Signal Temporal Logic Task Decomposition via Convex Optimization
This work addresses task decomposition for multi-agent systems in control and robotics, but it appears incremental as it builds on existing STL frameworks with specific parameterization methods.
The paper tackles the problem of decomposing a global Signal Temporal Logic (STL) formula into local tasks for multi-agent systems with pre-defined sub-teams, using convex optimization to parameterize predicate functions as hypercubes and proving that satisfying the conjunction of local tasks ensures global formula satisfaction.
In this paper we focus on the problem of decomposing a global Signal Temporal Logic formula (STL) assigned to a multi-agent system to local STL tasks when the team of agents is a-priori decomposed to disjoint sub-teams. The predicate functions associated to the local tasks are parameterized as hypercubes depending on the states of the agents in a given sub-team. The parameters of the functions are, then, found as part of the solution of a convex program that aims implicitly at maximizing the volume of the zero level-set of the corresponding predicate function. Two alternative definitions of the local STL tasks are proposed and the satisfaction of the global STL formula is proven when the conjunction of the local STL tasks is satisfied.