Dynamics and control of a 3D pendulum

Shen, Jinglai; Sanyal, Amit K.; Chaturvedi, N.A.; Bernstein, Dennis S.; McClamroch, Harris

doi:10.1109/cdc.2004.1428650

Cited by 46 publications

(6 citation statements)

References 29 publications

(33 reference statements)

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“…which is the same as the model presented in Shen et al (2004). We find that, for a point mass, the acceleration about the wire axis is small, and the velocity is therefore approximately constant.…”

Section: Spherical Pendulum Dynamicssupporting

confidence: 67%

An EKF for Lie Groups with Application to Crane Load Dynamics

Sjøberg¹,

Egeland²

2019

MIC

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An extended Kalman filter (EKF) for systems with configuration given by matrix Lie groups is presented. The error dynamics are given by the logarithm of the Lie group and are based on the kinematic differential equation of the logarithm, which is given in terms of the Jacobian of the Lie group. The probability distribution is also described in terms of the logarithm as a concentrated Gaussian distribution that is a tightly focused distribution around the identity of the Lie group. The filter is applied to estimation on SO(3) a case where a stereo camera setup tracks a crane wire with a payload. The wire, which is under tension and forms a line is monitored by two 2D-cameras, and a line detector is used to obtain a description of how the wire is projected onto each image plane. A model of a spherical pendulum is applied and the estimator is validated by applying it on simulated data, as well as experimental data.

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Section: Spherical Pendulum Dynamicssupporting

confidence: 67%

An EKF for Lie Groups with Application to Crane Load Dynamics

Sjøberg¹,

Egeland²

2019

MIC

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“…Note that all these variables are introduced relative to the body-fixed coordinate frame. Similar representations of the dynamics of a pendulum have been proposed and can be found in [18,24,25]. We use this dynamic model and control theory (Pontryagin minimum principle) to develop optimal control strategies for building maintenance units.…”

Section: System Dynamicsmentioning

confidence: 92%

“…Note that it is also possible to express the control moment M in other forms. However the expression given by (7) can maintain the symmetry [18] of the rigid BMU dynamics.…”

Section: System Dynamicsmentioning

confidence: 99%

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Optimal control and stabilization of building maintenance units based on minimum principle

Wang¹,

Ahmed²

2021

JIMO

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In this paper we present a mathematical model describing the physical dynamics of a building maintenance unit (BMU) equipped with reaction jets. The momentum provided by reaction jets is considered as the control variable. We introduce an objective functional based on the deviation of the BMU from its equilibrium state due to external high-wind forces. Pontryagin minimum principle is then used to determine the optimal control policy so as to minimize possible deviation from the rest state thereby increasing the stability of the BMU and reducing the risk to the workers as well as the public. We present a series of numerical results corresponding to three different scenarios for the formulated optimal control problem. These results show that, under high-wind conditions the BMU can be stabilized and brought to its equilibrium state with appropriate controls in a short period of time. Therefore, it is believed that the dynamic model presented here would be potentially useful for stabilizing building maintenance units thereby reducing the risk to the workers and the general public.2010 Mathematics Subject Classification. Primary: 49J15; Secondary: 93C95.

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“…Li et al (2022) introduced adaptive fuzzy control to eliminate crane swing. Shen et al (2004) studied a new pendulum model. The control problem of rigid pendulum and multi-body pendulum is proposed.…”

Section: Introductionmentioning

confidence: 99%

Attitude oscillation suppression control of a XK-I spherical robot

Lin,

Wang,

Yang

et al. 2024

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Purpose In complex environments, a spherical robot has great application value. When the pendulum spherical robot is stopped or disturbed, there will be a periodic oscillation. This situation will seriously affect the stability of the spherical robot. Therefore, this paper aims to propose a control method based on backstepping and disturbance observers for oscillation suppression. Design/methodology/approach This paper analyzes the mechanism of oscillation. The oscillation model of the spherical robot is constructed and the relationship between the oscillation and the internal structure of the sphere is analyzed. Based on the oscillation model, the authors design the oscillation suppression control of the spherical robot using the backstepping method. At the same time, a disturbance observer is added to suppress the disturbance. Findings It is found that the control system based on backstepping and disturbance observer is simple and efficient for nonlinear models. Compared with the PID controller commonly used in engineering, this control method has a better control effect. Practical implications The proposed method can provide a reliable and effective stability scheme for spherical robots. The problem of instability in real motion is solved. Originality/value In this paper, the oscillation model of a spherical robot is innovatively constructed. Second, a new backstepping control method combined with a disturbance observer for the spherical robot is proposed to suppress the oscillation.

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Dynamics and control of a 3D pendulum

Cited by 46 publications

References 29 publications

An EKF for Lie Groups with Application to Crane Load Dynamics

An EKF for Lie Groups with Application to Crane Load Dynamics

Optimal control and stabilization of building maintenance units based on minimum principle

Attitude oscillation suppression control of a XK-I spherical robot

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