H-TRIP: Exact Many-to-Many Distance Index for Multi-Robot Exploration

Repeated directed reachability queries arise in online path planning, task-agent allocation, and swarm control on static grid maps, where reachability is asymmetric and full transitive closure is storage-prohibitive. We introduce H-BRICK, a Hierarchical Boundary Reachability Index with Compressed Kleene closure for exact cell-to-cell queries on directed grid graphs. H-BRICK partitions the graph into tiles, computes a local Boolean Kleene closure within each tile, and projects it onto the tile's boundary ports. The resulting directed port-to-port summaries are then composed recursively across shared interfaces up to a single root covering the graph. We prove algebraically that the construction is exact: in the Boolean Kleene algebra of binary relations, every composed summary equals the boundary projection of the regional reflexive transitive closure, and every cell-to-cell query agrees with reachability in the original graph. Experiments on directed grid graphs across diverse map topologies compare H-BRICK against directed search and component-based baselines, and compare its storage requirements against full transitive closure. A batched reachability evaluation further demonstrates that sharing endpoint lifts across many-source/many-target queries amortizes hierarchical traversal and, at k=64, yields a 5.0x-22.9x throughput improvement over the scalar query loop. The results show that hierarchical boundary compression is most advantageous in query-intensive spatial graphs where online search traverses large reachable regions and the hierarchy maintains compact boundary interfaces.

Autonomous rovers navigating large unstructured environments need efficient global planning that accounts for terrain traversability. However, searching dense grid-based costmaps becomes computationally expensive as the mapped area grows. We introduce STAG, a Sparse Traversability-Aware Graph that converts costmaps into compact graphs. STAG combines a medial-axis topological backbone, representative nodes for homogeneous traversability regions, and transition nodes near strong traversability gradients. Edges encode geometry and traversability to account for path length and terrain difficulty. We compare A* on STAG and dense grids using synthetic cave maps, mine maps and the DARPA CERBERUS dataset. Across five benchmark categories comprising 203 map instances and 101,200 queries, STAG reduces median planning time by 3.4x to 9.9x and peak query memory by 2.1x to 15.4x, with median relative path-length differences of -2.9% and +7.6%. STAG offers a compact representation for global planning, trading dense-grid traversability optimality for faster, less memory-intensive search.

Multi-robot exploration under communication and mobility constraints requires balancing information gain with reachability. We present a distributed semantic exploration framework that combines Dirichlet mapping, budget-constrained trajectory selection, and Resource-Aware distributed Greedy (RAG) coordination. Each robot clusters frontiers, computes terrain- and heading-aware least-cost paths with a single budget-limited Dijkstra search, and selects feasible paths by marginal information gain, represented by the expected reduction in Dirichlet entropy. Each robot's per-round selection is exact, the team's joint per-round information gain is at least half the centralized optimum, and the bound degrades gracefully under limited communication. Ten-run gridworld ablations show improved coverage, semantic mIoU, and map certainty with lower entropy and traversal cost per unit distance than shortest-distance frontier selection. Budget-sensitivity experiments show that an intermediate budget best balances path reach and receding-horizon execution. In photorealistic full-system simulation against five coordination rules run in their native published forms, the proposed method attains the highest mean coverage and semantic accuracy while being the only one that respects the per-trajectory mobility budget.