**6. Conclusions**

In this paper, we present an algorithm, Canonical Ordering Dynamic Brushfire (CODB), to speed up the incremental updating of grid-based Distance Maps (DMs). CODB only updates those cells which are affected by local changes, and it employs the strategy of Canonical Ordering to guide the search direction; therefore, the algorithm requires much fewer cell visits and less computation costs compared to its competing approaches. Furthermore, we propose algorithms to compute DM-based subgoal graphs which are used to provide high-level, collision-free roadmaps for agents with certain safety radius to engage fast and rational path planning tasks. We present our algorithms both intuitively and through pseudocode, compare them to current approaches on typical scenarios, and demonstrate their usefulness for fast path planning tasks.

**Author Contributions:** Conceptualization, L.Q., Y.H. and J.Z.; Data curation, L.Q.; Formal analysis, L.Q.; Funding acquisition, Q.Y.; Methodology, L.Q., Y.H. and J.Z.; Project administration, Q.Y.; Resources, Q.Y.; Software, L.Q.; Supervision, Q.Y.; Writing—original draft, L.Q.; Writing—review & editing, L.Q., Y.H. and J.Z.

**Funding:** This work described in this paper is sponsored by the National Natural Science Foundation of China under Grant No. 61473300.

**Acknowledgments:** This work described in this paper is sponsored by the National Natural Science Foundation of China under Grant No. 61473300. We appreciate the fruitful discussion with the Sim812 group: Qi Zhang, Kai Xu, Weilong Yang, and Cong Hu.

**Conflicts of Interest:** The authors declare no conflict of interest. The founding sponsors had no role in the design of the study; in the collection, analysis, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.
