Consensus Control of Rigid Body Spacecraft in Orbital Relative Motion using TSE(3) and Exponential Coordinates

In this paper, two consensus control algorithms are proposed for control of multi-agent rigid body spacecraft in orbital relative motion. In the first approach, a proportional-derivative (PD) consensus control method, an extension of the Morse-Lyapunov analysis in the framework of the tangent bundle TSE(3) associated with Lie group SE(3) is used where rotation matrices parameterize the attitude of the rigid bodies. In the second approach, a proportional-integral-derivative (PID) consensus control protocol is introduced where the configurations of the rigid bodies are described in terms of the exponential coordinates associated with the Lie group SE(3). The control objective is to stabilize the relative pose configurations with velocity synchronization of the spacecraft which share their states according to a static communication topology in the presence of gravitational forces and torques. Finally, simulation examples are given to demonstrate the proposed methods.