  Inspired by the concept of network algebraic connectivity, we adopt an
extended notion named rigidity preservation index to characterize the rigidity
property for a formation framework. A gradient based controller is proposed to
ensure the rigidity preservation of multi-robot networks in an unknown
environment, while the rigidity metric can be maximized over time during
robots' motions. In order to implement the controller in a distributed manner,
a distributed inverse power iteration algorithm is developed which allows each
robot to estimate the global rigidity index information. Simulation results are
provided to demonstrate the effectiveness of the estimation and control scheme.
