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Abstract. In multi-agent planning problems agents are requested to jointly solve a complex task consisting of a set of interrelated tasks. Since none of the agents is capable to solve the whole task on its own, usually each of them is assigned to a subset of tasks. If agents are dependent upon each other via interrelated tasks they are assigned to, moderately-coupled teams of agents are called for. Such teams solve the task by coordinating during or after planning and revising their plans if necessary. In this paper we show that such complex tasks also can be solved by looselycoupled teams of agents that are able to plan independently, although the computational complexity of the coordination problems involved is high. We also investigate some of the factors influencing this complexity.

Abstract. Task-based planning problems for multi-agent systems require multiple agents to find a joint plan for a constrained set of tasks. Typically, each agent receives a subset of tasks to complete. Due to task interdependencies, such task allocations induce interdependencies between agents as well. These interdependencies will prevent the agents from making a plan for their subset of tasks independently from each other, since the combination of such autonomously constructed plans will most probably result in conflicting plans. Therefore, a plan-coordination mechanism is needed to guarantee a conflict-free globally feasible plan. In this paper, we first present a brief overview of the main results achieved on plan coordination for autonomous planning agents, distinguishing between problems associated with deciding whether a coordination mechanism is necessary, designing an arbitrary coordination mechanism, and designing an optimal (minimal) coordination mechanism. After finding out that designing an optimal coordination mechanism is difficult, we concentrate on an algorithm that is able to find a (non-trivial) coordination mechanism that is not always minimal. We then discuss some subclasses of plan-coordination instances where this algorithm performs very badly, but also some class of instances where a nearly optimal coordination mechanism is returned. Hereafter, we discuss the price of autonomy as a measure to determine the loss of (global) performance of a system due to the use of a coordination mechanism, and we offer a case study on multi-modal transportation where a coordination mechanism can be designed that offers minimal restrictions and guarantee nearly optimal performance. We will also place the use of these coordination mechanisms in a more general perspective, claiming that they can be used to reuse existing (single) agent software in a complex multi-agent environment. Finally, we briefly discuss some recent extensions of our coordination framework dealing with temporal planning aspects.

In many task-planning domains, assemblies of autonomous agents need to construct plans and schedules for executing their assigned sets of tasks in order to complete them. Often, there will be dependencies between tasks to be executed by different agents. In such a situation, a plan-coordination problem arises when the joint plan is required to be feasible, whatever locally-feasible plans the individual agents come up with. This problem can be solved by plan decoupling, which is to add a minimum number of constraints such that each agent can make a plan for its set of tasks independently of the others while still joint-plan feasibility is guaranteed. Previous work on plan decoupling concentrated on a coordination framework where the only dependencies between tasks are precedence constraints. In this paper an extension of the framework is discussed where not only precedence constraints, but also synchronisation constraints can be used in order to express qualitative temporal constraints between tasks. It is shown that adding synchronisation constraints does not add any complexity to the plan-decoupling problem, and that a previously-developed approximation algorithm for plan decoupling can be extended to cope with synchronisation constraints as well.

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