There are a number of constraints on the problem that come from the physics of flight, but also from the rules of the race. By rule, the aircraft accelerations cannot exceed 10 g. (1 g is the acceleration due to gravity.) In addition, the aircraft will stall if the coefficient of lift exceeds a threshold, and so the available lift depends on the speed of the aircraft. Aircraft must past through the air gates (double pylons) in a level attitude, and within a narrow altitude range. The aircraft ground speed cannot exceed 200 kt at the start gate. It’s often beneficial to cross through an air gate at a heading different than the heading of the air gate, but the Team 99 pilot Michael Goulian maneuvers around pylons during the first more oblique the crossing, the less space round of the Red Bull Air Race in the United Arab Emirates on March 12, 2016. there is to fit through the gate. So there’s a (Predrag Vuckovic/Red Bull Content Pool photograph) limit to the gate crossing angle. (The actual limit used depends on the risk the pilot is willing take that he will strike a pylon and incur a time penalty.) In addition, there are often safety lines to protect spectators that the aircraft may not cross, and which constrain the optimal path through the course. The optimization itself is performed using the same techniques we teach in AeroAstro class 16.323, “Principles of Optimal Control.” Using custom software, the problem is transcribed, meaning that the continuous trajectory is represented by the aircraft state at many discrete points in time. This reduces the original infinite-dimensional problem into a nonlinear program (NLP), which has a finite (but very large!) number of variables and constraints. Typically, the resulting NLP will have thousands of variables and constraints. Solving the NLP numerically yields the optimal control solution.
Applying optimal control theory to air racing
Published on Nov 18, 2016
Annual magazine review of MIT Aeronautics and Astronautics Department research and educational initiatives.