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

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

**Authors**:

Mavridis, Christos N.

Kyriakopoulos, Kostas,

Vrohidis, Constantinos

**Conference**: 2019 IEEE Conference on Decision and Control (CDC) pp. 232-237 , Nice, France

**Date**: December 11 - December 13, 2019

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 modeltheproblems (a) and (b) asMITLformulas,deﬁnedupon 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.

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