We present a study of the dynamics and control of a 28-gram quadrotor during the execution of aerobatic maneuvers in the presence of propeller-aerodynamic-coefficient and torque-latency time-variations. First, through a momentum-theory-based analysis of the flow field surrounding the robot during aerobatic flight, we develop a dynamic linear time-varying (LTV) description of the torque acting on the flyer in which both considered effects explicitly appear as distinct mathematical terms. Then, an adaptive control scheme, composed of a backstepping controller and a modified recursive least-squares (RLS) estimator, is designed to counteract the negative effects produced by the time-varying dynamics of the torque that drives the flyer. The suitability and efficacy of the proposed methods are demonstrated through real-time flight experiments in which the quadrotor autonomously performs three different types of aerobatic maneuvers: triple flips, Pugachev's Cobras and mixed flips. Furthermore, analyses of the experimental data compellingly show that the proposed control scheme consistently improves the performance of the aerial vehicle during aerobatic flight, compared to those achieved by using a high-performance linear time-invariant (LTI) controller that does not account for time-varying torque generation.

The dynamics of quadrotors are affected by time-varying torque latency, which can greatly alter the stability robustness and performance of the closed-loop control schemes employed for flight; this issue is especially relevant during the execution of aerobatic maneuvers such as high-speed multi-flips. To address this problem, we propose two controller synthesis methods associated with two different modeling approaches. In the first approach, we describe torque latency with a linear time-invariant (LTI)model, identified through ground experiments, which is then used to design a backstepping-based nonlinear controller. In the second approach, we employ an improved linear time-varying (LTV)model with a priori unknown parameters, which is used to synthesize and implement a novel nonlinear adaptive control scheme updated in real time using the recursive least-squares (RLS)algorithm. Empirical observations suggest that the torque delay affecting the system depends on the time-varying angular speed of the flyer and its derivative. This phenomenon is explained by the fact that the aerodynamic forces produced by, and acting on, the rotating propellers vary with the local velocity of the incident flows. Hence, in the proposed adaptive structure, we define the parameters of the LTV latency model as linear functions of the angular speed reference and its derivative. Experimental results compellingly demonstrate the efficacy of the methods introduced in this paper; compared to the highperformance linear controller in [1]-[3], the backstepping-based control scheme and adaptive controller decrease the average root mean square (RMS)value of the control error by 17.82 % and 38.42 %, respectively.

We present a new experimental method for the generation and real-time implementation of high-speed aerobatic maneuvers, including multiple flips, on a 19-gram autonomous quadrotor. A key element in the proposed approach is the design and experimental tuning of a gain scheduling control strategy in which two linear time-invariant (LTI) controllers are alternatingly activated and deactivated to switch between a normal flight mode and an aerobatic mode, enabling the flyer to perform consecutive multiple flips in a robustly stable manner. The implementation of the controllers is done using on-board power, sensors and computing capabilities, so that the quadrotor remains fully autonomous during flight. Notably, the attainment of autonomy, using real-time control, is made possible by the development of a new method for speed planning based on cubic functions, the geometric generalization of the notion of multi-flip and the empirical identification of the flyer's dynamics, required for trajectory generation and controller synthesis. Compelling experimental results demonstrate the suitability of the proposed approach. In particular, we present maneuvers that include consecutive single, double, and triple flips about the flyer's roll principal axis and a non-principal axis. To the best of our knowledge, to this date, the flyer used in this research is the smallest controlled quadrotor to have autonomously accomplished three consecutive flips while remaining stable.