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...ization of coupled oscillators [81, 39, 72, 73, 14], algebraic connectivity 6 of complex networks [65, 12, 43], asynchronous distributed algorithms [54, 26], formation control for multi-robot systems =-=[21, 68, 69, 24, 89, 88, 48, 96, 20]-=-, optimization-based cooperative control [75, 42, 37, 2], dynamic graphs [56, 61, 40, 99], complexity of coordinated tasks [36, 44, 52, 53], and consensus-based belief propagation in Bayesian networks...

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... history in the field of Computer Science. In [1], the importance of the relation between graph Laplacian, a well-known matrix in algebraic graph theory [2], and special cases of consensus problems were realized. In that work, all the vehicles have linear dynamics and the network has ideal links (i.e. the transfer function of the links is 1). In addition, certain Nyquist plots were useful in stability analysis for a multi-vehicle formation stabilization in Fax et al.. A more appropriate alternative to formation stabilization is to represent formations as rigid and unfoldable graphs/structures [7]. In this work, we do make use of a standard multivariable frequency domain analysis for convergence of linear consensus protocols. Two main contributions of this paper are to consider networks with time-delay and dynamic systems with bounded inputs. In [5], graph Laplacians appear in the context of attitude alignment of multiple spacecraft (i.e. a special agreement problem). An informal algorithm on attitude alignment for flocking of flying dynamic agents in a 3-D space was first introduced by Reynolds in 1987 without a convergence proof [8]. In [3], the authors made an attempt to prove the c...

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... comment on all of this work, but we can broadly group them in several categories. One class focuses on the effect of interconnection topology on the type of formation equilibrium configurations [1], =-=[2]-=-, where it was shown that the rigidity of the interconnection graph plays a crucial role. Another class of coordination algorithms uses potential functions to express the group task [3], [4], [5]. Pot...

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...entsof our control law. We show figures that demonstrate the ap-splication of this control law to a collision avoidance scenario,sknown as the splitlrejoin maneuver, coined by Olfati-Sabersand Murray =-=[6]-=-. Since this paper only outlines preliminarysresults on collision avoidance and multi-vehicle maintenance,swe will discuss some of our ongoing and future work. Wesconclude this paper by highlighting a...

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... the graph for the agents is rigid. According to [197], a graph of n agents is rigid if at least 2n− 3 edge distances are available. Motivated by the graph rigidity, research has been conducted 10 in =-=[198]-=-–[202] to drive a group of agents to the desired interagent configuration by ensuring that a certain number of edge distances are identical to the desired ones. The graph rigidity recovery after loss ...

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...the cost functions needed to pose an optimal control problem. The obtained (centralized) optimal control problem is then solved using the nonlinear trajectory generation (NTG) software package [11]. The issues regarding the distribution of this optimization problem is also discussed. In [12], we introduced the notion of “formation graphs” and their importance in unique (and unambiguous) representation of multi-vehicle formations. These graphs are used to obtain bounded and distributed control laws for formation stabilization of vehicles with linear (i.e. double-integrator) dynamics. Later, in [13], we formalized the notion of formations of multiple agents/vehicles and minimal requirements, in terms of the number of edges, for uniquely specifying a formation. This is done based on the notion of “combinatorial graph rigidity” [7]. A related formalism is suggested in [4] that relies on “infinitesimal rigidity”. Here, we add specification of “foldability” [12] to the definition of a formation graph. In addition, we explicitly specify the required cost for navigation and tracking in formation. In [3], the problem of formation stabilization using Model Predictive Control (MPC) is explored. H...