Koopman-Operator-Based Attitude Dynamics and Control on SO(3)
Ti Chen, Jinjun Shan
Abstract
This paper presents an attitude control method based on Koopman operator theory. A set of observables is discovered to represent the nonlinear attitude dynamics on using an infinite-dimensional linear system. With the assumption of low angular velocities, a finite-dimensional linear system is obtained by removing the high-order terms. An attitude control synthesis method is developed on the basis of the linear optimal control algorithm for the reduced linear system. The proposed controller design method is compared with some classical nonlinear optimal controllers to show its advantages. Also, the leaderless attitude synchronization problem is solved with the help of the reduced linear system and the well-studied linear multiagent system theory. Furthermore, a possible solution to the case with a high angular velocity is provided. Simulations and experiments are conducted to verify the effectiveness of the theory.