The Space-Time Transform: Memory-Augmented Control Barrier Functions

Engineering notes

Engineering notes will be added by the Robot Papers editorial team.

Chinese explanation / 中文解读

中文解读待补充：本站会优先为 VLA、具身智能、人形机器人控制、机器人操作等高价值论文补充中文说明。

Original abstract

Control Barrier Functions (CBFs), their High-Order variants (HOCBFs) and Exponential CBFs (ECBFs) are standard geometric tools for enforcing nonlinear safety constraints. CBFs, and their variants, offer an elegant geometric framework for nonlinear safety, yet mathematically, they reduce to continuous-time convolutions restricted by zero-memory kernels. In the presence of high-frequency measurement noise, these memoryless operators act as improper filters, leading to significant control chattering and the potential loss of active control authority due to Quadratic Program (QP) infeasibility. To address this structural limitation, this paper introduces a space-time transform that embeds dynamic temporal filtering directly into the safety constraint synthesis. By designing a proper spatio-temporal kernel, this approach inherently attenuates high-frequency noise while preserving affine control authority. Crucially, we prove the robust forward invariance of the designed STT-CBF. Monte Carlo simulations of a third-order system demonstrate that the proposed framework achieves a 100% safety rate while reducing control total variation by over 99% compared to conventional parameterized barrier methods, mitigating hardware hazards and enabling reliable deployment on physical robotic platforms.

Links and sources

• Official / arXiv page
• PDF from original source

Comments