Robot Navigation Under MITL Constraints Using Time-Dependent Vector Field Based Control

In this work, we consider the problem of robot navigation, under spatial and temporal constraints, modeled as Metric Interval Temporal Logic (MITL) formulas. We introduce appropriate control schemes, driven by time-dependent vector fields, that satisfy both the problems of (a) entering an arbitrary neighborhood of the workspace within a given time interval, and, (b) avoiding collision with any given obstacle. We model the problems (a) and (b) as MITL formulas, defined upon a specific class of atomic propositions, and proceed in building more complex MITL expressions that can be decomposed into a conjunction of the former formulas. Finally, we propose a way to generate a hybrid automaton, whose execution satisfies the given MITL formula, by appropriately composing the control schemes. We validate our methodology via a numerical simulation.