Mining Asteroids: The Antipodes' Bold Mission

In the 12th Global Trajectory Optimization Competition (GTOC 12), our team, TheAntipodes, took on the exciting challenge of sending mining ships to asteroids. We had to find the best way to send these ships to collect as much material as possible and bring it back to Earth. Imagine trying to aim a dart at a spinning dartboard that is way out in space while also having to deal with the fact that dartboard is made of asteroids.

#Overview of Our Approach

We devised a plan that involved five main steps:

1. Generate Asteroid Subsets: We looked for groups of asteroids that could be mined efficiently.
2. Chain Building with Beam Search: We created sequences of asteroids for our ships to visit using a smart searching technique.
3. Low-Thrust Trajectory Optimization: We calculated the best paths for our ships to take with minimal fuel use.
4. Manual Refinement of Rendezvous Times: We fine-tuned the timing of when our ships would meet the asteroids.
5. Optimal Solution Set Selection: Finally, we picked the best solutions based on what would yield the most return.

#The Challenge of Asteroids

The GTOC is a competition that really puts the scientific community to the test. The goal is to come up with creative solutions for what seems like impossible problems related to space missions. In GTOC 12, we had to send ships from Earth to visit multiple asteroids and bring back as much material as possible.

There were many factors to consider. We didn’t know the order in which the ships would visit the asteroids, which made things tricky. Each ship needed to figure out the best route while also considering the time it took to travel between asteroids and back to Earth. Additionally, we had to work with a whopping 60,000 asteroids and plan missions that could last up to 15 years.

#Finding Asteroid Subsets

We started by figuring out the best groups of asteroids to target. This was all about finding sets of asteroids that would allow us to make successful mining trips. To do this, we worked with a method that helped us eliminate the asteroids that weren’t going to work well for our missions.

We then grouped the remaining asteroids based on their paths. By looking at the best times for traveling between asteroids, we identified groups that could be mined in one go, which we called "self-cleaning" sequences. The more we could minimize travel time, the more material we could return to Earth.

#Beam Search for Asteroid Sequences

After we had our groupings, we used a technique called "beam search." Think of this as a way to create paths for our ships to follow, one asteroid at a time. In this step, we figured out the best order for the ships to visit asteroids by adding one asteroid at a time and testing the routes.

Beam search helps to narrow down the best options by looking at a limited number of promising paths at each step. It’s like trying to find your way through a maze by only looking at the most likely paths instead of checking every single option.

#Optimizing the Paths

Once we had our asteroid sequences, we optimized the paths our ships would take. We had to ensure the ships used the least amount of fuel while reaching their destinations. For this, we used what’s called "sequential convex programming," which is a fancy way of saying we tackled the math needed to figure out the best routes step by step.

#Fine-Tuning the Rendezvous Times

After all that planning, we went through a manual process to fine-tune the rendezvous times of the ships with the asteroids. It’s like adjusting the timings in a dance routine – everyone had to be in sync to make it work. By refining these meeting times, we could ensure that our ships were operating at peak efficiency.

#Selecting the Best Solutions

Finally, we selected the best solutions from all the paths and sequences we had created. This involved picking a combination of ships and asteroid visits that would allow us to maximize our returns. We used a genetic algorithm, which is somewhat like nature’s way of selecting the fittest individuals, to determine which combinations performed the best.

#The Result

In the end, our team ranked fifth in the competition! We managed to send 27 ships to mine materials from 222 asteroids. This led to a pretty impressive score.

#The Lessons Learned

What we learned from this experience is vital for future competitions. Self-cleaning missions helped us simplify the problem and deliver good results quickly. Our method of generating asteroid subsets proved to be effective, and our final solution combined both creativity and practical calculations.

While we faced challenges, particularly in managing the complexity of the missions, the experience taught our team a lot about optimization strategies and the importance of cooperation.

#Future Directions

Looking ahead, there is tremendous potential for refining our methods and strategies. The success of our approach could lead to more effective solutions in future competitions. The techniques we developed may also inspire real-world applications in space exploration and mining.

In GTOC 12, we faced an incredible challenge, and it was a true test of creativity, teamwork, and scientific knowledge. By trying to shoot for the stars – or rather, the asteroids – we forged connections and learned lessons that will last long after the scores were tallied. Here’s to reaching new heights in the future!