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Controller Synthesis and Performance Optimization for Aerobatic Quadrotor Flight

We present a method for synthesizing high-performance controllers for the autonomous execution of aerobatic quadrotor maneuvers that are defined by rapid variations of the flyer’s angular velocity, such as multi-flips or the Pugachev’s cobra. In the proposed approach, we employ Lyapunov theory to find the sets of control parameters that make the unique fixed point of the closed-loop angular-velocity error dynamics exponentially stable during an aerobatic maneuver, provided that the angular-velocity reference satisfies a set of conditions. Then, we show that the resulting closed-loop attitude error dynamics remain bounded. The proposed controller synthesis method allows for the minimization of a parameterized performance figure of merit (PFM), which is employed to measure the angular-velocity control error accumulated during a maneuver. The approach adopted here is to show that a primal optimization problem can be reformulated as a series of quasiconvex sub-problems; then, we introduce a technique to find a solution and prove that this optimum is global. By design, the resulting controllers have a simple linear time-invariant (LTI) structure that depends on a small number of coefficients, which makes the experimental implementation of the control schemes extremely efficient and the associated real-time computational cost very low. The effectiveness of the introduced methods for controller design and performance optimization is compellingly demonstrated through theoretical analysis, simulations, and experiments in which high-speed multi-flip aerobatic maneuvers are executed.