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

TL;DR

This work tackles safety-critical control under irregular and time-varying unsafe regions by learning a control barrier function (CBF) with a cost-sensitive incremental RVFL network. SafeLink constructs a differentiable CBF from labeled safe/unsafe samples, enforcing safety via a quadratic program and delivering Lipschitz-continuous safe controls. The method introduces a cost-sensitive regularization term and provides incremental update theorems to rapidly adapt the CBF as unsafe regions change, with explicit gradient expressions for control. Experiments on a nonlinear two-link manipulator demonstrate rapid adaptation to dynamic obstacles, strong safety guarantees, and superior update efficiency compared to SVM- and MLP-based CBFs, illustrating practical impact for real-time safety-critical robotics applications.

Abstract

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.

Figures (7)

• Figure 1: Diagram of SafeLink. SafeLink first collects safe and unsafe state samples in the state space. Then, a cost-sensitive and incremental RVFL network is designed to train on these samples for CBF construction, where a QP solver is employed to output safe control inputs. When the unsafe region changes, the constructed CBF can be rapidly updated using samples from the new unsafe region to ensure system safety.
• Figure 2: Evolution of unsafe regions. The unsafe regions expand at $t = 1.1$ s and $t = 7.5$ s.
• Figure 3: Sampling in the state space. A total of 5000 state points are sampled.
• Figure 4: Endpoint trajectories at different stages: (a) before the first environmental change, (b) after the first change, (c) after the first SafeLink update, (d) after the second change, (e) after the second SafeLink update, and (f) upon reaching the target state.
• Figure 5: Time evolution of the safe control inputs $u_1$ and $u_2$.

Theorems & Definitions (16)

• Definition 1
• Definition 2
• Definition 3
• Definition 4
• Lemma 1
• Definition 5
• Lemma 2
• Theorem 1
• Remark 1
• Theorem 2