Inspired by Kevin Lynagh, I maintain an ongoing list of ideas that I want to work on eventually, and possibly pair on. Some of them are inspirde by research papers that I want to replicate to better understand the intricacies, some of them come from unanswered questions that came up in my life somewhere. Other things are topics that I simply wondered about at some point, and want do dig deeper for a bit.

Note that most of these ideass are not projects I am supervising as part of my PhD, these are things I am doing for fun, and in general not very academic.

Robotics

  • Optimal behavour of a vacuuming robot to cover the floor space efficiently: This would probably entail generating ‘realistic’ rooms automatically, deciding what sensors a vacuum robot should have (I am thinking only proximity), and what possible behaviours a robot can follow from that.
  • Landing a rocket: I am foremost interested in simply building a model (possibly in 2D for a start), and applying various approaches to the problem.
  • Examining the effect of modern stepsize controllers in numerical control: This is a version of what I did in a Thesis during my masters, and I would like to dig a bit deeper here. This would go in the direction discussed here in the scipy numerical integration community.
  • Exploring SAT solvers: Not entirely sure what I am specifically looking for here. Kevin Lynagh has a few ideas to the topic on his page, I am mostly interested if this can be used for robotics applications.
  • Comparing the exploration of ‘traditional’ motion planners to reinforcement learning and MPC: This would probably involve setting up some simulations, and just diligently doing some experiments with lots of visualizations. Could be on the example of classical control tasks (torque limited pendulum, mountain car, inverted double pendulum).

Software

  • Traveling Salesman Problem-Art: This involves approximating an image via a bunch of dots, and connecting them with the shortest path. Possible topics to pursue here are: optimal stippling, benchmarking different approaches of TSP-solvers, interfacing between python and cpp.
  • Simulating a leg through a pedal-stroke: Following up on my project I did before, I want to see when (and how) we actually apply pressure on the pedal.
  • Passing networks (PDF) in soccer over the curse of a season. How do passing networks change if the coach is replaced? Are there general trends visible in winning teams?
    There is an additional paper doing a deep dive of FC Barcelona in their most successful season here. Data for one season for several leagues is available here.

Papers

  • Moving horizon estimation: Enabling (amongst various other things) constrained state estimation, this is the counterpart to MPC for state estimation. This is a catch-it-all item on the list for various topics - please reach out if you are into state estimation/control.
  • LQR-Trees [1] and LQR-RRT* [2]: Both papers are for control of nonlinear systems.
  • Swing up control of a triple pendulum [1]
  • Distributed multi robot planning: [1] Implementing the linked paper first for the same case as done in the paper itself (2d masspoints), and then see if that can be extended to robot arms.

Games

  • Dog: Dog is a version of the boardgame Mensch ärger dich nicht that is played wih cards. Here is an explanation in german, and here are the rules in english. I am interested if there is some sort of optimal stragtey, and building an artificial intelligence that can play (well?).
  • Käsekästchen/Dots and Boxes: This game is a childrens game, but has surprisingly many strategic nuances. I am interested in a computational approach to playing this game (Monte-carlo tree search? Reinforcement learning?)
  • Labyrith: This game has the goal to visit a set of symbols with a figure. The figures move on a maze, which can be altered by pushing in new parts of the maze (and pushing others out). As in the previous two points, I am interested in figuring out if there is some optimal way to play this game.