Dynamics and control of robotic aircraft with articulated wings

摘要

There is a considerable interest in developing robotic aircraft, inspired by birds, for a variety ofmissions covering reconnaissance and surveillance. Flapping wing aircraft concepts have been putforth in light of the efficiency of flapping flight at small scales. These aircraft are naturally equipped with the ability to rotate their wings about the root, a form of wing articulation. This thesis coverssome problems concerning the performance, stability and control of robotic aircraft with articulated wings in gliding flight. Speci cally, we are interested in aircraft without a vertical tail, which would then use wing articulation for longitudinal as well as lateral-directional control. Although the dynamics and control of articulated wing aircraft share several common features with conventional fi xed wing aircraft, the presence of wing articulation presents several unique benefi ts as well as limitations from the perspective of performance and control. One of the objectives of this thesis is to understand these features using a combination of theoretical and numerical tools.The aircraft concept envisioned in this thesis uses the wing dihedral angles for longitudinaland lateral-directional control. Aircraft with flexible articulated wings are also investigated. Wederive a complete nonlinear model of the flight dynamics incorporating dynamic CG location and the changing moment of inertia. We show that symmetric dihedral con guration, along with aconventional horizontal tail, can be used to control flight speed and flight path angle independentlyof each other. This characteristic is very useful for initiating an efficient perching maneuver.It is shown that wing dihedral angles alone can e ffectively regulate sideslip during rapid turns and generate a wide range of equilibrium turn rates while maintaining a constant flight speed and regulating sideslip. We compute the turning performance limitations that arise due to the use of wing dihedral for yaw control, and compare the steady state performance of rigid and flexible winged aircraft. We present an intuitive but very useful notion, called the e ffective dihedral, which allows us to extend some of the stability and performance results derived for rigid aircraft to flexible aircraft. In the process, we identify the extent of flexibility needed to induce substantialperformance bene fits, and conversely the extent to which results derived for rigid aircraft apply to a flexible aircraft. We demonstrate, interestingly enough, that wing flexibility actually causes a deterioration in the maximum achievable turn rate when the sideslip is regulated.We also present experimental results which help demonstrate the capability of wing dihedral forcontrol and for executing maneuvers such as slow, rapid descent and perching. Open loop as well as closed loop experiments are performed to demonstrate (a) the e ffectiveness of symmetric dihedral for flight path angle control, (b) yaw control using asymmetric dihedral, and (c) the elements of perching.Using a simple order of magnitude analysis, we derive conditions under which the wing isstructurally statically stable, as well as conditions under which there exists time scale separationbetween the bending and twisting dynamics. We show that the time scale separation depends on the geometry of the wing cross section, the Poisson's ratio of the wing material, the flightspeed and the aspect ratio of the wing. We design independent control laws for bending andtwisting. A key contribution of this thesis is the formulation of a partial diff erential equation (PDE) boundary control problem for wing deformation. PDE-backstepping is used to derive tracking andexponentially stabilizing boundary control laws for wing twist which ensure that a weighted integralof the wing twist (net lift or the rolling moment) tracks the desired time-varying reference input.We show that a control law which only ensures tracking of a weighted integral improves the stability margin of the twisting dynamics sixteen fold. A tracking control law is derived for the wing tip displacement which uses motion planning and a novel two-stage perturbation observer. This work on PDE-based control of wing deformation allows for the use of highly flexible wings on MAVs.Put together, the thesis provides a comprehensive understanding of the flight dynamics of arobotic aircraft equipped with articulated wings, and provides a set of control laws for performingagile maneuvers and for honing the bene fits of using highly flexible wings.