This study considers the coordination control problem of a group of moving rigid bodies. Each rigid body communicates with other bodies via the distance-induced neighbour graphs. The authors design the distributed control laws for the angular velocity and linear velocity of rigid bodies, and establish sufficient conditions without relying on the dynamical properties of neighbour graphs, to guarantee that the rigid bodies reach the attitude synchronisation and avoid collision with nearby bodies while the communication networks keep connected. Moreover, they introduce a leader into the system to guide all rigid bodies to the desired attitude. Simulation examples are given to illustrate the authors' results.