Linear Temporal Logic-based Mixed-Integer Linear Problem Planning with the Koopman Operator

We present a formulation for a linear temporal logic (LTL)-based task planning using the Koopman operator. The dynamics of nonlinear systems can be represented as linear systems by lifting them to a space of augmented states using the Koopman operator. On the other hand, the lifted linear system can...

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Veröffentlicht in:IECON 2022 – 48th Annual Conference of the IEEE Industrial Electronics Society S. 1 - 6
Hauptverfasser: Tokuda, Shumpei, Yamakita, Masaki, Oyama, Hiroyuki, Takano, Rin
Format: Tagungsbericht
Sprache:Englisch
Veröffentlicht: IEEE 17.10.2022
Schlagworte:
Closed loop systems
Linear systems
Nonlinear dynamical systems
Nonlinear systems
Numerical simulation
Planning
Programming
ISSN:2577-1647
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Zusammenfassung:We present a formulation for a linear temporal logic (LTL)-based task planning using the Koopman operator. The dynamics of nonlinear systems can be represented as linear systems by lifting them to a space of augmented states using the Koopman operator. On the other hand, the lifted linear system cannot capture the nonlinear effects of inputs, which appear in many robotic systems. Therefore, instead of a lifted linear system, we can consider representing control-affine bilinear systems. However, since the lifted bilinear systems are nonlinear, we need to solve nonlinear programming problems for trajectory optimization. This paper presents a methodology for the trajectory optimization problem of the lifted bilinear system. Using the mixed-integer convex approximation, we can solve the trajectory optimization problem of the lifted bilinear systems as a mixed-integer linear programming problem. This formulation allows us to solve LTL-based task planning problems for nonlinear systems. The effectiveness of the proposed method was confirmed by numerical simulations.
ISSN:2577-1647
DOI:10.1109/IECON49645.2022.9969097