Design, Modeling and Control of an Octocopter
This master’s thesis project from the Department of Mathematics at KTH, Royal Institute of Technology, Stockholm, Sweden was carried out at Saab Dynamics, Linköping, Sweden. In this thesis, an octocopter was studied, which is a multirotor vehicle, a rotorcraft with more than two rotors. Multirotors have recently become very popular and have various interesting applications needing further research. Since the market for powerful credit-card-sized computers is continuously increasing, the development and research of multirotors is simplified.
The main purpose of this thesis project was to develop a complete open-sourced octocopter including control laws which should be used in future thesis projects at Saab Dynamics. Since the authors field is within Applied Mathematics, this thesis report has focused on the theoretical and analytical part of the project rather than the development process. Nevertheless, the report includes and gives a detailed overview of the complete octocopter and its final configuration. In addition, the report features system identifications which were carried out in order to estimate important properties of the vehicle.
In order to carry out mathematical analyses and propose control laws, a mathematical model of the vehicle was required. Since the vehicle moves in 6DoF (six-degrees of freedom), a suitable coordinate system handling these freedoms was needed. In this thesis, Euler angles and quaternions were used for representing attitude. The complete nonlinear model was derived using Newton’s second law of motion in a rotating reference frame. Additional effects such as aerodynamics, precession torques and motor dynamics were analyzed and modeled.
The main content of this report which can be divided into two part deals with the control of the octocopter. The first part investigates approaches for converting of the model control inputs, forces and torques, to corresponding motor commands, angular-rates. This issue is seldom covered in research articles proposing control laws for multirotors and requires special attention when developing multirotors. By minimizing the L2-norm, deriving control boundaries and using a priority algorithm which handles situations where the control demanded is greater than the momentary available control input, it was shown that the conversion between these properties was possible, even in critical situations.
The second part proposes control laws and approaches for controlling the vehicle in 6DoF. Three different control strategies have been proposed: pilot-based, attitude and position control. The pilot-based control is intended to be used by a pilot, controlling the in aviation standard roll, pitch and yaw-rate. The control method used is a full state feedback controller using a reduced observer, observing the motor dynamics. The attitude controller is an alteration of the pilot-based controller, controlling roll, pitch and yaw. Lastly, a position controller is derived, controlling the translational position of the vehicle, allowing for autonomous flying. The position controller uses a nonlinear Lyapunov based controller where the control inputs are converted to desired attitude reference inputs, send to the attitude controller.
The control laws were evaluated using a Simulink model where the complete nonlinear system was implemented. All derived control laws showed promising results and were able to accomplish desired behavior. The model featured a visualization of the vehicle in 6DoF running in real time and enabled for the use of a pc gaming controller, allowing for training and testing of e.g., the pilot-based controller. At the end, real flying data is presented and analyzed using the pilot-based controller. The report is finished of with a discussion, covering previously chapters of the thesis, proposing future interesting research and work.
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