## Section: New Results

### Fundamentals results and algorithms: distributed planning

Participants : Eric Fabre, Loig Jézéquel.

A planning problem consists in organizing some actions in order to reach an objective. Formally, this is equivalent to finding a path from an initial state to a goal state in a huge automaton. The latter is specified by a collection of resources, that may be available or not, and actions that consume and produce resources. In the case of optimal planning, actions have a cost, and the objective is to find a path of minimal cost to the goal.

Our interest in this problem is threefold. First, it is naturally an instance of a concurrent system, given that actions have local effects on resources. Secondly, it is a weak form of an optimal control problem for a concurrent/distributed system. Finally, we are interested in distributed solutions to such problems, which is a very hot topic in the planning community under the name of “factored planning.”

Our contribution to this topic is the first optimal factored planning algorithm [23] . It is based on the observation that a planning problem can be translated into a network of components, modeled as weighted automata in our case. We have then designed a message passing procedure on this network, based on weighted automata calculus, where each component determines its part of the best global action plan using only local information: its local model, and messages received from neighbors about shared actions. This distributed solution resolves both a constraint solving problem, and an optimization problem. The optimal plan is given as a tuple of partially synchronized local plans, therefore as a partial order of actions. We are currently experimenting this approach on benchmarks of planning problems.