Robust Low Altitude Behavior Control of a Quadrotor Rotorcraft Through Sliding Modes

This paper gives the full dynamical model of a commercially available quadrotor rotorcraft and presents its behavior control at low altitudes through sliding mode control. The control law is very well known for its robustness against disturbances and invariance during the sliding regime. Theplant, on the other hand, is a nonlinear one with state variables are tightly coupled. The simulations have shown that the algori thm successfully drives the system towards the desired traject ory with bounded control signals. I. UNMANNED AERIAL VEHICLES (UAV S) A UAV is a flying robot having its own power supply, having no human pilot and maintaining the flight through an appropriate scheduling of aerodynamic forces either autonomous ly or by remote control. The UAV systems are capable of being invisible to radars and of performing formation flight. With such properties, a UAV system is cheap enough to sacrifice and powerful enough to carry sensors, camera and communication systems and lightweight weapons. More importantly, a UAV can maintain the flight beyond the limits of a human pilot. Such kind of small scale and highly versatile systems are used in a wide spectrum of applications. For instance, colle ting information (imaging, pursuit, searching, video acqui sition and reconnaissance), security, surveillance, control (sm uggling prevention), targeting, meteorologic and agricultural ap plications, traffic management and steering, telemetry (remot sizing) and crisis management after natural disasters are s om examples at a first glance. Accomplishing these high level missions with UAV systems is critically dependent upon the performance at low level command and control schemes. This fact has made the design, prototyping, implementation and manufacturing of autopil t systems a growing industry. The choice of the autopilot for a UAV system may depend upon the mission statement yet, regardless of the mission statement, the vehicle must be robust enough to cope with the difficulties of the operating environment. Sliding mode control systems are very well known for their robustness against disturbances and invari ance during the sliding mode. The technique is known also as Variable Structure Control (VSC) as the system during the sliding regime operates in a predefined subset of the phase space. This work is supported by TOBB ET̈ U BAP Program (Contract No: ET̈ U BAP 2006/04) Corresponding Author, TOBB Economics and Technology Unive rs ty, Department of Electrical and Electronics Engineering, Sö güt zü, Ankara, Turkey, E-mail: onderefe@ieee.org, Phone: +90-312-292-4 064, Fax: +90-312292 4091 VSC scheme is well-known for its robustness to uncertainties and disturbances. Conceptually, the controller d esign in this framework is based on the nominal representation of the system about which the bounds of the uncertainties are assumed to be available. The decision mechanism operates on the basis of switching on the different sides of a decision boundary, which is called the sliding hypersurface [1], [2] , [3], and the goal of the design is to enforce the error vector toward this hypersurface during the reaching phase. Once th e error vector is confined to the sliding hypersurface, it obey s the behavior imposed by the set of equations describing the hype rsurface, i.e. sliding mode starts and the error vector conve rges to origin. The control strategy is therefore called Sliding Mode Control (SMC) in the related literature, [1], [2], [3]. Duri ng the sliding mode, the control system becomes insensitive to the disturbances and uncertainties unless the decision mechan ism violates the physical limits for maintaining the sliding mo tion. SMC strategy has been applied successfully in a wide variety of design problems ranging from the control of motio n control systems, and chemical processes to the control of chaotic systems. Hung et al., [1], review the control strate gy for linear and nonlinear systems and discusses the design fo r systems represented in canonical forms. Another systemati c examination of SMC approach is presented in [4], in which the practical aspects of SMC design are assessed for both continuous-time and discrete-time cases and a special consideration is given to the finite switching frequency, limit ed bandwidth actuators and parasitic dynamics. Misawa discus ses the SMC design for discrete-time systems in [5] for the linear case and in [6] for the nonlinear case with unmatched uncertainties, Sabanovic et al. [7] elaborate the chatteri ng f ee SMC design, Bartolini et al. [8] formulate the chattering-f ree SMC for MIMO systems, and Erbatur et al. [9] investigate the robustness properties of SMC technique on a 2-DOF direct drive SCARA robot. Extensive range of application domains of the SMC scheme with robustness properties motivate us to design the low lev el control laws for the quadrotor rotorcraft system considere in this paper and by some other researchers. For example Castillo et al. [10], [11] have performed real time experime nts and assessed the performance of a nonlinear controller. In [12], classical PID controller is considered and model base d design is experimented. Hanford et al., [13], present a simp le closed loop equipped with MEMS sensors and PIC based processing unit. Hoffman et al., [14], achieve the formatio n control by SMC technique and focuse on collision and obstacl e avoidance by extracting the state variables with a Kalman filter. Vision based control of the quadrotor rotorcraft sys tem is studied in [15], which exploits the Moiré patterns, and in [ 16], which utilizes double cameras. Camlica dwells on a linear quadratic controller in [17], and Waslander puts an emphasi s on the insufficiency of classical control methods and propos es the integral SMC associated with reinforcement learning to achieve multi agent control. In [19], vehicle stabilizatio n based on the backstepping technique is presented with successful results. The current SMC design problem is involved with coupled and highly nonlinear dynamics, noisy observations and demanding performance requirements. The organization of the paper is as follows: The dynamic model of the vehicle is presented in the next section, the SMC technique is presented in the third section, behavior control is discussed next, simu lation results and concluding remarks are given at the end of the paper. II. T HE DYNAMIC MODEL OF THE VEHICLE A sketch of the quadrotor rotorcraft system studied in this study is shown in Fig. 1, where the Euler angles and the cartesian coordinate frame are shown. The equations of moti on are given in (1) and the values of some variables seen are tabulated in Table I.