From Bundles to Backstepping: Geometric Control Barrier Functions for Safety-Critical Control on Manifolds
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911228050276352 |
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| author | de Sa, Massimiliano Ong, Pio Ames, Aaron D. |
| author_facet | de Sa, Massimiliano Ong, Pio Ames, Aaron D. |
| contents | Control barrier functions (CBFs) have a well-established theory in Euclidean spaces, yet still lack general formulations and constructive synthesis tools for systems evolving on manifolds common in robotics and aerospace applications. In this paper, we develop a general theory of geometric CBFs on bundles and, for control-affine systems, recover the standard optimization-based CBF controllers and their smooth analogues. Then, by generalizing kinetic energy-based CBF backstepping to Riemannian manifolds, we provide a constructive CBF synthesis technique for geometric mechanical systems, as well as easily verifiable conditions under which it succeeds. Further, this technique utilizes mechanical structure to avoid computations on higher-order tangent bundles. We demonstrate its application to an underactuated satellite on SO(3). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_20202 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From Bundles to Backstepping: Geometric Control Barrier Functions for Safety-Critical Control on Manifolds de Sa, Massimiliano Ong, Pio Ames, Aaron D. Systems and Control Optimization and Control Control barrier functions (CBFs) have a well-established theory in Euclidean spaces, yet still lack general formulations and constructive synthesis tools for systems evolving on manifolds common in robotics and aerospace applications. In this paper, we develop a general theory of geometric CBFs on bundles and, for control-affine systems, recover the standard optimization-based CBF controllers and their smooth analogues. Then, by generalizing kinetic energy-based CBF backstepping to Riemannian manifolds, we provide a constructive CBF synthesis technique for geometric mechanical systems, as well as easily verifiable conditions under which it succeeds. Further, this technique utilizes mechanical structure to avoid computations on higher-order tangent bundles. We demonstrate its application to an underactuated satellite on SO(3). |
| title | From Bundles to Backstepping: Geometric Control Barrier Functions for Safety-Critical Control on Manifolds |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2510.20202 |