Nonlinear control for systems with bounded inputs: Real-time embedded control applied to UAVs Farid Kendoul, David Lara, Isabelle Fantoni and Rogelio Lozano Abstract—In this paper, we propose a nonlinear controller for the stabilization of a rotary-wing aircraft class. The control strategy is based on nested saturation technique which results in uncoupled and explicitly-given inputs. The introduction of positive gains in the control law has permitted to take into account the coupling terms, and to improve the dynamical performance of the closed-loop system especially the conver- gence speed. The controller performances have been confirmed in simulations when we have compared this approach with other existing controllers. We also present the testbed and the implementation of the control law on a quadrirotor aircraft. Using embedded sensors and onboard control, we performed a real-time autonomous flight. Indeed, experimental results have shown that the proposed control strategy is able to perform autonomously the tasks of taking-off, hovering and landing. I. INTRODUCTION In the last decade, a significant progress toward au- tonomous aerial vehicles with onboard intelligent capabilities has occurred. These systems open new applications in the field of robotics including surveillance, disaster (environ- mental, industrial and urban) remediation, search, rescue and many others. Recently, many different Vertical Take-Off and Land- ing (VTOL) UAVs including conventional helicopters, four- rotors aircraft (Draganflyer) and several designs such as the Guardian from Bombardier, and the Sikorksy Cypher or DragonWarrior have appeared and have been extensively studied. The main advantage of helicopters and other VTOL platforms is the manoeuvrability, needed for many robotic applications. Fig. 1. The modified Draganflyer rotorcraft When designing control laws for small aerial vehicles, some restrictions and conditions specific to small UAVs have to be considered. First, saturation nonlinearities are This work was supported by the French Picardie Region Council The authors are with the Heudiasyc laboratory, UMR CNRS 6599, Université de Technologie de Compiègne, 60200 Compiègne, France {fkendoul,dlara,ifantoni,rlozano}@hds.utc.fr particulary prevalent, where actuator saturation has a sig- nificant effect on the overall stability of the aircraft. Further- more, onboard or embedded microprocessors have a limited computational power, so that control algorithms have to be simple and easy to implement and to compute with minimum nonlinear terms. Several new nonlinear tools have been introduced for analyzing and controlling linear and nonlinear systems with saturation [1], [2]. One of the fundamental method is the Nested saturation technique proposed by Teel [3]. Exploiting this technique, Castillo et al. [4] have proposed a strategy to stabilize a four-rotors mini-helicopter with bounded inputs. They have considered that the quadrirotor is composed of two independent PVTOLs. The control strategy aimed to stabilize the altitude z, then the first PVTOL (φ − y displacement) and finally, to control the second PVTOL (θ − x movement) without taking into account the coupling between these three subsystems [4], [5]. Moreover, the convergence speed of the closed-loop dynamics turns out to be very slow. The present paper extends previous works from [4], [5]. The main contributions are first to prove the global asymp- totic stability of the complete model of rotary-wing aircraft category, considering the coupling between the PVTOLs and the influence of the altitude movement control on the horizontal (longitudinal and lateral) displacement. We also provide convergence analysis for a large range of saturation levels. This allows us to have more flexibility in the adjust- ment of the controller and to reduce the time of convergence. Moreover, some positive gains have been added in the control law in order to improve the convergence speed of the closed- loop system, and to guarantee the robustness against the nonlinear coupling terms. In addition, a real-time applica- tion with embedded control (embedded sensors for position and attitude measurement and onboard microprocessor for control inputs computing) has also been provided. In Section II, we present the nonlinear model of a class of aerial vehicles. Section III considers the stabilization prob- lem, and the convergence analysis of the closed-loop system is presented in Section IV. The dynamical performance of the proposed control law are compared in simulations to those of [4] and the simulation results are shown in Section V. Section VI is devoted to the testbed description and experiment setup. The paper ends with some conclusions in Section VII. II. ROTORCRAFT’S NONLINEAR MODEL Modeling the UAV dynamics is a main issue [6]. In most cases, the aerial robot is considered as a rigid body which is subject to body force F ∈ R 3 and torque τ ∈ R 3 , applied Proceedings of the 45th IEEE Conference on Decision & Control Manchester Grand Hyatt Hotel San Diego, CA, USA, December 13-15, 2006 FrIP1.2 1-4244-0171-2/06/$20.00 ©2006 IEEE. 5888