Physics-constrained learning framework for trustworthy microrobot navigation autonomy.

Machine learning has become an emerging paradigm for microrobotics, enabling autonomous micro-/nanorobot navigation in complex and highly disturbed environments without requirements of precise models. However, the state-of-the-art learning-based methods adopt "black-box" neural networks (NNs), which raises critical concerns about the trustworthiness of the generated navigation policies, especially for biomedical scenarios. Motivated to address this issue, we propose a physics-constrained learning framework that embeds deterministic physical laws into network architectures to achieve trustworthy microrobot navigation. Instead of learning from scratch, we explicitly encode the monotonic relationships of kinematics and safety rules into NNs. These constraints serve as structural inductive biases, theoretically guaranteeing that navigation policies operate strictly within the trustworthy action domains. Experiments demonstrate that microrobots can autonomously reach random targets without collision with obstacles during long-time and long-distance navigation, proving our framework's reliability owing to its explainable nature. This work can bridge the gap between data-driven performance and rigorous safety requirements, constituting a meaningful step toward trustworthy artificial intelligence-empowered microrobotics.