{"ID":2850971,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.20202","arxiv_id":"2510.20202","title":"From Bundles to Backstepping: Geometric Control Barrier Functions for Safety-Critical Control on Manifolds","abstract":"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).","short_abstract":"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 cont...","url_abs":"https://arxiv.org/abs/2510.20202","url_pdf":"https://arxiv.org/pdf/2510.20202v1","authors":"[\"Massimiliano de Sa\",\"Pio Ong\",\"Aaron D. Ames\"]","published":"2025-10-23T04:38:31Z","proceeding":"eess.SY","tasks":"[\"eess.SY\",\"math.OC\"]","methods":"[]","has_code":false}