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Article

Matrix-Guided Safe Motion Planning for Smart Parking Systems

by
Dewan Mohammed Abdul Ahad
* and
Dipankar Maity
Department of Electrical and Computer Engineering, University of North Carolina at Charlotte, Charlotte, NC 28223, USA
*
Author to whom correspondence should be addressed.
Robotics 2025, 14(11), 171; https://doi.org/10.3390/robotics14110171
Submission received: 17 September 2025 / Revised: 5 November 2025 / Accepted: 13 November 2025 / Published: 20 November 2025

Abstract

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.
Keywords: smart parking; autonomous driving; path-planning; temporal logic; product automaton matrix; conditional block product smart parking; autonomous driving; path-planning; temporal logic; product automaton matrix; conditional block product

Share and Cite

MDPI and ACS Style

Ahad, D.M.A.; Maity, D. Matrix-Guided Safe Motion Planning for Smart Parking Systems. Robotics 2025, 14, 171. https://doi.org/10.3390/robotics14110171

AMA Style

Ahad DMA, Maity D. Matrix-Guided Safe Motion Planning for Smart Parking Systems. Robotics. 2025; 14(11):171. https://doi.org/10.3390/robotics14110171

Chicago/Turabian Style

Ahad, Dewan Mohammed Abdul, and Dipankar Maity. 2025. "Matrix-Guided Safe Motion Planning for Smart Parking Systems" Robotics 14, no. 11: 171. https://doi.org/10.3390/robotics14110171

APA Style

Ahad, D. M. A., & Maity, D. (2025). Matrix-Guided Safe Motion Planning for Smart Parking Systems. Robotics, 14(11), 171. https://doi.org/10.3390/robotics14110171

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