denkbots’ cRi3D [Part 2] Strategy and Research

With a thorough understanding of the **this season’s game** and **game manual **along with** **tools discussed in** Part 1 – Game Theory **we are ready to talk strategy!

Strategery

Now that we have a tool to evaluate the optimal scoring of an FRC game we can add constraints to our rational agent (for example, the robot is only allowed to score in the low goal) and approximate the scoring potential of other strategies and confirm/deny our initial assumptions.

The optimal strategy we found in Part 1 had no constraints, the robot could do everything. We will consider this our “MAX” points to start. The evaluation from Part 1 determined the following scores:

- “MAX” Autonomous Mode: 20 pts
- “MAX” Teleoperation Mode:
- “MAX” End Game: 15 pts

The “MAX” strategy achieved **115 pts + 1 RP**.

But what if the robot could only score in the low goal? We will call this our “MID” strategy. Repeating the exercise from Part 1, the following scores can be determined:

- “MID” Autonomous Mode: 15 pts
- “MID” Teleoperation Mode: 56 pts + 1 RP
- “MID” End Game: 15 pts

The “MID” strategy can achieve **86 pts + 1 RP**.

Finally, we ask: What is the bare minimum a robot able to navigate the easiest objectives of the game could score? We will call this our “MIN” strategy. Assuming a robot could move and fit under the Low Bar, the following scores can be determined:

- “MIN” Autonomous Mode: 10 pts
- “MIN” Teleoperation Mode: 5 pts
- “MIN” End Game: 5 pts

The “MIN” strategy can achieve **20 pts**.

As we walk through each of these baseline strategies, we can go back and evaluate all of the previous assumptions we made and take each of the strategies to their logical end. For example, what if we designed the best robot for tackling all of the DEFENSES? We will call this our “SEIGE” strategy. Assuming a robot could move through all of the DEFENSES with ease and SCALE the tower, the following scores can be determined:

- “SEIGE” Autonomous Mode: 10 pts
- “SEIGE” Teleoperation Mode: 45 pts + 1 RP
- “SEIGE” End Game: 15 pts

The “SEIGE” strategy can achieve **70 pts + 1 RP**.

Next, what if we optimized a robot to only score Low Tower Goals? We have to reevaluate some of our previous assumptions at this point. Since we are not worried about crossing every DEFENSE, what path would we take in Autonomous Mode? The easiest obstacle to traverse is the Low Bar, so if the robot starts in the Neutral Zone and chooses the optimal path under the Low Bar (10 pts), then scores a Boulder in the Low Tower Goal (5 pts), we start Teleoperation Mode in the Courtyard ready to go back through the Low Bar and pick up another Boulder.

Before we look at Teleoperation Mode, lets review the field layout.

Once Teleoperation Mode starts, our rational agent (the robot) will choose the optimal path back to the Neutral Zone to pickup a Boulder. The robot goes back under the Low Bar, into the Neutral Zone and picks up a Boulder. Then the robot takes the optimal path back to the Courtyard, via the Low Bar, and scores a Boulder in the Low Tower Goal (2 pts). We will call this our “LOW” strategy.

Now we have to challenge our previous assumption that the cycle time is the same as the duration of the time to complete the cycle in Autonomous Mode. Before, our cycle time assumed we had to CROSS every DEFENSE which made our average cycle time plausible at 15 seconds. Now the robot is simply dashing under the Low Bar, back and forth between the Neutral Zone and the Courtyard, and dropping a Boulder in the Low Tower Goal. Given the difficulty of crossing the other defenses and the ease of going under the Low Bar, along with the optimized distance of traveling between the two zones by the shortest path, we will assume the cycle time is approximately half of the original. This gives us 16 cycles, instead of the original 8 cycles. Please note, that with your students and mentors, you should test this assumption with the “duck walk” method listed in Part 1.

Moving into the End Game, we have to challenge the assumption that it will take 15 seconds to accomplish the End Game, given that the robot no longer has to SCALE the tower; it simply has to drive onto the BATTER and park. Applying the same logic above, we can assume half of the time previously allotted, returning 7.5 seconds (or 1 cycle) to Teleoperation Mode. This brings our total number of cycles to 17.

Assuming a robot could move through the Low Bar optimally, score in the Low Tower Goal quickly, and then CHALLENGE the Tower, the following scores can be determined:

- “LOW” Autonomous Mode: 15 pts
- “LOW” Teleoperation Mode: [(17 cycles x 2 pts/cycle)+(second Low Bar crossing for 5 pts)] 39 pts
- “LOW” End Game: 5 pts

The “LOW” strategy can achieve **59 pts**

Finally, what if we optimized a robot to only score High Tower Goals? We will call this our “HIGH” strategy. Building off of our optimized path and cycle time adjustment above, we can assume a cycle time less than 15 seconds, but we have to account for the extra time it will take to aim and hurl a Boulder into the High Tower Goal. Since this is a theoretical calculation, and the difficulty is in-between the two, we will assume a cycle time of 10 seconds. This gives us 10 cycles, instead of the original 8 cycles. Feel free to play with this number and see how the calculations turn out with different cycle times.

Moving into the End Game, we can use the same logic above to determine that since we are only parking on the BATTER, we will not take the entire 15 seconds. Assuming we can drive forward and park on the BATTER in 5 seconds after completing our final cycle in the Courtyard, we return 10 seconds (or 1 cycle) to Teleoperation Mode. This brings our total number of cycles to 13.

Assuming a robot could move through the Low Bar optimally, score in the High Tower Goal quickly, and then CHALLENGE the Tower, the following scores can be determined:

- “HIGH” Autonomous Mode: 20 pts
- “HIGH” Teleoperation Mode: [(13 cycles x 5 pts/cycle)+(second Low Bar crossing for 5 pts)] 70 pts
- “HIGH” End Game: 5 pts

The “high” strategy can achieve **105 pts**

Decisions Decisions Decisions

After reviewing different strategies with our new tool, we can make some observations:

- The 1 RP awarded in the qualifying rounds for a BREACH, equal to 20 pts in the playoff rounds, is approximately equal to 10 LOW cycles or ~7 HIGH cycles.
- By specializing on one task, a robot can have the largest individual impact on a qualifying match by scoring High Tower Goals.
- By focusing on DEFENSES, a robot can assure at least 1 RP per qualifying match and 20 pts per playoff match.
- Per second, a robot can score points the most optimally in Autonomous Mode.
- During a qualification match, on average with our models, approximately 25% of points will be scored in Autonomous Mode, 60% of points will be scored in Teleoperation Mode, and 15% of points will be scored in the End Game.

Before we choose a strategy, we have to decide what we want to accomplish with our robot. Do we want to build a robot that might perform average in the qualifying matches, but will position us to be picked onto a strong Alliance for the Finals? Do we want to build a robot that will best position us to win all of our matches and be a top Alliance Captain? Do we have limited resources and want to build the simplest robot that can give us the highest impact in any given match? That is up to each team to decide for themselves, as a group. Approach this question realistically, but don’t sell yourself short. Pick an attainable goal and stick to it. For the purposes of this article, we are going to choose to accomplish a goal in-between winning over 50% of our matches at any given event and winning a world championship. We are going to compete for a State Championship. To accomplish this goal, our robot will need to qualify for the State Championship by winning a District Event. We will define this goal as our Robot Mission Statement. This term will be the basis of our next article, so tuck it in the back of your head for later.

Given our models, observations, and Robot Mission Statement; we are going to choose the strategy that allows us to have the largest individual impact on a qualifying match. This means we will evaluate designs for a robot that can most efficiently score Boulders in the High Tower Goal.

Now this is a very good stopping point for your first “brainstorm/strategy” meeting. Before students leave, we always give the most important homework assignment of the season: RESEARCH EXISTING TECHNOLOGIES!

Research

Once you have gone over the game, ran through the game theory, and reasoned out an initial strategy it is time to step back and gather perspective on your assumptions and aspirations. A great way to do this is to see what other teams were able to accomplish in previous games with similar scoring objects and objectives. For example, this year’s game has poof-style balls and a hanging bar. If we look back at previous games that had poof-style balls, we find **Rebound Rumble [2012]** and **Aim High [2006]** are good candidates. If we look for games where robots had to lift themselves off the ground and hang, we find **Ultimate Ascent [2013]** and **FIRST Overdrive [2008]** at the top of the list. If we look extra hard, we can even find a game that fits both of these criteria: **FIRST Frenzy [2004]**.

By researching the strategies used in previous games with similar scoring objects and objectives, and by researching the mechanisms teams used to manipulate those scoring objects and complete those objectives, students can put into perspective what is possible and begin to formulate better and more efficient ways of accomplishing the game objectives by building on the work of their forerunners. This is the same approach college engineering students use when evaluating their Senior Design Projects, scientists use when writing papers to be published, and inventors use when patenting new creations. This process allows us to, as Sir Isaac Newton once said, stand on the shoulders of giants.

Below are the game animations for the aforementioned games to research and a match from each game:

**Ultimate Ascent [2013] Game Animation****Rebound Rumble [2012] Game Animation****FIRST Overdrive [2008] Game Animation****Aim High [2006] Game Animation****FIRST Frenzy [2004] Game Animation**

Summary

So what value did these exercises add? By maximizing each individual scoring objective, and questioning our previous assumptions, we were able to determine the impact of each scoring objective. By walking through the optimal match flow for each maximized scoring objective, new strategies and design considerations can be found. By researching previous games with similar scoring objectives, strategies can be put in perspective and novel approaches can be uncovered.

These exercises also build buy-in with the students and mentors on a strategy, reducing confusion and conflict later in the season, and provide a focus moving forward for defining Robot Requirements.

Please feel free to join the conversation on our **Facebook** or **Twitter** with your questions, thoughts, and feedback on these articles!

**Updated 20160112 to fix second DEFENSE crossing error*

**Updated 20160113 to fix REACH vs CROSS scoring error*