HOPHY: Hierarchical Off-Road Planning using Hypergraphs

HOPHY: A Hypergraph-Based Hierarchical Terrain Representation for Off-Road Path and Mission Planning

University at Buffalo

HOPHY terrain hierarchy and query pipeline

HOPHY turns map-scale terrain into a reusable planning state. Geometric-semantic nodes, coarse regions, and typed hyperedges support fast repeated path queries, localized context updates, and mission planning for heterogeneous robot teams.

Abstract

Mission-level autonomy for disaster response, search and rescue, and tactical ground vehicles requires repeated path and mission planning as terrain conditions, agent types, and objectives change. Pixel-grid planners are accurate but too slow for repeated queries at kilometer scale, while existing semantic abstractions are fast but costly to update. HOPHY (Hierarchical Off-Road Planning using Hypergraphs) organizes terrain into geometric-semantic nodes, connectivity-preserving coarse regions, and typed hyperedges for terrain, agent, and weather context. Hyperedges modify only affected nodes and incident edges, avoiding full-graph recomputation. Across kilometer-scale benchmarks, HOPHY preserves path quality close to pixel A* while enabling repeated planning, localized replanning, multi-agent task allocation, and physical-robot deployment.

Hierarchical Hypergraph Planning

HOPHY groups connected terrain with consistent landcover and grade into GSNodes, then aggregates them into coarse regions that bound long-range search. Typed hyperedges index overlapping contextual memberships—such as terrain class, weather response, or agent feasibility—so a change can be applied to the relevant terrain subset without rebuilding the full representation. Each query searches from coarse regions to GSNodes and refines the selected corridor into a continuous route.

Planned Paths

HOPHY planned path on Wharton — **Wharton · 9 km²**Coarse-to-fine search selects and refines a feasible route corridor.

HOPHY planned path on Humphrey — **Humphrey · 50 km²**The hierarchy prunes irrelevant terrain before committing to a route.

HOPHY planned path on UB Campus — **UB Campus**The same query process transfers to a compact deployment map.

Path Planning and Replanning

On Wharton, Humphrey, and Rainier, the current direct implementation succeeds on all 270 static benchmark queries and records a 0.00% median cost difference from pixel A*. Under light rain, medium rain, and localized blockage, it succeeds on all 810 replanning queries while keeping the median cost and length differences at 0.00%.

HOPHY query time and path-quality results

Query time as route length increases across the three terrain maps.

HOPHY rain and blockage replanning results

Context-sensitive replanning under weather changes and localized blockage.

Multi-Agent Mission Planning

HOPHY can serve as the repeated path-cost oracle inside a larger task-allocation loop. This lets heterogeneous teams compare many candidate assignments and routes without repeating dense pixel-level search for every task pair.