Quadrotors have promising applications such as payload transportation, which can change the future of the package delivery industry. However, many challenges block the way of implementing payload transportation in reality. Slung payload vibrations and quadrotor's energy consumption are among the major challenges, which are related to each other because payload vibrations affect energy consumption.

In this dissertation, the kinematics, dynamics, and energy models are first developed for both a single quadrotor and a transportation system consisting of a quadrotor with a slung payload. The proposed energy model is novel and introduces the concepts of power and energy quotients that, unlike the existing models, do not depend on quadrotor-related parameters such as motor and propeller parameters. This is the first energy model for such a transportation system.

Second, this dissertation focuses on polynomial trajectories, where a generic framework to design feasible polynomial trajectories of arbitrary degree with a large number of waypoints is presented. This allows for extending the capabilities of polynomial trajectories to overcome some kinematic limitations associated with continuous-path trajectories, e.g., arbitrary kinematic constraints.

Third, extensive vibration analyses of the transportation system and polynomial trajectories are conducted. As a result, a novel controller-independent payload vibration reduction method is proposed. The proposed method is more generic than the existing methods, e.g., anti-swing controllers.

Fourth, the effects of polynomial trajectories, payload mass, and cable length on quadrotor's energy consumption are studied. The comparison with an energy-minimized trajectory shows that polynomial trajectories are not only energy-efficient, but their design is simpler than energy-minimized trajectories and does not require quadrotor-related parameters.

Lastly, a robust energy-saving sliding mode controller with input saturation is designed for the transportation system. The experimental results show that the proposed controller is robust and energy-efficient when, qualitatively, compared with an existing energy-saving controller. The proposed controller is the first energy-saving controllers for such a transportation system.

This dissertation opens the door for package delivery with quadrotors by providing the first energy analysis, and energy-saving trajectories and controllers for quadrotors with slung payloads.