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In this paper, a general biased min‐consensus protocol for continuous‐time multi‐agent systems is presented. In this protocol, agents considered as sources maintain static states, while the state of each non‐source agent evolves using a general min‐consensus‐like function, which takes the states of its neighbours and a biased term as inputs. The properties of the general function have been identified so that the proposed protocol can achieve global asymptotic stability. Unlike conventional consensus protocols where a network of agents reach an agreement on certain quantities of interest, agents under the general biased min‐consensus protocol will converge to different states but can generate various design results pertaining to complex combinatorial optimization problems, such as the shortest path problem and its variants. [ABSTRACT FROM AUTHOR]

This work focuses on the construction of rigid formation from non‐rigid ones in the two‐dimensional space. Analogously to operations of Henneberg sequence aiming to guarantee the minimal rigidity of formation, two new operations are introduced, allowing one to sequentially build any rigid graph by connecting non‐rigid ones. A systematic construction sequence is developed based on proposed operations, and is shown to be able to restore rigidity by introducing minimum number of new edges during the construction process. Further applications of the proposed operations are also presented, one of which is successfully employed in the problem of persistence analysis of directed graphs, and can verify the persistence of a given graph with a speed two times faster comparing with existing solution. [ABSTRACT FROM AUTHOR]

A robotic sensor network is advantageous in performing a coverage task compared to the static sensor network because of its ability to self‐deploy and self‐reconfigure. However, since the sensor has a limited sensing range, when mobile sensors are initially deployed, sensors located far away from the region of interest may not be able to self‐deploy themselves, that is, participate in the coverage task. This results in a degradation of coverage performance by the robotic network. This paper proposes a novel algorithm in order to improve the coverage performance by the whole mobile sensor network by guaranteeing the participation of all sensors in the coverage task. The algorithm is a combination of the standard gradient‐based coverage algorithm and a leader‐following algorithm and is designed to maximise the joint detection probabilities of the events in the region of interest. As a strategy, first a set of leader sensors are selected based on the information which each sensor has gathered. The rest of the sensors will follow their leaders until they have sufficient information on the region of interest and then switch to the standard coverage algorithm. The proposed algorithm can be performed in a distributed manner. The results are validated through several numerical simulations. [ABSTRACT FROM AUTHOR]