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Inspired by the concept of network algebraic connectivity, we adopt anextended notion named rigidity preservation index to characterize the rigidityproperty for a formation framework. A gradient based controller is proposed toensure the rigidity preservation of multi-robot networks in an unknownenvironment, while the rigidity metric can be maximized over time duringrobots' motions. In order to implement the controller in a distributed manner,a distributed inverse power iteration algorithm is developed which allows eachrobot to estimate the global rigidity index information. Simulation results areprovided to demonstrate the effectiveness of the estimation and control scheme.

Distributed estimation and control for preserving formation rigidity for mobile robot teams