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From High-Level Task Specifications to Geometric Control via Lyapunov Abstractions


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The goal of this research project is to narrow the existing gap between high-level discrete task planning and low-level continuous control in complex multi-agent missions within a control theoretic framework. We develop techniques that enable consistent mappings between high level spec cations and low-level control commands. We propose novel forms of Lyapunov-like barrier functions that capture high-level spatiotemporal spec cations and interactions among agents, and low-level geometric ows capturing feasible system trajectories. The main idea lies on the pairing of a Lyapunov-like barrier function and a geometric ow using notions and tools from geometric control and dynamical systems theory. The proposed method oers a reactive motion planning, decision-making and control design mechanism that is scalable with the number of agents and tasks, and thus applicable to large-scale systems involving hundreds of agents. The expected research outcomes will advance knowledge and the state-of-the-art in real-time planning, decision making and control in situations involving multiple autonomous and semi-autonomous agents. The proposed methods will allow safety-critical and time-critical missions to be carried out with minimal human supervision and minimal eort on planning and coordinating the mission. This will increase the situational awareness and readiness of the Air Force personnel and will provide better means to implement strategies and tactics in unknown, uncertain environments.



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