For one of the ideas below, or one that you didn’t examine from a previous list (you pick), do some reading and thinking. Then for each of those ideas, type about one single-spaced page answering the following questions:
What’s your understanding of the problem? Are there variants of the problem you can phrase that you think is more interesting, practical, or solvable? What are some approaches you can imagine using to attack one of the variants of the problem? What are potential obstacles to each approach, and what approaches do you think are most promising? What is an extremely simplified version of the problem that you might solve first, if you attacked this problem?
Probabilistic roadmaps are constructed once, and then queried perhaps many times. There’s a tradeoff between computation at construction, the memory required to store the data structure, the “work” done at query time, and the resulting path quality. For example, PRM* builds a very dense graph, which takes memory, and may make queries slower.
The first paper below takes a different approach, and removes vertices and edges that may be somehow redundant in a PRM, reducing memory costs and speeding search – but the paths might be less good.
Research idea: are there better approaches to building a low-memory roadmap? How should obstacles be represented? (See paper 2.) Can optimality be maintained in some way, perhaps by performing optimization after some set of imperfect but useful paths has been found? If so, how can multiple diverse paths be extracted from the graph?
Sometimes the simplest robot is best. The papers below explore designing a fixture (a rigid-body shape) that causes a box to fold or a knot to be tied when force pushes the cardboard or string up against the fixture. How should such fixtures be developed?
Even though there are existing papers, I think there are interesting extensions possible. Can the knot-tying work be made practical, with a portable tool? How should the boxes themselves be designed to be suitable for fixture-based folding?
How can a shipping company pack irregular objects into a box most effectively? The problem has been previously studied, but I think there might be interesting variations on it. For example, what if all objects must be packed into the box from the top down, using a robot arm (directional packing)? If you had a nice solution, you could use the robot arm in our lab to demonstrate some results.