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Hybrid Terrain-Aware Path Planning: Integrating VD-RRT* Exploration and VD-D* Lite Repair

Akshay Naik, William R. Norris, Dustin Nottage, Ahmet Soylemezoglu

TL;DR

Problem: autonomous ground vehicles must plan curvature-feasible paths over terrain where soil strength and slope hazards vary in real time. Approach: derive a bounded, monotone terrain cost field from Bekker's pressure–sinkage law, augmented by slope and attitude penalties, and embed this into a curvature-feasible lattice with exact steering primitives; global exploration uses Vehicle-Dynamics RRT* and local repair uses Vehicle-Dynamics D* Lite. Contributions: a closed-form soil term with $p(z) = frac{k_c}{b} + k_{ abla}\, z^{n}$, a dimensionless $C_{ ext{soil}} = z/R$, and an edge cost $J(e) = abla ext{?}$, and an edge cost $J(e) = igl\int [1 + ext{terms}]igr m ds$; a curvature-feasible lattice for Dubins/Reeds–Shepp or bicycle primitives; and a real-time, CPU-only VD–RRT* / VD–D* Lite pipeline validated on hardware. Significance: enables real-time navigation across deformable terrain with physics-grounded costs, reusable across deterministic, sampling-based, or learning-driven planners.

Abstract

Autonomous ground vehicles operating off-road must plan curvature-feasible paths while accounting for spatially varying soil strength and slope hazards in real time. We present a continuous state--cost metric that combines a Bekker pressure--sinkage model with elevation-derived slope and attitude penalties. The resulting terrain cost field is analytic, bounded, and monotonic in soil modulus and slope, ensuring well-posed discretization and stable updates under sensor noise. This metric is evaluated on a lattice with exact steering primitives: Dubins and Reeds--Shepp motions for differential drive and time-parameterized bicycle arcs for Ackermann steering. Global exploration is performed using Vehicle-Dynamics RRT\(^{*}\), while local repair is managed by Vehicle-Dynamics D\(^{*}\) Lite, enabling millisecond-scale replanning without heuristic smoothing. By separating the terrain--vehicle model from the planner, the framework provides a reusable basis for deterministic, sampling-based, or learning-driven planning in deformable terrain. Hardware trials on an off-road platform demonstrate real-time navigation across soft soil and slope transitions, supporting reliable autonomy in unstructured environments.

Hybrid Terrain-Aware Path Planning: Integrating VD-RRT* Exploration and VD-D* Lite Repair

TL;DR

Problem: autonomous ground vehicles must plan curvature-feasible paths over terrain where soil strength and slope hazards vary in real time. Approach: derive a bounded, monotone terrain cost field from Bekker's pressure–sinkage law, augmented by slope and attitude penalties, and embed this into a curvature-feasible lattice with exact steering primitives; global exploration uses Vehicle-Dynamics RRT* and local repair uses Vehicle-Dynamics D* Lite. Contributions: a closed-form soil term with , a dimensionless , and an edge cost , and an edge cost ; a curvature-feasible lattice for Dubins/Reeds–Shepp or bicycle primitives; and a real-time, CPU-only VD–RRT* / VD–D* Lite pipeline validated on hardware. Significance: enables real-time navigation across deformable terrain with physics-grounded costs, reusable across deterministic, sampling-based, or learning-driven planners.

Abstract

Autonomous ground vehicles operating off-road must plan curvature-feasible paths while accounting for spatially varying soil strength and slope hazards in real time. We present a continuous state--cost metric that combines a Bekker pressure--sinkage model with elevation-derived slope and attitude penalties. The resulting terrain cost field is analytic, bounded, and monotonic in soil modulus and slope, ensuring well-posed discretization and stable updates under sensor noise. This metric is evaluated on a lattice with exact steering primitives: Dubins and Reeds--Shepp motions for differential drive and time-parameterized bicycle arcs for Ackermann steering. Global exploration is performed using Vehicle-Dynamics RRT, while local repair is managed by Vehicle-Dynamics D Lite, enabling millisecond-scale replanning without heuristic smoothing. By separating the terrain--vehicle model from the planner, the framework provides a reusable basis for deterministic, sampling-based, or learning-driven planning in deformable terrain. Hardware trials on an off-road platform demonstrate real-time navigation across soft soil and slope transitions, supporting reliable autonomy in unstructured environments.
Paper Structure (7 sections, 6 equations, 11 figures, 4 tables, 2 algorithms)

This paper contains 7 sections, 6 equations, 11 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methodology
  4. Results and Analysis
  5. Hardware Validation
  6. Discussion
  7. Conclusion and Future Work

Figures (11)

  • Figure 1: End-to-end planning pipeline coupling a static VD--RRT$^{*}$ seed with real-time VD--D$^{*}$ Lite repair.
  • Figure 2: Terrain cost as a function of cohesive modulus ($k_c$) and frictional modulus ($k_\phi$). Softer soils (low $k_c$, $k_\phi$) correspond to higher traversal cost.
  • Figure 3: Cost map construction: soil (top-left) and slope (top-right) fuse into the combined raster $C_{\text{total}}$ (bottom).
  • Figure 4: VD--RRT$^{*}$: samples concentrate in low-cost regions; the final path is curvature-feasible and avoids soft soil.
  • Figure 5: Synthetic test map generated with octave-summed Perlin noise. The same noise field defines both the elevation layer and the soil raster.
  • ...and 6 more figures