Decoupled Design of Time-Varying Control Barrier Functions via Equivariances
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914190023720960 |
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| author | Wiltz, Adrian Dimarogonas, Dimos V. |
| author_facet | Wiltz, Adrian Dimarogonas, Dimos V. |
| contents | This article presents a systematic method for designing time-varying Control Barrier Functions (CBF) composed of a time-invariant component and multiple time-dependent components, leveraging structural properties of the system dynamics. The method involves the construction of a specific class of time-invariant CBFs that encode the system's dynamic capabilities with respect to a given constraint, and augments them subsequently with appropriately designed time-dependent transformations. While transformations uniformly varying the time-invariant CBF can be applied to arbitrary systems, transformations exploiting structural properties in the dynamics - equivariances in particular - enable the handling of a broader and more expressive class of time-varying constraints. The article shows how to leverage such properties in the design of time-varying CBFs. The proposed method decouples the design of time variations from the computationally expensive construction of the underlying CBFs, thereby providing a computationally attractive method to the design of time-varying CBFs. The method accounts for input constraints and under-actuation, and requires only qualitative knowledge on the time-variation of the constraints making it suitable to the application in uncertain environments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08607 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Decoupled Design of Time-Varying Control Barrier Functions via Equivariances Wiltz, Adrian Dimarogonas, Dimos V. Systems and Control Robotics This article presents a systematic method for designing time-varying Control Barrier Functions (CBF) composed of a time-invariant component and multiple time-dependent components, leveraging structural properties of the system dynamics. The method involves the construction of a specific class of time-invariant CBFs that encode the system's dynamic capabilities with respect to a given constraint, and augments them subsequently with appropriately designed time-dependent transformations. While transformations uniformly varying the time-invariant CBF can be applied to arbitrary systems, transformations exploiting structural properties in the dynamics - equivariances in particular - enable the handling of a broader and more expressive class of time-varying constraints. The article shows how to leverage such properties in the design of time-varying CBFs. The proposed method decouples the design of time variations from the computationally expensive construction of the underlying CBFs, thereby providing a computationally attractive method to the design of time-varying CBFs. The method accounts for input constraints and under-actuation, and requires only qualitative knowledge on the time-variation of the constraints making it suitable to the application in uncertain environments. |
| title | Decoupled Design of Time-Varying Control Barrier Functions via Equivariances |
| topic | Systems and Control Robotics |
| url | https://arxiv.org/abs/2512.08607 |