The paper presents the development and implementation of a modified Wavefront pathfinding algorithm for operation in both static and dynamic environment. Unlike the classical approach, which requires a full recomputation of the wavefront map after each environmental change, the proposed method applies event-triggered replanning. This means that route recomputation is performed only in cases where the appearance or movement of an obstacle directly affects the agent's current path, thereby improving overall computational efficiency, adaptive performance and real-time responsiveness significantly. Such an approach significantly reduces computational costs and lowers peak memory usage. Simulation results have shown that the proposed method maintains comparable accuracy and memory consumption to the classical Wavefront in static environments. In dynamic scenarios, the algorithm demonstrated high robustness: it correctly updates the route when new obstacles appear, while minimizing full-map recomputation and reducing the computational load through event-triggered replanning. This makes it a promising tool for real-time robotic systems.