SafeLink: Safety-Critical Control Under Dynamic and Irregular Unsafe Regions

Control barrier functions (CBFs) provide a theoretical foundation for safety-critical control in robotic systems. However, most existing methods rely on explicit analytical expressions of unsafe state regions, which are often impractical for irregular and dynamic unsafe regions. This paper introduces SafeLink, a novel CBF construction method based on cost-sensitive incremental random vector functional-link (RVFL) neural networks. By designing a valid cost function, SafeLink assigns different sensitivities to safe and unsafe state points, thereby eliminating false negatives in classification of unsafe state points. Under the constructed CBF, theoretical guarantees are established regarding system safety and the Lipschitz continuity of the control inputs. Furthermore, incremental update theorems are provided, enabling precise real-time adaptation to changes in unsafe regions. An analytical expression for the gradient of SafeLink is also derived to facilitate control input computation. The proposed method is validated on the endpoint position control task of a nonlinear two-link manipulator. Experimental results demonstrate that the method effectively learns the unsafe regions and rapidly adapts as these regions change, achieving computational speeds significantly faster than baseline methods while ensuring the system safely reaches its target position.

💡 Research Summary

The paper “SafeLink: Safety-Critical Control Under Dynamic and Irregular Unsafe Regions” addresses a fundamental challenge in robotic safety: guaranteeing safe operation in environments where hazards are irregularly shaped and dynamically changing, and where obtaining precise analytical models of these unsafe regions is impractical. Control Barrier Functions (CBFs) provide a powerful framework for enforcing safety by modifying a nominal control input, but traditionally require an explicit mathematical description of the unsafe set. SafeLink proposes a novel, data-driven method to construct and continuously adapt CBFs in real-time, removing this dependency.

The core innovation of SafeLink is a cost-sensitive incremental Random Vector Functional Link (RVFL) neural network for CBF synthesis. The framework starts from a dataset of state points labeled as safe or unsafe. The RVFL network, known for its universal approximation capability and closed-form solution via ridge regression, is used as a classifier. Crucially, SafeLink modifies the standard RVFL training objective by incorporating a cost-sensitive term. This term imposes a significantly higher penalty (cost c1) for misclassifying an unsafe state as safe (a false negative) compared to the penalty (cost c2) for the opposite error. This design enforces a conservative safety bias, ensuring the learned CBF overestimates rather than underestimates danger, which is critical for real-world applications.

The paper provides strong theoretical foundations for the proposed method. First, it proves that under a static unsafe region, the trained CBF guarantees zero false negatives on the training dataset, meaning all known unsafe states are correctly identified. Second, it establishes the Lipschitz continuity of the resulting safety-filtered control input, ensuring smooth and stable controller behavior. To handle dynamically evolving hazards, the authors derive incremental update theorems. These theorems allow the RVFL network’s output weights to be updated efficiently when new safety data arrives, enabling real-time adaptation of the CBF without retraining from scratch. Furthermore, an analytical expression for the gradient of the learned CBF is provided, which is essential for efficiently solving the Quadratic Programming (QP) problem that computes the final safe control input.

The method is validated through comprehensive simulations on a nonlinear two-link manipulator performing endpoint position control. The experiments involve both static and dynamic (moving) unsafe regions. SafeLink is compared against a standard RVFL-based CBF (without cost-sensitive learning) and a more complex Multi-Layer Perceptron (MLP)-based approach. The results demonstrate that SafeLink successfully learns and avoids unsafe regions. Its incremental update capability allows it to quickly adapt as hazards move. Most notably, SafeLink achieves computational speeds hundreds of times faster than the MLP-based baseline while completely eliminating false negatives, a critical safety metric. The standard RVFL-CBF, while fast, fails to prevent false negatives, highlighting the importance of the cost-sensitive component.

In conclusion, SafeLink presents a robust, efficient, and theoretically grounded framework for safety-critical control in complex, non-stationary environments. By combining the computational efficiency and closed-form properties of RVFL networks with a cost-sensitive learning objective and incremental update rules, it enables real-time, learning-based safety assurance where traditional model-based CBF methods fall short. This work significantly advances the practical deployment of CBFs in real-world robotics applications such as human-robot collaboration and autonomous navigation in unstructured settings.