The ability to navigate and interact with complex environments is central to real-world embodied agents, yet navigation in unseen environments remains challenging due to "experiential amnesia," where existing trajectory-driven or reactive policies fail to synthesize generalizable strategies from past interactions. We propose Robo-Cortex, a self-evolving framework that enables robots to autonomously induce navigation heuristics and refine cognitive strategies through a continuous reflection-adaptation loop. By abstracting success patterns and failure pitfalls into natural-language heuristics, Robo-Cortex enables a transition from passive execution to active strategy evolution. Our core innovation is an Autonomous Knowledge Induction (AKI) mechanism that distills multimodal trajectories into a structured Navigation Heuristic Library for knowledge generalization. The architecture further incorporates a Dual-Grain Cognitive Memory system, comprising a Short-term Reflective Memory (SRM) for real-time local progress analysis, and a Long-term Principle Memory (LPM) that abstracts past trajectories into reusable guiding and cautionary principles. To ensure robust decision-making, we introduce a multimodal Imagine-then-Verify loop, where a world model simulates potential outcomes and a VLM-based evaluator validates action plans. Extensive evaluations on IGNav, AR, and AEQA show that Robo-Cortex consistently outperforms strong baselines in both task success and exploration efficiency, with gains of up to +4.16% SPL over the strongest prior method and up to +15.30% SPL under heuristic transfer to unseen environments. Preliminary real-world robotic experiments further support the effectiveness of Robo-Cortex in physical settings.

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