Modeling and nonlinear dynamic analysis of angular velocity system of 2-DOF aerial manipulator

Abstract

This paper establishes the dynamic model of the angular velocity system of the 2-DOF (degree of freedom) aerial manipulator, describes the coupling relationship between the quadrotor aircraft and the manipulator, and provides the rotational speed relationship of each propeller during open-loop control. On this basis, the dynamic parameters, the nonlinear dynamics under static and dynamic conditions, and the Casimir energy of the system are studied in four parts. In the part of system dynamics parameters, the influence of manipulator configurations and postures on system moment of inertia, yaw motion, and lifting motion are analyzed, and their influence on gyroscopic effect is discussed. In the nonlinear dynamics of the system under static conditions, this paper analyzes the nonlinear dynamics of a typical aerial manipulator by the nonlinear dynamics methods. It reveals for the first time that the angular velocity of the system can produce dynamic behaviors such as sinks, chaotic oscillations, and period-doubling oscillations. The system is a non-autonomous system when it is under dynamic conditions. In this part, this paper considers the dynamic behaviors of the aerial manipulator in three situations: grasping operation, presence of external interference, and presence of time-varying yaw control quantity. It can be seen from the analysis that the dynamic conditions make the nonlinear dynamic behaviors of the system more complicated, which is worthy of further study. In the energy analysis, the Casimir energy of the three cases in this paper is calculated respectively when the sink, chaotic oscillation, and periodic oscillation are generated, and their mean, variance, and standard deviation are calculated. When the system is a sink, the three indexes are the smallest, the energy consumption is the least, and it is easier to control.