Decomposability of global tasks for multi-agent systems

Abstract

Multi-agent system is a rapidly developing research area with strong support from both civilian and military applications. One of the essential problems in multi-agent system research is how to design local interaction rules and coordination principles among agents such that the whole system achieves desired global behaviors. To tackle this problem, a divide-and-conquer approach was proposed in [1], and the basic idea is to decompose the requested global specification into subtasks for individual agents in such a way that the fulfillment of these subtasks by each individual agent should lead to the satisfaction of the global specification. Then, the design reduces to achieving the assigned subtasks for corresponding individual agents. In [1], it was shown that not all global tasks can be decomposed, and a necessary and sufficient condition on the decomposability of a task automaton between two agents was presented. For more than two agents, we then proposed a hierarchical algorithm as a sufficient condition for decomposability. This paper aims to extend the necessary and sufficient decomposability conditions for any arbitrary finite number of cooperative agents. A new necessary and sufficient condition on decomposability of a task automaton is proposed, here. Several examples are provided to illustrate the decomposition scheme and conditions.

Decentralized modular hybrid supervisory control for the formation of unmanned helicopters

“…The collision avoidance supervisor, $$A_C$$, is a centralized supervisor for $$UAV_k$$, $$k=1,..,n$$. To implement this supervisor in a decentralized way and to realize local supervisors, we utilize our proposed decomposition scheme introduced in [2] and [53]. Here, local supervisors can be found by the projection of the global supervisor to each agent's local event set.…”

“…The collision avoidance supervisor, A C , is a centralized supervisor for UAV k , k = 1, .., n. To implement this supervisor in a decentralized way and to realize local supervisors, we utilize our proposed decomposition scheme introduced in [2] and [53].…”

“…Lemma 3 Theorem 1 in [53]. A deterministic automaton A C = (Q, q 0 , E = ⋃ n i=1 E i , 𝛿) is decomposable with respect to the parallel composition and natural projections, P i , i = 1, … , n, such that A C ≅ || n i=1 P i (A C ) if and only if…”

On conditional decomposability

“…It has been shown in [2] that decomposability is important because it is computationally cheaper to compute locally synthesized supervisors that constitute a solution of the supervisory control problem for this decomposable specification. Recently, the notion of decomposability has also been extended to automata as an automaton decomposability in, e.g., [6].…”

On the revision problem of specification automata

“…A more recent attempt to use Context Free Languages (CFL) for robotic control appears in [3]. Finite automata are used as a specification language in [4]. Another very popular formal specification language is temporal logics with multiple applications in robotics [5]- [12].…”