ΔΦ Field-Gradient Navigation: An Event-Driven Compute Primitive for Edge Robotics

This work introduces ΔΦ field-gradient navigation, an event-driven compute primitive for autonomous edge robotics operating under severe energy, latency, and sensing constraints. The framework models the environment as a dynamic electrostatic potential field and computes navigation decisions using the lightweight algebraic operator ΔΦ = ρv, where ρ represents local charge density and v relative motion.Instead of constructing geometric maps or processing dense pixel streams, the method detects spatial-potential changes and triggers computation only when gradient thresholds are crossed. This converts continuous perception into a bounded, event-driven process with constant per-event computational cost. Scalar-field updates and local gradient evaluations replace convolutional vision pipelines and point-cloud processing, enabling direct deployment on microcontrollers, FPGAs, and neuromorphic hardware.By partially externalizing memory into persistent physical field structure, the system performs pathfinding without global maps or high-resolution sensing. The result is a low-latency, low-power navigation operator suitable for GPS-denied, visually degraded, and resource-constrained environments.The paper formalizes ΔΦ field-gradient navigation as a foundational compute primitive for embodied AI and provides a reproducible experimental protocol for validating constant-time event complexity against classical vision-centric and SLAM-based approaches.