We consider the problem of controlling a group of vehicles to a rigid formation. Our approach mimics the development of dynamics of a system of particles subject to constraints. In particular, we use the notion of constraint forces to achieve, and maintain, a given formation. As opposed to the potential function approach used in the literature, the proposed constraint force approach directly compensates for only those parts of the applied forces which act against the constraints. We develop a stable control algorithm that will achieve the formation while ensuring navigation of the group based on the desired trajectories that are consistent with the constraints. Simulation results on an example are shown to verify the proposed method.