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

IF 4.5 1区 工程技术 Q1 ENGINEERING, MECHANICAL Mechanism and Machine Theory Pub Date : 2024-09-21 DOI:10.1016/j.mechmachtheory.2024.105795
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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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基于线性化非整体多体模型的球-板系统动态反转和优化跟踪控制
球-板系统是一种著名的非全局系统,本文采用多体动力学方法对其进行优化控制。通过设计一个线性-二次调节器,可实现对球在板上的稳态圆周运动的轨迹跟踪控制,该运动的半径不限,且可能相对于板的支点偏离中心。考虑了球-板系统的空间多体模型。其主要贡献在于通过动态反演分析计算了球的圆周稳定运动,包括实现该参考解的控制行动。这样就能分析计算出沿着该参考运动的线性化方程,从而形成周期性线性时变(LTV)系统,并应用 LTV 系统的线性可控性标准。在线性化过程中,利用方便的坐标分割,得到了一个涉及接触点笛卡尔坐标和球体偏航角的可控线性系统。与关于同一问题的现有结果相比,在圆轨迹的任何半径上都能实现对所需轨迹的闭环稳定性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Mechanism and Machine Theory
Mechanism and Machine Theory 工程技术-工程:机械
CiteScore
9.90
自引率
23.10%
发文量
450
审稿时长
20 days
期刊介绍: Mechanism and Machine Theory provides a medium of communication between engineers and scientists engaged in research and development within the fields of knowledge embraced by IFToMM, the International Federation for the Promotion of Mechanism and Machine Science, therefore affiliated with IFToMM as its official research journal. The main topics are: Design Theory and Methodology; Haptics and Human-Machine-Interfaces; Robotics, Mechatronics and Micro-Machines; Mechanisms, Mechanical Transmissions and Machines; Kinematics, Dynamics, and Control of Mechanical Systems; Applications to Bioengineering and Molecular Chemistry
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