Attitude Consensus Control with Disturbance Rejection for Incompletely Cooperative Multi-agent Systems on $SO(3)$

The three-dimensional orthogonal matrix group
$SO(3)$
offers global, unique, and nonsingular attitude representation of the rotational motion. This paper addresses the attitude consensus problem with disturbance rejection for multi-agent systems consisting of incompletely cooperative agents evolving on
$SO(3)$
. Firstly, we establish an individual cost functional that evaluates the agent consensus aim using the natural Riemannian metric on
$SO(3)$
, and formulate the considered consensus problem as a differential game. Secondly, a baseline consensus protocol is designed following the inverse optimal control procedure. In addition, a finite-time disturbance observer on
$SO(3)$
is developed based on the non-singular terminal sliding mode technique, which is used for estimating and compensating for disturbances. The effectiveness of the proposed schemes is verified with simulations on a 4-vehicle formation setting.