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Dynamics and Switching Control of a Class of Underactuated Mechanical Systems with Variant Constraints

1
Department of Mechanical and Electrical Engineering, North China University of Technology, Beijing 100144, China
2
State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China
*
Author to whom correspondence should be addressed.
Appl. Sci. 2019, 9(20), 4235; https://doi.org/10.3390/app9204235
Received: 19 August 2019 / Revised: 24 September 2019 / Accepted: 30 September 2019 / Published: 10 October 2019
(This article belongs to the Section Mechanical Engineering)
Locomotion systems with variant constraints are familiar in real world applications, but the dynamics and control issues of variant constraint systems have not been sufficiently discussed to date. From the viewpoint of Lagrange–d’Alembert equations with additional variable constraints, this paper investigates the modeling approaches of a class of hybrid dynamical systems (HDS) with instantaneously variant constraints and the switching control techniques of stabilizing the HDS to given periodic orbits. It is shown that under certain conditions there possibly exist zero impact periodic orbits in the HDS, and the HDS can be stabilized to the period-one orbits by a linear controller with only partial state feedback, even though the HDS are generally underactuated nonholonomic systems. As an example, a one-legged planar hopping robot is employed to demonstrate the main results of modeling and control of a class of HDS.
Keywords: dynamics modeling; orbital stability; robots; switching control; variant constraints dynamics modeling; orbital stability; robots; switching control; variant constraints
MDPI and ACS Style

Su, T.; Liang, X.; He, G.; Jia, T.; Zhao, Q.; Zhao, L. Dynamics and Switching Control of a Class of Underactuated Mechanical Systems with Variant Constraints. Appl. Sci. 2019, 9, 4235.

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