2000 character limit reached
On the Geometry of Virtual Nonlinear Nonholonomic Constraints
Published 3 Oct 2023 in math.OC, cs.SY, eess.SY, math-ph, and math.MP | (2310.01849v1)
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.
- B. Griffin, J. Grizzle Nonholonomic virtual constraints for dynamic walking. 54th IEEE Conference on Decision and Control 4053–4060 (2015).
- J. Horn, R.Gregg. Nonholonomic Virtual Constraints for Control of Powered Prostheses Across Walking Speeds. IEEE Transactions on Control Systems Technology. (2021).
- A. Moran-MacDonald. Energy injection for mechanical systems through the method of Virtual Nonholonomic Constraints. University of Toronto (2021).
- B. Schutz. A First Course in General Relativity (2nd ed.). Cambridge University Press (2009).
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.