General Information

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Project Description

This summer I will be working on determining a method for planning out a path for multiple robots with a starting and ending point in a 2 dimensional plane. The problem is simplified by focusing on discs in a 2d plane instead.

Continuous Example

Discrete Example

Weekly Log

Week 1:

This week I worked on putting together a presentation as well as making some headway into gathering data on how the number of discs, the radius, and maximum distance from starting point to ending point affect the number of pairwise collisions that occur. I layed out a plan for what I am going to be researching as well as getting my workspace organized and set up for working. I met with my mentor, Jingjin Yu, and we layed out moreso what I will be starting with.

Week 2:

This week, I ran simulations to determine how the properties of the system affected the interaction between the discs. The results of this step are so far inconclusive since no sharp transition was found yet. I set up python andpygame within visual studios and then started to work in/learn python to create a grid for the discs to be on. This will be useful later for creating models with pygame.

Week 3:

This week, I generated graphs based on how the locality of travel and density of the discs area in a unit square affect the number of collisions. Using plot.ly along with python, I was able to run simulations on the number of pairwise collisions. In the system there apeared to be no sharp transitions

Week 4:

This week, I became interested in being able to use my GPU for running the simulations and worked on installing and learning how to use the proper software. Furthermore, I worked on implementing the Discs into a discrete case so that I could study the behavior of the discs and the number of unavoidable collisions in the discrete case with some collision avoidance behavior

Week 5:

I gathered basic data on the collision behavior, but the more random method of determining solutions to the problem caused a few problems with the speed of solving and thus the speed of collecting data. I worked this week on making the process deterministic. I also collected some more data.

Week 6:

This week, I worked more on data collection and exploring the solution. I implemented the locality based on edge distance generation for starting and ending nodes for the discs. I also collected data based on the locality and total discs in the environment as without the locality the results were predictable and there was no sharp transition.

Week 7:

This week, I worked more with locality and discovered moreso how it affects the number of collisions overall. There were no unexpected results however and there was also no perceiveable sharp transition. So far it seems like I would have to increase the sophistication for the collision avoidance to get a sharp transition.

Week 8:

This week, I am running clean data collection. Also, working on writing the final research paper and the summary of my experience in the program.

Week 9:

This week, I am continuing to write my final research paper based upon the results that were found. I would like to thank DIMACS and NSF for the funding that I received and also for the great Summer of Research that I had; it was an unforgettable experience.

Presentations

• First Presentation

• Final Presentation

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