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Dynamic inversion and optimal tracking control on the ball-plate system based on a linearized nonholonomic multibody model

Year of publication

2024

Authors

Garcia-Agundez Blanco Alfonso; Saccon Alessandro; Garcia-Vallejo Daniel; Freire Emilio

Abstract

This paper addresses the optimal control of the ball-plate system, a well-known nonholonomic system in the context of nonprehensile manipulation, using a multibody dynamics approach. The trajectory tracking control of a steady-state circular motion of the ball on the plate, for any radius and potentially off-centric with respect to the plate’s pivoting point, is achieved by designing a Linear-Quadratic Regulator. A spatial multibody model of the ball-plate system is considered. A key contribution is the analytical computation of the circular steady motion of the ball by dynamic inversion, including the control actions to achieve this reference solution. This enables the analytical computation of the linearized equations along this reference motion, resulting in a periodic linear time-varying (LTV) system, and the application of linear controllability criteria for LTV systems. A controllable linear system, involving the Cartesian coordinates of the contact point and the yaw angle of the sphere, is obtained using a convenient coordinate partition in the linearization. Compared to existing results on the same problem, closed-loop stability about the desired trajectory is achieved for any radius of the circular trajectory.
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Organizations and authors

LUT University

Garcia-Agundez Blanco Alfonso

Publication type

Publication format

Article

Parent publication type

Journal

Article type

Original article

Audience

Scientific

Peer-reviewed

Peer-Reviewed

MINEDU's publication type classification code

A1 Journal article (refereed), original research

Publication channel information

Publisher

Elsevier

Volume

203

Article number

105795

​Publication forum

63096

​Publication forum level

2

Open access

Open access in the publisher’s service

Yes

Open access of publication channel

Partially open publication channel

Self-archived

No

Other information

Fields of science

Mechanical engineering

Keywords

[object Object],[object Object],[object Object],[object Object],[object Object]

Internationality of the publisher

International

International co-publication

Yes

Co-publication with a company

No

DOI

10.1016/j.mechmachtheory.2024.105795

The publication is included in the Ministry of Education and Culture’s Publication data collection

Yes