FMT$^{\mathrm{X}}$: Lazy Wavefront Search for Dynamic Replanning
Quick summary
arXiv:2509.08521v2 Announce Type: replace-cross Abstract: FMT$^{*}$ plans efficiently in static worlds by expanding a cost-ordered wavefront and collision-checking lazily, but its single-pass unvisited rule cannot revise paths when obstacles change. We present FMT$^{\mathrm{X}}$, an anytime, asymptotically optimal generalization of that wavefront for dynamic replanning. A cost-improvement test replaces the unvisited set, allowing a node to be revisited for best-parent selection whenever a lower-cost potential connection is found. This induces implicit rewiring within the wavefront while preser
Key takeaways
- arXiv:2509.08521v2 Announce Type: replace-cross Abstract: FMT$^{*}$ plans efficiently in static worlds by expanding a cost-ordered wavefront and collision-checking lazily, but its single-pass unvisited rule cannot revise paths when obstacles change.
- We present FMT$^{\mathrm{X}}$, an anytime, asymptotically optimal generalization of that wavefront for dynamic replanning.
- A cost-improvement test replaces the unvisited set, allowing a node to be revisited for best-parent selection whenever a lower-cost potential connection is found.
Why it matters
The importance of “FMT$^{\mathrm{X}}$: Lazy Wavefront Search for Dynamic Replanning” will be measured by what changes in practice. User behavior, access conditions, verifiable performance and responsible-use outcomes are the signals worth following.
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