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On the Geometry of Virtual Nonlinear Nonholonomic Constraints (2310.01849v1)
Published 3 Oct 2023 in math.OC, cs.SY, eess.SY, math-ph, and math.MP
Abstract: 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 non-integrable 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. We illustrate the theory with various examples and present simulation results for an application.
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