Applied veRification for Continuous and Hybrid Systems Benchmark : Quadrotor Attitude Control

We present a case study of attitude control for a quadrotor drone and propose the application of reachability analysis to investigate and improve the robustness of the control design. The controller is to be implemented and tested using an experimental platform, the CrazyFlie. We intend to use measured data to improve the models employed in reachability analysis. Category: academic Difficulty: medium 1 Context and Origins Recent advances in low-power embedded processors, wireless communications and miniature sensors and actuators have increased the interest on the development of drones with a wide range of indoors and outdoors applications: safety, security, defense, inspection, communication links, data acquisition, entertainment, package delivery, not being exhaustive. Quadrotors are of particular interest when implementing small-scale drones because of the simpler control and stabilization mechanisms and their ability to perform vertical take-off and landing (VTOL), omnidirectional movements, hovering, or low speeds flights [1]. One disadvantage is the high power consumption during the flight. When approaching the control of quadrotors, we can identify two main problems: the attitude stabilization and the guidance [2]. The attitude stabilization aims to enhance the vehicle dynamics by feedback control. It can be employed to enhance stability in remote piloting. The guidance has a broader objective that is to control the position and the orientation of the vehicle, aiming the autonomous behavior. Usual approaches in guidance are interception, surveillance or rendez-vous [2]. In general, the attitude stabilization and the guidance problems are treated by separated control loops, being an inner loop related to the first, and an outer loop to the second. Generally, the time constants of the two problems are different, being the attitude stabilization with faster dynamics than the guidance. We develop a case study of attitude control of a quadrotor. In our approach we propose a nested control architecture exploiting the modularity of the model. An inner loop takes care of the angular rates and vertical speed, and an outer loop takes care of the angular orientation ∗Work developed as a visitor researcher to VERIMAG, France. G.Frehse and M.Althoff (eds.), ARCH15 (EPiC Series in Computer Science, vol. 34), pp. 57–72 57 Benchmark: Quadrotor Attitude Control A. E. C. da Cunha and position. In order to investigate the robustness of the controller, we apply reachability analysis [3,4]. We present two nonlinear models for the quadrotor, one based on the Euler angles and the other on quaternions. A linearized model obtained from the Euler angles model is used for control design. On the other hand, a linearized model obtained from the quaternions model is used for reachability analysis. The quaternions model is polynomial and singularity free, when compared to the Euler angles model. This enables the application of many reachability analysis techniques suitable to polynomial systems as, for example, [5] or [6]. In this work we overapproximate the polynomial nonlinearities using McCormick relaxations [7]. Moreover, we will implement the controller into a real experimental quadrotor platform, the CrazyFlie, from BitCraze, and use measured data to improve the model employed in the reachability analysis. Identification techniques for piecewise affine systems as in [8] are to be used in this step. Another benchmark for reachability analysis based on a quadrotor is presented in [9]. They define a flight envelope protection used for safety-preserving controller synthesis. In their definition of the flight envelope, they address both attitude stabilization and guidance problems. But they present a nonlinear model that disregards many of the relevant dynamic interactions for the attitude stabilization problem, for example, the Coriolis forces in translational and rotational dynamics. Therefore we believe that the model in [9] is more suited to address guidance problems, while the model presented in this paper is suitable for both attitude stabilization and guidance problems. This paper is organized as follows. Section 2 presents the quadrotor model and the attitude controller design. Section 3 introduces our approach for applying the reachability analysis. Section 4 presents some remarks on the current results of the work.