Autonomous hover flight for a quad rotor helicopter: Linear Quadratic Controller, Piecewise Affine -Hybrid systems controller
Authors
Sørensen, Martin ; Kjaergaard, Morten ; Bjørn, Jakob
Term
10. term
Publication year
2007
Pages
209
Abstract
Afhandlingen undersøger to styretilgange for en quadrotorhelikopter: en Linear Quadratic (LQ) tilstandsfeedback-controller med fokus på autonom flyvning, samt en PAHS-baseret controller udviklet på teoretisk niveau. Der bygges en ny hardwareplatform med sensorer og indbygget beregningskraft samt software, der forbinder til sensorerne og skaber et miljø, hvor en tilstandsestimator og controller kan implementeres. En accepttest bekræfter, at platformen opfylder kravene. En tidligere afledt ikke-lineær model af quadrotoren revideres for at designe en modelbaseret LQ-controller. Simuleringer viser, at denne controller stabiliserer quadrotoren, men den blev ikke taget i brug på hardwaren. Inden for PAHS-rammen afledes en metode kaldet Combinatoric Controllability Method til at generere en styrelov over konvekse polytoper (geometriske områder defineret ved lineære begrænsninger) for et forenklet quadrotorsystem. Anvendt på en 3-kube (en tredimensionel kube) producerer metoden en styrelov, der i simuleringer til sidst opfylder styringsmålet. Resultaterne indikerer også, at én specifik trajektorie kortvarigt forlader en ikke-admissibel flade i 3-kuben, før den igen kommer ind og konvergerer mod den forventede flade.
This thesis examines two control approaches for a quadrotor helicopter: a Linear Quadratic (LQ) state-feedback controller aimed at autonomous flight, and a PAHS-based controller developed at a theoretical level. A new hardware platform is built, with sensors and onboard computing, and software that interfaces with the sensors and provides an environment in which a state estimator and controller can be implemented. An acceptance test confirms that the platform meets its requirements. A previously derived nonlinear model of the quadrotor is revised to design a model-based LQ controller. Simulation results show that this controller stabilizes the quadrotor, but it was not deployed on the hardware. Within the PAHS framework, a method called the Combinatoric Controllability Method is derived to generate a control law over convex polytopes (geometric regions defined by linear constraints) for a simplified quadrotor system. Applied to a 3-cube (a three-dimensional cube), the method produces a control law that, in simulation, ultimately achieves the control objective. The results also indicate that one specific trajectory briefly exits a non-admissible face of the 3-cube before re-entering and converging to the expected face.
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