This study presents an enhanced path planning framework for mobile robots operating in environments containing both static and dynamic obstacles. The proposed approach introduces the Recursive Heatmap Dijkstra (RH-Dijkstra) algorithm, which extends the classical Dijkstra method by embedding heatmap-based risk modeling and event-driven recursive re-planning into a unified navigation architecture. The algorithm initially computes the global shortest path on an obstacle-free map and subsequently updates the environment in real time using proximity-based collision detection. Upon detecting a potential safety violation, the robot executes a local maneuver through heading adjustment, followed by recursive path recomputation on the updated risk-aware cost map. Multiple simulation scenarios are investigated, including sudden obstacle appearances and dynamic obstacle interactions. The results demonstrate that the proposed RH-Dijkstra framework effectively adapts to environmental uncertainties while improving maneuver efficiency and reducing traversal time, thereby maintaining optimal and collision-free navigation. In addition, the closed-loop PID-based motion controller ensures stable trajectory tracking throughout the navigation process. In summary, the proposed recursive heatmap-based formulation provides a flexible, resilient, and computationally efficient solution for autonomous mobile robot path planning in dynamic environments.

This paper proposes a theoretical and practical approach for determining the stabilizing gain intervals for two-input, two-output (TITO) systems with a constant diagonal controller. Our main contribution is to present an algorithm which is more practical than the stabilizing methods that depend on the Nyquist stability criterion. Numerical examples illustrate the effectiveness of the proposed algorithm for TITO systems with reducible or irreducible characteristic equations.