Tiltrotor Tricopter Dynamics and Control Using the Gibbs–Appell Formulation and Integrated Feedback Linearization with LQR-PD Control

The equations of motion of a flying robot composed of n rigid arms, each equipped with a motor at its end to provide controllability during complex three-dimensional maneuvers, were previously derived in [1]. The most significant outcome of that study was the demonstration that the robot can reach any point in space while simultaneously achieving an arbitrary desired orientation. It was shown that accomplishing this objective requires at least six actuators and, consequently, six propellers. However, increasing the number of actuators results in higher manufacturing costs, greater energy consumption, and increased overall weight. Therefore, the development and analysis of more efficient flying robot configurations become increasingly important. In the design proposed in this paper, a three-arm flying base is employed instead of a six-arm configuration, with a propeller mounted at the end of each arm. A distinctive feature of this design is that each propeller, in addition to rotating about its primary axis, can also rotate about a secondary axis. This capability enables the thrust vector generated by the main propeller motor to be reoriented by means of a smaller auxiliary motor, thereby allowing the robot to achieve arbitrary orientations in space. To facilitate the analysis, the flying robot is decomposed into several open-chain robotic structures. The equations of motion of the individual chains are first derived using the Gibbs–Appell formulation and then combined, while accounting for the constraints governing the interactions among the chains, to obtain the dynamic model of the complete system. Finally, the capability of the proposed tiltrotor tricopter to perform complex three-dimensional maneuvers is evaluated through an integrated feedback-linearization and LQR–PD control framework.