Available online at www.sciencedirect.com Automatica 39 (2003) 1583–1596 www.elsevier.com/locate/automatica Nonlinear modelling and control of helicopters  J.C. Avila Vilchis a , B. Brogliato b; * , A. Dzul c , R. Lozano c a Universidad Aut onoma del Estado de M exico, Facultad de Ingenier a 50130 Toluca, Mexico b INRIA Rhˆ one-Alpes ZIRST Montbonnot, 655 avenue de l’Europe 38334 Saint-Ismier, France c Universit e de Technologie de Compi egne BP 20529, HEUDIASYC UMR CNRS 6599 60205, Compi egne cedex, France Received 5 June 2001; received in revised form 12 February 2003; accepted 28 April 2003 Abstract This paper presents the development of a nonlinear model and of a nonlinear control strategy for a VARIO scale model helicopter. Our global interest is a 7-DOF (degree-of-freedom) general model to be used for the autonomous forward-ight of helicopter drones. However, in this paper we focus on the particular case of a reduced-order model (3-DOF) representing the scale model helicopter mounted on an experimental platform. Both cases represent underactuated systems (u ∈ R 4 for the 7-DOF model and u ∈ R 2 for the 3-DOF model studied in this paper). The proposed nonlinear model possesses quite specic features which make its study an interesting challenge, even in the 3-DOF case. In particular aerodynamical forces result in input signals and matrices which signicantly dier from what is usually considered in the literature on mechanical systems control. Numerical results and experiments on a scale model helicopter illustrate the theoretical developments, and robustness with respect to parameter uncertainties is studied. ? 2003 Elsevier Ltd. All rights reserved. Keywords: Nonlinear systems; Nonlinear control; Underactuated; Helicopter; Drone; Aerodynamics 1. Introduction The interest for designing feedback controllers for vari- ous types of autonomous ying systems (so-called drones) has increased during the past decade due to important po- tential applications. Among these systems, helicopters con- stitute a very specic class due to their particular dynamical features (which make authors generally classify helicopters outside so-called VTOL aircrafts as in McCormick, 1995). The main diculties (at a theoretical level) for designing stable feedback controllers for helicopters stem from their nonlinearities and couplings (for the solid mechanics part) and the fact that the inputs are not torques nor forces but displacements of some elements which enter the dynamics through aerodynamical forces/torques. This work is part of a project that concerns the modelling and control of a VARIO Benzin-Trainer scale model helicopter at the University  This paper was not presented at any IFAC meeting. This paper is recommended for publication in revised form by Associate Editor Henk Nijmeijer under the direction of Editor Hassan Khalil. ∗ Corresponding author. E-mail addresses: jc avila@uaemex.mx (J.C. Avila Vilchis), Bernard.Brogliato@inrialpes.fr (B. Brogliato), Alejandro.Dzul@hds.utc.fr (A. Dzul), Rogelio.Lozano@hds.utc.fr (R. Lozano). of Technology of Compi egne, France (see photograph in Fig. 1). In this paper and in Avila-Vilchis (2001) the focus is on the derivation of a suitable model for control purpose, incorporating the main aerodynamical eects. Since it is not possible to provide all the detail of calculations that yield the form of the aerodynamical terms, in this paper we just indicate the general structure of the 3-DOF model. All calculations and hypotheses are described in detail in Avila-Vilchis (2001). Helicopter vertical ight (take-o, climbing, hover, de- scent and landing) can be analyzed with the particular 3-DOF system obtained when the helicopter is mounted on an experimental platform. Although simplied, this 3-DOF Lagrangian model presents quite interesting con- trol challenges due to nonlinearities, aerodynamical forces and underactuation. Though the mathematical model of this system is much simpler than that of the “free-ying” case, its dynamics will be shown to be non-trivial (nonlin- ear in the state, and underactuated). In Avila-Vilchis and Brogliato (2000) a specic nonlinear controller is proposed using the dissipativity properties of the model. Some other previous works have been developed for control problems in helicopters (Kaloust, Ham, & Qu, 1997; Kienitz, Wu, & Mansour, 1990; Koo, Homann, Sinopoli, & Sastry, 0005-1098/03/$ - see front matter ? 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0005-1098(03)00168-7