This paper introduces a new control approach to perform formation control tasks on multi-agent systems, called D-formation control. The D-formation controller is a gradient-descent control law that exploits a regularized potential function to efficiently achieve specific formations. Taking inspiration from the flocking of birds, this approach differentiates itself from the several formation control strategies that can be found in the literature thanks to its flexibility. In fact, the approach that is usually employed in formation control is to try to enforce a set of very strict constraints in order to achieve rigid, a priori defined structures. We will show that the D-formation approach greatly relaxes such conditions. In this paper, the D-formation control problem is introduced, and the equilibrium configurations of the controller are characterized. Additionally , a strategy for switching from one stable equilibrium to another one, i.e. for changing the shape of the formation, is proposed.