Orbital Stabilization of Underactuated Systems using Virtual Holonomic Constraints and Impulse Controlled Poincaré Maps
Abstract
The problem of orbital stabilization of underactuated mechanical systems with one passive degree-of-freedom (DOF) is revisited. Virtual holonomic constraints are enforced using a continuous controller; this results in a dense set of closed orbits on a constraint manifold. A desired orbit is selected on the manifold and a Poincaré section is constructed at a fixed point on the orbit. The corresponding Poincaré map is linearized about the fixed point; this results in a discrete linear time-invariant system. To stabilize the desired orbit, impulsive inputs are applied when the system trajectory crosses the Poincaré section; these inputs can be designed using standard techniques such as LQR. The Impulse Controlled Poincaré Map (ICPM) based control design has lower complexity and computational cost than control designs proposed earlier. The generality of the ICPM approach is demonstrated using the 2-DOF cart–pendulum and the 3-DOF tiptoebot.
Recommended Citation
N. Kant and R. Mukherjee, "Orbital Stabilization of Underactuated Systems using Virtual Holonomic Constraints and Impulse Controlled Poincaré Maps," Systems and Control Letters, vol. 146, article no. 104813, Elsevier, Dec 2020.
The definitive version is available at https://doi.org/10.1016/j.sysconle.2020.104813
Department(s)
Mechanical and Aerospace Engineering
Keywords and Phrases
Impulsive control; Orbital stabilization; Poincaré map; Underactuated system; Virtual Holonomic Constraint
International Standard Serial Number (ISSN)
0167-6911
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2025 Elsevier, All rights reserved.
Publication Date
01 Dec 2020
Comments
National Science Foundation, Grant 1462118