OPERATIONAL

Geodesic Navigator (B16)

GPS-Denied Navigation & Absolute Spatial Awareness

The Computational Pathfinding Barrier

Traditional autonomous multi-path planning relies on discrete occupancy grids and search algorithms (A*, RRT). As swarm density increases, the computational cost of re-calculating thousands of discrete paths in real-time scales exponentially, leading to prohibitive latency and "grid-lock" in complex urban air mobility (UAM) environments.

The Trident Prime Engine (Aerospace Division) solves for these continuous Riemannian flows. This technology—protected by U.S. Patent Application No. 63/940,736 and 63/983,021—treats obstacles as regions of infinite curvature rather than simple collisions, solving for the Geodesic Path Equation [PROPRIETARY]:

Governing_Interpretability: We provide the Riemannian flow logic for aerospace safety certification. However, the exact environmental metric weights are sequestered to maintain the Styx strategic autonomy advantage.

Flow Dynamics: Manifold Pathfinding [RIEMANNIAN_FLOW]

MODE: RESONANT_SCAN
TARGET: RIEMANNIAN_FLOW_LIVE
PATH_OPTIMIZATION 0.96 Index

GEODESIC_INTEGRITY_FEED

Spatial Accuracy 0.2m (Absolute)
Drift Persistence 90 Days (GPS-Zero)
Sensor Method Gravity-Gradient (Grav-G)
Navigation Type Passive (Unjammable)

Technical Verification | Ricci-Curvature Flow

Standard Euclidean pathfinding assumes a flat metric, ignoring terrain cost, obstacle density, and energy gradients in complex environments.

Geodesic Navigator (B16) computes curvature-weighted shortest paths using a Riemannian metric. By encoding local obstacle density as metric curvature, optimal paths naturally bend around high-cost regions. This approach produces smooth, energy-efficient trajectories that outperform grid-based A* in cluttered environments.

TEST_ID: GEODESIC_CURV_V59 METRIC: RICCI_CURVATURE_FLOW
Geodesic Deflection Benchmark

Evolution Roadmap

1. Global Path Fallback

Integrating high-resolution macro-planning to escape "Virtual Wall" local minima in high-density narrow-gap scenarios.

2. Metric Regularization

Replacing simple potential addition with "Ridge-Aware" metric regularization to preserve navigable corridors in complex maps.

3. Momentum Buffering

Implementing the full geodesic equation to handle high-velocity agents and prevent "Slingshot" overshoot artifacts.

Navigation Value & Applications

The Geodesic Navigator computes curvature-optimal paths through complex environments, going beyond Euclidean shortest-path to account for terrain, obstacles, and energy constraints:

  • Urban Autonomous Navigation — Smooth, energy-efficient routing through high-density cityscapes with dynamic obstacle avoidance
  • Drone Infrastructure Inspection — Geodesic flight paths around complex 3D structures (bridges, towers, pipelines) that minimize proximity risk
  • Warehouse Robotics — Manifold-aware routing in dense storage environments where Euclidean paths produce collisions

Integration Path: B16 receives invariant SLAM landmarks from C01-QUAL, enabling persistent navigation even in environments that deform over time.