  Flying insects can perform rapid, sophisticated maneuvers like backflips,
sharp banked turns, and in-flight collision recovery. To emulate these in
aerial robots weighing less than a gram, known as flying insect robots (FIRs),
a fast and responsive control system is essential. To date, these have largely
been, at their core, elaborations of proportional-integral-derivative
(PID)-type feedback control. Without exception, their gains have been
painstakingly tuned by hand. Aggressive maneuvers have further required
task-specific tuning. Optimal control has the potential to mitigate these
issues, but has to date only been demonstrated using approxiate models and
receding horizon controllers (RHC) that are too computationally demanding to be
carried out onboard the robot. Here we used a more accurate stroke-averaged
model of forces and torques to implement the first demonstration of optimal
control on an FIR that is computationally efficient enough to be performed by a
microprocessor carried onboard. We took force and torque measurements from a
150 mg FIR, the UW Robofly, using a custom-built sensitive force-torque sensor,
and validated them using motion capture data in free flight. We demonstrated
stable hovering (RMS error of about 4 cm) and trajectory tracking maneuvers at
translational velocities up to 25 cm/s using an optimal linear quadratic
regulator (LQR). These results were enabled by a more accurate model and lay
the foundation for future work that uses our improved model and optimal
controller in conjunction with recent advances in low-power receding horizon
control to perform accurate aggressive maneuvers without iterative,
task-specific tuning.
