Safety-Aware Trajectory Tracking using High-Order Control Barrier Functions

A novel method on safety-aware trajectory tracking is presented in this work. The proposed scheme employs Control Barrier Functions (CBFs) along with a latent-space representation over the barrier and its derivatives. While such representations have also been employed in the literature, the innovation of the proposed method lies in formulating a novel tracking problem on the latent space, enabling for the shape of linear class $-\mathcal{K}$ functions that are included in the safety condition induced by the control barrier function to be chosen constructively. Additionally, the aforementioned safety condition is modified based on the latent-space tracking through the addition of an extra term. This enables maintaining safety guarantees and is demonstrated to provide decreased tracking errors compared to the nominal control barrier function scheme. Numerical simulations validate the efficacy of the proposed scheme, as well as its ability for online implementation.