We present model predictive selection (MPS), a new method for selecting the stable closed-loop (CL) equilibrium attitude-error quaternion (AEQ) of an uncrewed aerial vehicle (UAV) during the execution of high-speed yaw maneuvers. In this approach, we minimize the cost of yawing measured with a performance figure of merit (PFM) that takes into account both the aerodynamic-torque control input and attitude-error state of the UAV. Specifically, this method uses a control law with a term whose sign is dynamically switched in real time to select, between two options, the torque associated with the lesser cost of rotation as predicted by a dynamical model of the UAV derived from first principles. This problem is relevant because the selection of the stable CL equilibrium AEQ significantly impacts the performance of a UAV during high-speed rotational flight, from both the power and control-error perspectives. To test and demonstrate the functionality and performance of the proposed method, we present data collected during one hundred real-time high-speed yaw-tracking flight experiments. These results highlight the superior capabilities of the proposed MPS-based scheme when compared to a benchmark controller commonly used in aerial robotics, as the PFM used to quantify the cost of flight is reduced by 60.30 %, on average. To our best knowledge, these are the first flight-test results that thoroughly demonstrate, evaluate, and compare the performance of a real-time controller capable of selecting the stable CL equilibrium AEQ during operation.

We present a new framework for implementing real-time embedded safety-critical controllers which utilizes hybrid computing to address the issue of limited computational resources, a problem that is particularly prevalent in microrobotics. In our approach, the nominal stabilizing control algorithm is implemented digitally while the safety-critical quadratic program is solved via a dedicated analog resistor array. We apply this hybrid computing architecture to a simulated collision avoidance task for a micro-aerial vehicle and show the benefit relative to a purely-digital implementation. By leveraging analog quadratic programming on the Crazyflie 2.1 micro quadrotor, a reduction in overall processing time from 8.9 ms to 0.6 ms is estimated for this computationally-limited system. We further display the viability of our proposed safety-critical control framework through real-time flight demonstrations, utilizing a novel prototype analog circuit tethered to the Crazyflie. The flight results confirm the functionality of the control structure and prototype circuit while highlighting the overall capabilities of hybrid computing.

We present a new method for synthesizing and implementing high-performancesix-degree-of-freedom($\boldsymbol{6}$-DOF) flight controllers for the Bee$^{++}$, an insect-scale flying robot driven by four independently-actuated flapping wings. Each wing of the Bee$^{++}$is installed with a preset orientation such that the stroke plane generated during flight is inclined, thus enabling reliable roll, pitch, and yaw torque generation. Leveraging this capability, we propose a Lyapunov-based nonlinear control architecture that enables closed-loop position and attitude regulation and tracking. The control algorithms presented in this article simultaneously stabilize position and attitude by independently varying the wingstroke amplitudes of the four flapping wings of the Bee$^{++}$. We use this particular control architecture to exemplify the process of controller synthesis and real-time implementation; however, the aerodynamic design of the Bee$^{++}$is compatible with a great variety of control structures and performance objectives. As a main result, we present the first set of experimental data demonstrating sustained and robust high-performance tracking of a$\boldsymbol{6}$-DOF reference signal during flight at the insect scale, which has been a long-standing control problem in the field of flapping-wing microrobotics. Furthermore, using data obtained through a series of systematic flight tests, we show that the Bee$^{++}$can achieve the highest$\boldsymbol{6}$-DOF performance ever recorded for an insect-scale flapping-wing flying robot during sustained flight.