multiple robots and attachments to clear advantage. In general, Team M2 is a great example of an efficient and focused team that produced a high-quality solution.
Team M2's Other Math
Team M2 did use Calculate-Test-Adjust, a math-based strategy for movement, but perhaps the most exceptional aspect of Team M2's strategy was a completely separate use of mathematical thinking. One of the students on Team M2 did a systematic analysis of the points that the team could get based on observations of their practice rounds. She measured the time they took to complete each mission and the points that they could get, and then identified the best ordering to help maximize their total points. She determined that their team could get the toilet paper tubes (and all 9 ping pong balls contained within them) back to base then deposit the balls into the gutter and the tubes into the end zone in 52 seconds for a total of 57 points. Then they would still have time to pursue the nests for additional points. In their winning round (see the video above), they execute this strategy almost perfectly, although a later mission ends up knocking one of their toilet paper tubes from the end zone scoring area.
Although the team no longer had documentation of their analysis when interviewers met with them after the competition, the research team attempted to recreate it in Table 1 to illustrate how powerful such an analysis can be. When the points are broken down in this way, it is clear that the large majority of points are to be gained by going after the ping pong balls, half of which are in the toilet paper tubes, and putting them in the gutter. And this is exactly what Team M2 did, doing so very efficiently and reliably. Thus, Team M2′s use of mathematics extended beyond programming into the planning process itself, and appears to have paid off very well.
Conclusion #2 – The most successful teams do use math purposefully and efficiently, and their math use is a prominent factor separating their solutions from the solutions of the rest of the teams.
It seems reasonable to think that Team M2 was an exceptional team, with some previous competiton experience among its team members, students who were generally considered smart and good at math, and an experienced mentor. Nevertheless, it also seems clear that a big part of Team M2's success was a direct result of their use of math in their solution strategy, and that their math use gave them real advantages at multiple levels.
A team that uses math effectively to quickly zero in on correct motor rotation values in their program can save valuable time. That time can then be used to make the rest of the robot more efficient and reliable, or even build a second specialized one to complement the first. In addition, using math as a larger strategy to do more systematic analysis of the points breakdown and the effectiveness of different mission solutions can have a major impact on a team's maximizing its performance at the competition.
In reality, of course, not every team will walk in the door with the background to apply math as effectively as Team M2. After all, the observations in Part 2 show that there were teams who tried to use a math-based strategy but ended up performing poorly, and that the View-Mode strategy, which doesn't include any math, was the most straightforward, reliable, and effective strategy on average.
Is math only a strategy that should be pursued by “elite” teams and students, then? Of course not! On the contrary, the final article in this series will provide evidence that the use of math in robotics competitions can produce winners in different ways… and more importantly, it can help produce the type of winning that will last long after the competition is over!
Written by Eli Silk
August 25th, 2010 at 8:08 pm