Phil came up with this idea. Play
the 2013 smash-hit game Flappy Bird using a model predictive
control approach where the model is phrased as a mixed integer program. You can see the result in the above
video. The red line shows our controller's planned route, which changes as new obstacles come into view. I'll break
this all down a little bit.

Model predictive control is a method of control where you model the system out to a finite horizon and optimize the
trajectory with respect to the series of inputs. Then you act according to the first step in your optimal input and
repeat the process at the next time step with a little bit of new information.

We expressed the model as a mixed integer linear program, an optimization problem with linear constraints and
objective functions where all or some of the variables can be integers or booleans. In this case, the constraints
impose both the physics of the game—ballistic motion with discrete impulses from flaps—and the objective
of avoiding the pipes, floor, and ceiling. The input in this case are a series of booleans describing whether or not
the bird jumps in each time step. We implemented the model in CVXPY, a Python package and domain-specific modeling
language for convex optimization problems.

We forked Sourabh Verma's Pygame implementation of Flappy Bird
and hacked it up a bit. At each time step, Flappy Bird calls our function for input. It passes the current state to
our controller, which updates the initial conditions and pipe positions, solves for a trajectory, and returns the
first action from its optimal input.

This technique works pretty well. It doesn't quite run in real time with the lookahead set to a distance that allows
it to succeed. We used a neat trick to improve the speed and look ahead distance. The model's time step increases
with look ahead time. In other words, the model is precise for its first few time steps, and gets less careful later
in its prediction. The thinking is that this allows it to make approximate long term plans about jump timing without
over-taxing the solver.

If you want to run it, you'll need to download Gurobi or switch to
an open source solver.