  In this paper, we consider multiple mobile agents moving in Euclidean space
with point mass dynamics. Using a coordination control scheme, we can make the
group generate stable flocking motion. The control laws are a combination of
attractive/repulsive and alignment forces, and the control law acting on each
agent relies on the position information of all agents in the group and the
velocity information of its neighbors. By using the control laws, all agent
velocities become asymptotically the same, collisions can be avoided between
all agents, and the final tight formation minimizes all agent global
potentials. Moreover, we show that the velocity of the center of mass is
invariant and is equal to the final common velocity. Furthermore, we study the
motion of the group when the velocity damping is taken into account. We prove
that the common velocity asymptotically approaches zero, and the final
configuration minimizes the global potential of all agents. In this case, we
can properly modify the control scheme to generate the same stable flocking.
Finally, we provide some numerical simulations to further illustrate our
results.
