Dynamic Modelling of a Quadrotor Aerial Vehicle with Nonlinear Inputs Armando S. Sanca*, Pablo J. Alsina* and J´ es de Jesus F. Cerqueira† Abstract— In this paper the quadrotor dynamic model with nonlinear inputs is presented. Deadzone and saturation non- linear inputs are considered for the quadrotor reflected to the actuators. The goal is to obtain a faithful mathematical representation of the mechanical system for system analysis and control design, not only in hover as presented in many works, but also in motion when take-off, land and flight for aerial navigation task. The model was implemented in Matlab/Simulink simulation model to optimize the design and to project control. Simulations of the model show that the nonlinear inputs must be considered in the control project. I. INTRODUCTION T HE unmanned aerial vehicles (UAV’s) are expected to become a major part of the aviation industry over the next years, primarily enabled by developments in computer science, automatic control, robotics, communications and sensor technologies [1]. UAV’s are important when they come to performing a desired task in a dangerous and/or unaccessible environment [2]. More recently, a growing interest in unmanned aerial vehicles has been shown among the research community. One type of aerial vehicle with a strong potential is the rotorcraft and the especial class of four-rotor aerial vehicles, also called quadrotor. This vehicle, has been chosen by many researchers as a very promising vehicle for indoor/outdoor navigation using multidisciplinary concepts [3], [4], [5], [6], [7]. The quadrotor configuration is more propitious to be used and not requires complex mechanical control linkages for rotor actuation and their high payload-to-power ratio makes it a good candidate for inspection and other tasks. For example, the possible application in the aerial supervision of oil and gas plants and detection having the potential to significantly reduce cost and risk to human life [1]. The quadrotor is an under-actuated and dynamically unsta- ble system; the dynamic behavior is nonlinear with deadzone and saturation inputs that have to be stabilized by a suitable control. The model that represents the dynamic behavior of the quadrotor is complex. Many works presented in the literature use simplified models, where nonlinear effects and performance of the actuators are ignored [1], [3], [4]. In addition to this functional complexity, the algorithms also This work was supported by Human Resources Program of the National Petroleum Agency 14 in UFRN (PRH ANP - 14 and 22) * is with Computing Engineering and Automation Department, Federal University of Rio Grande do Norte, Natal RN CEP 59072-970, Brazil armando;pablo@dca.ufrn.br †is with Electrical Engineering Department, Federal University of Bahia, Salvador BA CEP 40210-630, Brazil jes@ufba.br f(u) -¯ u2 -¯ u1 ¯ u1 ¯ u2 u Fig. 1. Saturation and deadzone nonlinearity. have to be implemented in the embedded hardware and have to fulfil realtime requirements while limited memory and processing onboard capacity have to be considered [1], [2]. This paper presents the development of a dynamic mo- delling of a quadrotor including actuator nonlinearities. The paper is organized in five sections, including the present introduction. Section II presents the preliminary theories. Section III presents the mathematical modelling of a quadro- tor aerial vehicle. Section IV present some simulations results and finally section V provides the conclusions and the future works. II. BACKGROUND A. Saturation and deadzone nonlinearity Saturation, deadzone, backlash, and hysteresis, are most common actuator nonlinearities in practical control systems [8]. Saturation nonlinearity exists in almost real control system. The actuator saturation not only deteriorates the con- trol performance causing large overshoots and large settling times, but also lead to instability since the feedback loop is broken in such situations. A general term for this phenomena is the reset windup [9]. The standard saturation nonlinearity function is expressed by: sat ¯ u (u)=  sgn(u)¯ u if |u| > ¯ u; u if |u|  ¯ u, (1) where sgn(·) is the sign function. sat(·) denote the symmetric saturation function having saturation level ¯ u on the input control signal u. For all u ∈ R. Deadzone is a static nonlinearity that describes the insen- sitivity of the system to small signals, having undesirable effects on the feedback loop dynamics and control system performance. It represents “a loss of information” when the