FMT$^{x}$: An Efficient and Asymptotically Optimal Extension of the Fast Marching Tree for Dynamic Replanning
This provides a more effective solution for real-time robotic navigation in unpredictable spaces like warehouses and roads, though it is incremental as it builds on an existing method.
The paper tackles path planning in dynamic environments by extending the Fast Marching Tree algorithm to enable efficient replanning, resulting in FMT^x, which outperforms RRT^x with faster reactions and lower computational overhead.
Path planning in dynamic environments remains a core challenge in robotics, especially as autonomous systems are deployed in unpredictable spaces such as warehouses and public roads. While algorithms like Fast Marching Tree (FMT$^{*}$) offer asymptotically optimal solutions in static settings, their single-pass design prevents path revisions which are essential for real-time adaptation. On the other hand, full replanning is often too computationally expensive. This paper introduces FMT$^{x}$, an extension of the Fast Marching Tree algorithm that enables efficient and consistent replanning in dynamic environments. We revisit the neighbor selection rule of FMT$^{*}$ and demonstrate that a minimal change overcomes its single-pass limitation, enabling the algorithm to update cost-to-come values upon discovering better connections without sacrificing asymptotic optimality or computational efficiency. By maintaining a cost-ordered priority queue and applying a selective update condition that uses an expanding neighbor to identify and trigger the re-evaluation of any node with a potentially suboptimal path, FMT$^{x}$ ensures that suboptimal routes are efficiently repaired as the environment evolves. This targeted strategy preserves the inherent efficiency of FMT$^{*}$ while enabling robust adaptation to changes in obstacle configuration. FMT$^{x}$ is proven to recover an asymptotically optimal solution after environmental changes. Experimental results demonstrate that FMT$^{x}$ outperforms the influential replanner RRT$^{x}$, reacting more swiftly to dynamic events with lower computational overhead and thus offering a more effective solution for real-time robotic navigation in unpredictable worlds.