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首页三阶段欠驱动PAA机械手控制策略:稳定性与能量提升
三阶段欠驱动PAA机械手控制策略:稳定性与能量提升
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本文探讨了一种创新的欠驱动三连杆被动-主动-主动(PAA)机械手的运动控制策略,该策略分为三个关键阶段,旨在实现高效、稳定的运动控制。首先,研究者提出了一个非线性控制定律,其目标是让第三连杆的角速度和角加速度趋向于零,这有助于机械手达到静态平衡状态。这种设计利用Lyapunov理论,确保系统的稳定性。 接着,作者设计了一个上冲控制律,旨在增加系统的能量储备,并精确控制第二连杆的姿态。这个阶段的目的是克服欠驱动带来的局限性,使机械手能够有效地执行动态操作,如抓取或释放物体。通过这种方法,机械手能够自然地驱动第三连杆向第二连杆伸展,简化了后续的控制过程,提高了整体的执行效率。 最后,为了实现机械手的平稳过渡到平衡阶段,研究者融合了线性控制与非线性控制技术。这种集成策略利用LaSalle不变性原理,确保了机械手能够稳定地定位在垂直方向,实现了稳定性和性能的双重优化。 整个控制策略的独特之处在于它通过预先设置的准备阶段,使机械手在自然状态下逐步过渡到所需的操作状态,避免了突然和剧烈的动作,从而降低了对系统的要求,并且减少了外部干扰导致的不稳定性。通过数值模拟,作者验证了这一控制策略的有效性和实用性,对比其他方法,它展现出更高的控制精度和更佳的性能。 研究团队由来自中国地质大学、湖南科技大学和加拿大圭尔夫大学的研究人员组成,他们的合作展示了跨学科的优势,对于欠驱动机械手领域的运动控制理论和技术发展具有重要的推动作用。
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Xu-Zhi Lai
School of Automation,
China University of Geosciences,
Wuhan, Hubei 430074, China
e-mail: laixz@cug.edu.cn
Chang-Zhong Pan
School of Information and Electrical Engineering,
Hunan University of Science and Technology,
Xiangtan, Hunan 411201, China
e-mail: cpan@hnust.edu.cn
Min Wu
School of Automation,
China University of Geosciences,
Wuhan, Hubei 430074, China
e-mail: wumin@cug.edu.cn
Simon X. Yang
School of Engineering,
University of Guelph,
Guelph, ON N1G 2W1, Canada
e-mail: syang@uoguelph.ca
Wei-Hua Cao
1
School of Automation,
China University of Geosciences,
Wuhan, Hubei 430074, China
e-mail: weihuacao@cug.edu.cn
Control of an Underactuated
Three-Link Passive–Active–
Active Manipulator Based
on Three Stages and Stability
Analysis
This paper presents a novel three-stage control strategy for the motion control of an
underactuated three-link passive–active–active (PAA) manipulator. First, a nonlinear
control law is designed to make the angle and angular velocity of the third link conver-
gent to zero. Then, a swing-up control law is designed to increase the system energy and
control the posture of the second link. Finally, an integrated method with linear control
and nonlinear control is introduced to stabilize the manipulator at the straight-up posi-
tion. The stability of the control system is guaranteed by Lyapunov theory and LaSalle’s
invariance principle. Compared to other approaches, the proposed strategy innovatively
introduces a preparatory stage to drive the third link to stretch-out toward the second
link in a natural way, which makes the swing-up control easy and quick. Besides, the
intergraded method ensures the manipulator moving into the balancing stage smoothly
and easily. The effectiveness and efficiency of the control strategy are demonstrated by
numerical simulations. [DOI: 10.1115/1.4028051]
1 Introduction
This paper concerns the motion control of a class of underactu-
ated mechanical systems, called a PAA manipulator, which have
fewer actuators than degrees of freedom (DOF) [1–3]. The PAA
manipulator is a rigid three-link gymnastic robot operating in a
vertical plane with its first joint being passive and the rest being
actuated. A common control objective for the PAA manipulator is
to drive it away from any arbitrary initial position and balance it
at the straight-up unstable equilibrium position. The merits of this
system are downsizing, lightening, energy-saving, and cost-
reduction. Moreover, it is subject to a second-order nonholonomic
constraint and cannot be completely linearized in the whole
motion space. Therefore, the investigation of the PAA manipula-
tor is of great importance in both control theory and applications.
Over the past few years, a remarkable research activity has
been devoted to the control of underactuated mechanical systems,
such as acrobot/pendulum-like robot, overhead crane and under-
water vehicle [4–7]. Among them, the acrobot is considered as a
highly simplified model of a human gymnast on a high bar, where
the underactuated first joint models the gymnast’s hands on the
bar, and the actuated second joint models the gymnast’s hips. A
number of methodologies have been proposed, such as partial-
feedback linearization [8], fuzzy control [9], impulse–momentum
approach [10], rewinding approach [11], interconnection and
damping assignment passivity-based approach [12–14] and
energy-based method [15–17] etc. More recently, a three-link
underactuated manipulator that can describe the mechanical sys-
tems in real world more realistically and precisely has drawn
increasing attention. For example, the three-link planar
manipulator [18,19], the three-link human-like walking robot
[20], and the three-link PAA manipulator [21–24]. The three-link
PAA manipulator, which consists of arm, trunk, and leg, can
mimic a gymnastic routine more realistically than the acrobot. But
the motion control problem is more complicated and challenging
due to the strong coupling characteristic of its control inputs.
Although Takashima [21] and Jian and Zushu [22] studied the
dynamic model of the PAA manipulator and gave some funda-
mental motion analysis, they did not present effective control
methods. Spong [23] studied the motion control based on collo-
cated partial feedback linearization, but few analysis of the swing-
up control for the PAA manipulator was found. Xin and Kaneda
[24] studied the swing-up control problem based on the concept of
virtual composite link by devising a virtual composite-link formu-
lation. However, the coordinate transformation is complicated.
Recently, researchers are paying more and more attention to find a
single controller to realize the motion control of a 2-DOF under-
actuated system. For example, an equivalent-input-disturbance
approach was proposed in Ref. [25]. However, it is very hard to
extend this single controller to the 3-DOF case because of its com-
plex structure. In Ref. [26], we discussed a motion control design
method for the PAA manipulator based on the combination of
energy and the posture of the third link, but the posture of the
entire manipulator was unconcerned, which makes the stability
analysis of the overall control system hard.
Motivated by the above considerations, this paper aims to pro-
pose an efficient control strategy for the motion control of the
three-link PAA manipulator. The control strategy contains three
stages. The first stage, called preparatory stage, is to force both
the angle and angular velocity of third link to converge to zero,
which makes it stretch-out toward the second link in a natural
way. The control law of the third link is first designed based on a
Lyapunov function, and is maintained throughout the whole con-
trol process. Whereas the control law of the second link is first set
to constant to simplify the control law design. Due to the control
1
Corresponding author.
Contributed by the Dynamic Systems Division of ASME for publication in the
J
OURNAL OF DYNAMIC SYSTEMS,MEASUREMENT, AND CONTROL. Manuscript received
March 18, 2014; final manuscript received July 16, 2014; published online
September 10, 2014. Assoc. Editor: Heikki Handroos.
Journal of Dynamic Systems, Measurement, and Control FEBRUARY 2015, Vol. 137 / 021007-1
Copyright
V
C
2015 by ASME
Downloaded From: http://dynamicsystems.asmedigitalcollection.asme.org/ on 11/25/2015 Terms of Use: http://www.asme.org/about-asme/terms-of-use
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