On the Geometry of Virtual Nonlinear Nonholonomic Constraints

• 成果类型: Article
• 署名作者: Stratoglou, Efstratios; Simoes, Alexandre Anahory; Bloch, Anthony; Colombo, Leonardo J.
• 署名单位: Madrid Open University, UDIMA; Universidad Politecnica de Madrid; IE University; University of Michigan System; University of Michigan; Consejo Superior de Investigaciones Cientificas (CSIC); Universidad Politecnica de Madrid; CSIC-UPM - Centro de Automatica y Robotica
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3508543
• 发表日期: 2025
• 页码: 3362-3369
• 关键词: VECTORS; MANIFOLDS; mechanical systems; Legged locomotion; FORCE; geometry; DYNAMICS; Extraterrestrial measurements; Aerospace electronics; nonlinear dynamical systems; Feedback control; geometric control; nonholonomic systems; virtual constraints

摘要

Virtual constraints are relations imposed on a control system that become invariant via feedback control, as opposed to physical constraints acting on the system. Nonholonomic systems are mechanical systems with nonintegrable constraints on the velocities. In this work, we introduce the notion of virtual nonlinear nonholonomic constraints in a geometric framework which is a controlled invariant submanifold and we show the existence and uniqueness of a control law preserving this submanifold.