Trajectory Generation under Metric Interval Temporal Logic Specifications
نویسندگان
چکیده
Metric interval temporal logic (MITL) provides a tool to formulate high level tasks in an easy way. This allows to specify behaviour of a dynamical system in a given environment which lies beyond the scope of simple stabilization. Finding an input of the system which satisfies the MITL formula, demands new techniques and algorithms. In this thesis, a novel approach is presented which abstracts the dynamical system into a time optimal weighted transition system (WTS) and converts the MITL formula into a Timed Büchi Automaton (TBA). From the graph product of the WTS and TBA a sequence of environment states together with time constraints is obtained. Together with a user specified cost function, the sequence is translated into an optimization problem. The solution of this final optimization problem satisfies the MITL formula for the dynamical system in the given environment and is obtained by using methods from optimal control. Sammanfattning Metric interval temporal logic (MITL) ger ett verktyg för att formulera uppgifter p̊a hög niv̊a p̊a ett enkelt sätt. Detta gör det möjligt att specificera beteendet hos ett dynamiskt system i en given miljö som ligger utanför ramen för enkel stabilisering. Att hitta en insignal till systemet som uppfyller MITL-formeln kräver nya tekniker och algoritmer. I denna avhandling presenteras ett nytt tillvägag̊angssätt som abstraherar det dynamiska systemet till ett tidsoptimerat weighted transition system (WTS) och omvandlar MITL-formeln till en Timed Büchi Automaton (TBA). Fr̊an grafprodukten av WTS och TBA erh̊alls en sekvens av sakens tillst̊and tillsammans med tidsbegränsningar. Tillsammans med en användardefinierad kostnadsfunktion är sekvensen översatt till ett optimeringsproblem. Lösningen av det här slutliga optimeringsproblemet uppfyller MITL-formeln för det dynamiska systemet i den givna miljön och erh̊alls genom att använda metoder fr̊an optimal kontroll.
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