Relative position and attitude coordinated control based on unit dual quaternion

Abstract

In traditional algorithms, relative pose controls of a leader–follower rigid body consider the position and attitude as two subsystems in designing control laws. Since relative pose of a leader–follower rigid body is coupled, having a pose coupling control is a smarter choice. For deficiencies in decentralized control of relative pose, this article establishes a coupled dynamic and kinematic model of a leader–follower rigid body based on the dual-number and dual-quaternion theory framework. Furthermore, based on the proposed model, the sliding mode control theory is used to conduct coordinated control for relative pose of a leader–follower rigid body. The coupled algorithm does not need to design two sets of control laws for relative pose of a leader–follower rigid body; therefore, the complexity of the control system is reduced. Simulation results show that this algorithm does not only demonstrate the coupled control law of the relative pose but also show good tracking control performance.