Contribution of Koopman operator in path an‎d motion planning for nonlinear control systems

11/22/2025 12:00:00 AM

This thesis presents a comprehensive framework for enhancing path an‎d motion planning in mobile robotics through the systematic application of Koopman operator theory. The Koopman operator provides a powerful mathematical tool that transforms nonlinear dynamical systems into linear operators acting on infinite-dimensional function spaces, enabling the use of linear control techniques on inherently nonlinear robotic systems. We de- velop three novel algorithmic contributions that leverage thislinearization property. First, we introduce a hybrid Koopman-GraphAttention Network (Koopman-GAT) architecture that combines the globaldynamics modeling capabilities of Koopman operators with the local spatialreasoning of graph neural networks, achieving supe- rior path quality an‎dcomputational efficiency compared to classical methods. Second, we presenta Koopman- enhanced belief propaGATion framework for multi-agentcoordination that linearizes the nonlinear dynamics of belief evolutionduring message passing, resulting in 30-70% reduction in convergenceiterations. Third, we integrate Koopman operator theory with Soft ActorCritic reinforcement learning, treating the value function as a Koopmanobservable to achieve 93.4% success rate in naviGATion tasks withsignificantly improved sample efficiency. Experimental validation across multiple robotic platforms, includingdifferential drive robots an‎d the UR5 manipulator, demonstrates thatKoopman-based methods consistently outperform traditional approaches. TheKoopman-LQR controller achieves 3.1× faster convergence an‎d 40% reductionin control effort compared to feedback linearization, while maintainingcomputational efficiency suitable for real-time implementation. The- seresults establish Koopman operator theory as a unifying framework thatbridges model-based control with data- driven learning, providing boththeoretical guarantees an‎d practical performance improvements for autonomous naviGATion systems.

عملگر كوپمن , شبكه عصبي گراف , يادگيري تقويتي , سيستم هاي چند عامله , كنترل غير خطي

Koopman operator , graph neural networks , Reinforcement learning , multi-agent systems , nonlinear control

Amir Mahdi Izadi

Esmaeel Khanmirza