In this paper, we propose AUKAI, an Adaptive Unified Knowledge-Action Intelligence for embodied cognition that seamlessly integrates perception, memory, and decision-making via multi-scale error feedback. Interpreting AUKAI as an embedded world model, our approach simultaneously predicts state transitions and evaluates intervention utility. The framework is underpinned by rigorous theoretical analysis drawn from convergence theory, optimal control, and Bayesian inference, which collectively establish conditions for convergence, stability, and near-optimal performance. Furthermore, we present a hybrid implementation that combines the strengths of neural networks with symbolic reasoning modules, thereby enhancing interpretability and robustness. Finally, we demonstrate the potential of AUKAI through a detailed application in robotic navigation and obstacle avoidance, and we outline comprehensive experimental plans to validate its effectiveness in both simulated and real-world environments.

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