Controlling formations with double integrator and passive actuation

This paper considers the problem where a group of agents must achieve a rigid formation specified by a subset of interagent distances. They must do so by being only able to sense the positions of their neighbors, agents with whom they share a specified desired distance, and knowing only their own velocities. The paper builds upon the work of [12] and [16]. The former assumes that the agents are modeled as single integrators. The latter assumes double integrator dynamics and assumes that agents can also sense the velocities of their neighbors, increasing the communication/sensing burden. In contrast this paper assumes that the agent velocities are generated by the actuation signals through a Positive Real dynamics. Double integrator dynamics happen to be a special case of this. Further, unlike [16] no agent needs its neighbor's velocities. We enunciate a control law consistent with our specification, argue that no law for this problem can be globally stable, and as is done in [12] and [16] for the laws therein, prove its local stability.