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Inspired by the interesting findings regarding the hierarchy and coordination of pigeons in Nagy et al.  [Nature, 2010], we revisit the discrete-time leader–follower consensus problem with switching topologies. The purpose of this paper is to investigate the impact of hierarchical topologies and followers’ self-loops on the convergence performance of leader–follower consensus, including the convergence rate and robustness to switching topologies. We first study the fixed topology case, and show that the followers converge to the leader's state in finite time if and only if each follower has no self-loops and the topology is hierarchical. However, we show via counterexample, that leader–follower consensus may not be achieved when some followers have no self-loops and the topology is switching; even if each interaction graph has a spanning tree rooted at the leader. With the aid of binary relation theory, we further develop a new approach to present a novel sufficient condition for leader–follower consensus with switching topologies and with some followers having no self-loops. We prove that when no followers have self-loops and the same hierarchical organization is kept under the switching topologies, then the fastest rate of convergence in leader–follower consensus can be achieved; even in the presence of complex dynamic topologies. This is consistent with the natural phenomena found in pigeons by Nagy et al. [ABSTRACT FROM AUTHOR]

In this paper, we investigate distributed multi-agent tracking of a convex set specified by multiple moving leaders with unmeasurable velocities. Various jointly connected interaction topologies of the follower agents with uncertainties are considered in the study of set tracking. Based on the connectivity of the time-varying multi-agent system, necessary and sufficient conditions are obtained for set input-to-state stability and set integral input-to-state stability for a nonlinear neighbor-based coordination rule with switching directed topologies. Conditions for asymptotic set tracking are also proposed with respect to the polytope spanned by the leaders. [ABSTRACT FROM AUTHOR]

This paper addresses passivity-based pose synchronization in the Special Euclidean group SE(3). We first develop a passivity-based distributed velocity input law to achieve pose synchronization. We next show that the pose synchronizes exponentially fast under an assumption on the initial states of the bodies, with an exponential convergence rate given by algebraic connectivity of interconnection graphs. We also prove pose synchronization in the presence of communication delays and topology switches. We moreover give further extensions of the present law, where desirable velocities and collision avoidance are taken into account. Finally, the effectiveness of the present inputs is demonstrated through numerical simulations and experiments on a planar (2D) test bed. [ABSTRACT FROM AUTHOR]