@article {97,
	title = {Decentralized rigidity maintenance control with range measurements for multi-robot systems},
	journal = {International Journal of Robotics Research},
	volume = {34},
	year = {2015},
	month = {01/2015},
	pages = {128},
	chapter = {105},
	abstract = {This work proposes a fully decentralized strategy for maintaining the formation rigidity of a multi-robot system using only range measurements, while still allowing the graph topology to change freely over time. In this direction, a first contribution of this work is an extension of rigidity theory to weighted frameworks and the rigidity eigenvalue, which when positive ensures the infinitesimal rigidity of the framework. We then propose a distributed algorithm for estimating a common relative position reference frame amongst a team of robots with only range measurements in addition to one agent endowed with the capability of measuring the bearing to two other agents. This first estimation step is embedded into a subsequent distributed algorithm for estimating the rigidity eigenvalue associated with the weighted framework. The estimate of the rigidity eigenvalue is finally used to generate a local control action for each agent that both maintains the rigidity property and enforces additional constraints such as collision avoidance and sensing/communication range limits and occlusions. As an additional feature of our approach, the communication and sensing links among the robots are also left free to change over time while preserving rigidity of the whole framework. The proposed scheme is then experimentally validated with a robotic testbed consisting of six quadrotor unmanned aerial vehicles operating in a cluttered environment. },
	keywords = {Decentralized control, distributed algorithm, distributed estimation, graph rigidity, multi-robot},
	doi = {10.1177/0278364914546173},
	url = {http://ijr.sagepub.com/content/34/1/105},
	author = {Daniel Zelazo and Antonio Franchi and Heinrich H. B{\"u}lthoff and Paolo Robuffo Giordano}
}
@conference {98,
	title = {Rigidity Maintenance Control for Multi-Robot Systems},
	booktitle = {2012 Robotics: Science and Systems Conference},
	year = {2012},
	month = {07/2012},
	address = {Sydney, Australia},
	abstract = {Rigidity of formations in multi-robot systems is important for formation control, localization, and sensor fusion. This work proposes a rigidity maintenance gradient controller for a multi-agent robot team. To develop such a controller, we first provide an alternative characterization of the rigidity matrix and use that to introduce the novel concept of the rigidity eigenvalue. We provide a necessary and sufficient condition relating the positivity of the rigidity eigenvalue to the rigidity of the formation. The rigidity maintenance controller is based on the gradient of the rigidity eigenvalue with respect to each robot position. This gradient has a naturally distributed structure, and is thus amenable to a distributed implementation. Additional requirements such as obstacle and inter-agent collision avoidance, as well as typical constraints such as limited sensing/communication ranges and line-of-sight occlusions, are also explicitly considered. Finally, we present a simulation with a group of seven quadrotor UAVs to demonstrate and validate the theoretical results.},
	keywords = {Decentralized control, Formation control, Motion control of multiple robots, Multi-robot systems, Rigidity mainenance},
	author = {Daniel Zelazo and Antonio Franchi and Frank Allg{\"o}wer and Heinrich H. B{\"u}lthoff and Paolo Robuffo Giordano}
}
