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math.OC2026
Virtual Holonomic and Nonholonomic Constraints on Lie groups
A. Anahory Simoes, A. Bloch, L. Colombo +1
This paper develops a geometric framework for virtual constraints on Lie groups, with emphasis on mechanical systems modeled as affine connection systems. Virtual holonomic and vir…
math.OC2024
Nonholonomic mechanics and virtual constraints on Riemannian homogeneous spaces
Efstratios Stratoglou, Alexandre Anahory Simoes, Anthony Bloch +1
Nonholonomic systems are, so to speak, mechanical systems with a prescribed restriction on the velocities. A virtual nonholonomic constraint is a controlled invariant distribution…
math.OC2024
Geometric stabilization of virtual linear nonholonomic constraints
Alexandre Anahory Simoes, Anthony Bloch, Leonardo Colombo +1
In this paper, we give sufficient conditions for and deduce a control law under which a mechanical control system converges exponentially fast to a virtual linear nonholonomic cons…