Abstract
The paper studies the time-invariant formation problem of second-order multi-agent systems under a time-invariant directed communication topology. Extensions of the consensus protocol are introduced in the formation control. By choosing appropriate consensus states, the state-linear-transformation approach and the partial stability theory are adopted to analyze the formation problem. Sufficient and necessary algebraic criteria are derived for the formation regulation problem with or without velocity constrains and the formation tracking problem. They are expressed in terms of Hurwitz stability of matrices which are constructed from the gain matrices of formation control protocols.
Highlights
Formation control is one of the fundamental problems of multi-agent systems (MASs) where each agent maintains a desired geometric distance with its neighbors [1], [2]
Ren [19] introduced the consensus-based formation control strategies in the second-order multi-agent system to guarantee accurate formation maintenance in the general case of arbitrary information flow between agents. It proved that many existing leader-follower, virtual structure, and behavior-based formation control strategies can be unified in the general framework of consensus building and treated as special cases of consensus-based formation control strategies
We have investigated consensus problems of MASs and proposed a linear-transformation-based partial stability approach in [24] to analyze them
Summary
Formation control is one of the fundamental problems of multi-agent systems (MASs) where each agent maintains a desired geometric distance with its neighbors [1], [2]. X. Qu et al.: Consensus-Based Formation of Second-Order MASs via Linear-Transformation-Based Partial Stability Approach achieve an agreement on a common value. Qu et al.: Consensus-Based Formation of Second-Order MASs via Linear-Transformation-Based Partial Stability Approach achieve an agreement on a common value It is closely related with formation control [18]. Ren [19] introduced the consensus-based formation control strategies in the second-order multi-agent system to guarantee accurate formation maintenance in the general case of arbitrary information flow between agents It proved that many existing leader-follower, virtual structure, and behavior-based formation control strategies can be unified in the general framework of consensus building and treated as special cases of consensus-based formation control strategies. The linear-transformation-based partial stability approach is extended to the formation field These formation problems include formation forming and maintaining under a time-invariant directed communication topology.
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