Fractional PID Attitude Control of Multi-Agent Rigid Body Systems Using Rotation Matrices

A fractional proportional-integral-derivative (PID) attitude controller for multi-agent rigid-body systems is proposed in order to achieve attitude synchronization or balancing. The controller is designed on the tangent bundle of the special orthogonal group (SO(3)) and employs states comprising the rotation matrices and angular velocities of the bodies along with proportional, fractional derivative, and fractional integral feedback of these states. The performance of the closed-loop responses are evaluated numerically for both cases of synchronization and balancing.