Distributed scaling control of rigid formations

Recently it has been reported that biased range measurements among neighboring agents in the gradient distance-based formation control lead to an undesired collective motion. In this paper we take advantage of this effect and by introducing distributed parameters to the prescribed inter distances we are able to manipulate the steady-state motion of the formation. This manipulation is in the form of inducing simultaneously a combination of a constant translational and angular velocities and a controlled scaling of the rigid formation. Whereas the computation of the distributed parameters for the translational and angular velocities is based on the well-known graph rigidity theory, the parameters responsible the scaling are based on the recent findings of bearing rigidity theory. We carry out a stability analysis of the modified gradient system and simulations in order to validate the main result