Robust Attitude Tracking for Aerobatic Helicopters: A Geometric Approach

Abstract

This paper highlights the significance of the rotor dynamics in control design for small-scale aerobatic helicopters, and proposes two singularity free robust attitude tracking controllers based on the available states for feedback. 1. The first, employs the angular velocity and the flap angle states (a variable that is not easy to measure) and uses a backstepping technique to design a robust compensator (BRC) to actively suppress the disturbance induced tracking error. 2. The second exploits the inherent damping present in the helicopter dynamics leading to a structure preserving, passively robust controller (SPR), which is free of angular velocity and flap angle feedback. The BRC controller is designed to be robust in the presence of two types of uncertainties: structured and unstructured. The structured disturbance is due to uncertainty in the rotor parameters, and the unstructured perturbation is modeled as an exogenous torque acting on the fuselage. The performance of the controller is demonstrated in the presence of both types of disturbances through numerical simulations. In contrast, the SPR tracking controller is derived such that the tracking error dynamics inherits the natural damping characteristic of the helicopter. The SPR controller is shown to be almost globally asymptotically stable and its performance is evaluated experimentally by performing aggressive flip maneuvers. Throughout the study, a nonlinear coupled rotor-fuselage helicopter model with first order flap dynamics is used.

Attitude Control of Novel Tail Sitter: Swiveling Biplane–Quadrotor

“…The linearized equation is given by i=1ê i PR eqêi , and I I I is the 3 × 3 identity matrix. Details of the linearization procedure are given in [24]. For positive values of the gains k R , k ω , ζ i , Ω i it is observed that S(R eq ) is hyperbolic for all R eq ∈ Θ.…”

“…The gain matrices K X , K Y and D X , D Y are composed of natural frequency and damping parameters as in (24).…”

“…Since the sum of vector relative degree about each axes (4+4+4) is equal to the dimension of the state space of the extended system, the feedback linearization has trivial zero dynamics [15]. The authors' previous work on attitude tracking of aerobatic helicopters [16] has resulted in rigid body dynamics augmented with first order moment dynamics. Equations (19a) and (19b) represent the rigid body dynamics and the solution to its tracking problem has been obtained previously with geometric control techniques [17,18,19,20,21].…”

“…Here ζ i and Ω i (i ∈ {x, y, z}) are respectively the damping coefficient and natural frequency of the individual axes. With the control input (24), the error dynamics of the dynamically extended nominal system (19) reduces to Ṙe = R e êω (25a)…”

“…and Ω i > 0, the control input u given by (24), renders the desired equilibrium (I, 0, 0, 0) of the error dynamics (25) almost-globally asymptotically stable.…”