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This paper addresses the collision-free consensus problem in a network of agents with single-integrator dynamics. Distributed algorithms with local interactions are proposed to achieve consensus while guaranteeing collision-free among agents during the evolution of the multi-agent networks. The novelty of the proposed algorithms lies in the definition of neighbors for each agent, which is different from the usual sense that neighbors are selected by the distance between agents in the state space. In the proposed strategies, the neighbor set for each agent is determined by the distance or difference between agents in the index space after ordering and labeling all agents according to certain ordering rules including weighted order and lexicographic order. The consensus analysis of the proposed algorithms is presented with some existing results on algebraic graph theory and matrix analysis. Meanwhile, by realizing the relations between order preservation and collision-free, a systematic analysis framework on order preservation and hence collision-free for agents in arbitrary dimension is provided based on tools from monotone systems theory. Illustrated numerical examples are presented to validate the effectiveness of the proposed strategies. [ABSTRACT FROM AUTHOR]

Abstract: This paper considers the consensus problem of double integrator multi-agent systems where: (i) each agent is subject to input saturations, and (ii) the velocity (second state) of each agent is not available for feedback. We present new consensus algorithms that handle simultaneously the above mentioned situations. Sufficient conditions are derived such that consensus algorithms developed for first- and second-order multi-agent systems in ideal situations can be used to account for input saturations and remove the requirement of velocity measurements. To illustrate the effectiveness of the proposed approach, we propose solutions to two different second-order consensus problems in the case where the input is saturated and the velocity states are not available for feedback and simulation results are provided in each case. [Copyright &y& Elsevier]

Abstract: In this paper, we study the distributed containment control problem for networked Lagrangian systems with multiple dynamic leaders in the presence of parametric uncertainties under a directed graph that characterizes the interaction among the leaders and the followers. We propose a distributed adaptive control algorithm combined with distributed sliding-mode estimators. A necessary and sufficient condition on the directed graph is presented such that all followers converge to the dynamic convex hull spanned by the dynamic leaders asymptotically. As a byproduct, we show a necessary and sufficient condition on leaderless consensus for networked Lagrangian systems under a directed graph. Numerical simulation results are given to show the effectiveness of the proposed control algorithms. [Copyright &y& Elsevier]