Matrix-Guided Safe Motion Planning for Smart Parking Systems

This paper presents a matrix-based approach for motion planning of autonomous vehicles in structured parking environments under Temporal Logic (TL) constraints. Instead of relying solely on traditional automaton models, we construct a product automaton matrix by fusing environment connectivity with task-specific logical requirements. This formulation captures both spatial feasibility and temporal logic within a unified matrix representation, enabling efficient synthesis of feasible trajectories via graph-based search algorithms. The method supports task updates and traffic-aware replanning by dynamically updating the underlying matrix structures. We demonstrate the approach using representative parking scenarios with realistic constraints, including one-way lanes, static and dynamic obstacles, and mid-mission task changes. The proposed matrix fusion strategy offers a scalable and rigorous framework for mission-critical autonomous navigation.