Communication-Constrained STL Task Decomposition Through Convex Optimization

We propose a method to decompose signal temporal logic tasks for multi-agent systems under communication constraints. Specifically, given a task graph representing task dependencies among couples of agents in the system, we propose to decompose tasks assigned to couples of agents not connected in the communication graph by a set of sub-tasks assigned to couples of communicating agents over the communication graph. To this end, we parameterize the predicates' level set of tasks to be decomposed as hyper-rectangles with parametric centres and dimensions. Convex optimization is then leveraged to find optimal parameters maximising the volume of the predicate's level sets. Moreover, a formal treatment of conflicting conjunctions of formulas in the considered STL fragment is introduced, including sufficient conditions to avoid the insurgence of such conflicts in the final decomposition.