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The dual-quadrotors slung system may be utilized in the handling service of heavy and bulky loads. However, the coupled oscillations between the quadrotor attitudes and suspended load exhibit complicated dynamic behaviors, which degrade the safety and efficiency of the transport system. Although many works have been focused on the multiple quadrotors suspending a load, those prior studies did not consider the coupling effects between the quadrotor attitudes and the cable pendulum. This paper established a nonlinear dynamic model of dual-quadrotors carrying a slender beam undergoing planar motions, which described the coupled attitude-pendulum oscillations. Then a frequency estimator was resulted from the system parameters for investigating the dynamics. In addition, a novel combined modified model-following control and discontinuous piecewise smoother was proposed to suppress oscillations. The technical results in the simulations not only describe the dynamic behavior of the analytical model but also validate the effectiveness of the control method. [ABSTRACT FROM AUTHOR]

• A dynamic model of an underwater soft-link manipulator with vortex flows is derived. • Dynamic interaction between the soft-body structure and water flow is described. • A non-smooth piecewise smoother is presented to reduce coupled vibrations. • Experimental validation is provided for dynamic model and control method. While significant work has been directed at dynamics and control of underwater soft-body manipulators, less success has been achieved with interaction between soft structures and fluid flow. The complicated behavior of the interaction may corrupt operational efficiency and safety of underwater manipulators. The equations of the motion of underwater soft-link manipulators are reported in this article. The interaction among the water flow, the lateral vibrations and vortex-induced vibrations of the soft link has been described thoroughly in the analytical model. Furthermore, a novel control method is proposed to suppress coupled vibrations induced by the interaction. Comparing with previous control methods, the proposed method can provide more robustness to variations in the design frequency. Numerous experimental data obtained from a soft-body link implanted in water validated the behavior of the dynamic model and the effectiveness of the vibration-control method. The theoretical findings may also be acceptable for other types of soft-body structures immersed in the fluid. [ABSTRACT FROM AUTHOR]

Motion-induced oscillations of the flexible single link and its payload at the tip have negative impact on the anticipated performance of the flexible manipulators and thus should be suppressed to achieve tip positioning accuracy and high-speed operation. Because of the structural flexibility, the dynamics of the flexible manipulator can be described by coupled Duffing oscillators when considering the inherent structural nonlinearity of the flexible link into the dynamic modeling. However, little research has been focused on addressing the dynamic coupling issue in the nonlinear modeling of flexible-link manipulators using coupled Duffing oscillators. This article presents coupled Duffing oscillators for the nonlinear modeling of flexible single-link manipulators and then proposes a control method for suppressing the nonlinear vibrations of the coupled Duffing oscillators. Simulated and experimental results obtained from a flexible single-link manipulator test bench are in good agreement with the proposed nonlinear modeling and also demonstrate the effectiveness of the proposed control techniques for vibration suppression of the flexible manipulator. [ABSTRACT FROM AUTHOR]

Motion-induced unwanted cable swing and liquid sloshing degrade the effectiveness and safety of suspended liquid container. The manipulations of cable-suspended liquid container become more challenging due to the coupled pendulum-sloshing dynamics. This article develops the dynamic modeling of cable-suspended liquid container with coupled pendulum-sloshing dynamics. Afterward, a novel control method is proposed for controlling the coupled pendulum-sloshing dynamics. Numerous simulated and experimental results obtained from a small-scale industrial crane carrying a liquid container validated the dynamic behavior of the nonlinear model and demonstrated the effectiveness of the control method. [ABSTRACT FROM AUTHOR]

The inevitable oscillations of the payload decrease the positioning accuracy and lessen the safety in dual cranes carrying a large payload. In the presence of the structural flexibility, the dynamics of dual cranes are governed by the payload swing, pitch, and twisting after considering three-dimensional motions. However, little research has been directed at the modeling and control of three-dimensional dual cranes. A dynamic model of three-dimensional dual cranes including the payload swing, pitch and twisting is described. Moreover, a combined modified extra-insensitive input shaper and four-pieces smoother method is proposed to control the swing, pitch, and twisting of the payload. The dynamic behavior of the nonlinear model and the effectiveness of the new control method are verified experimentally on dual cranes carrying a slender beam. [ABSTRACT FROM AUTHOR]

Airflow-induced vibrations of the flexible structure are large, especially when the structure is made of lightweight material. Therefore, the interaction between the flexible structure and airflow should be considered. Although significant work has been placed on the flexible structures, less effort has been directed at the interaction between flexible structures and airflows. A dynamic equation of the motion of interaction between the flexible cantilever link and airflow has been derived in this article. The complicated link-airflow interaction has been captured by the analytical model. Furthermore, a new method has been presented to control coupled vibrations induced by the interaction. Numerous experiments have been performed on a Cartesian coordinate manipulator moving a polyurethane cantilever link to validate the effectiveness of the dynamic model and vibration-control method. The investigative findings may also acceptable for other types of flexible structures interacting with airflows. [ABSTRACT FROM AUTHOR]

Highlights • Model of dual planar cranes carrying a distributed-mass beam is derived. • A new method is developed for estimating the natural frequency of dual planar cranes. • MEI input shaper is presented for limiting oscillations of dual cranes. • Experiments validate dynamic behaviour and the effectiveness of MEI shaper. Abstract Unwanted oscillations caused by the operator-commanded motions lower the capable operating speeds and degrade the safety of dual cranes moving distributed-mass payloads. Mounting numbers of works have been devoted to the dynamics and control of dual cranes. However, few studies have been dedicated to the accurate estimation of natural frequency, which is a critical factor for controlling the dual cranes. This paper develops a new method to predict the natural frequency of dual planar cranes with different cable lengths. Furthermore, a modified extra-insensitive (MEI) input shaper is proposed to suppress the oscillations of the payload swing and pitch in the dual cranes. The MEI shaper has good robustness to large changes in the frequency, and has good performance in the jerk limitation. Simulated and experimental investigations are performed on small-scale dual cranes transporting a slender beam to validate the system dynamic behavior and the effectiveness of the MEI shaper. [ABSTRACT FROM AUTHOR]

Highlights • A new dynamic model is developed for a flexible single-link manipulator. • The model includes an infinite number of uncoupled Duffing oscillators. • Two methods are presented for controlling the vibrations of Duffing oscillators. • Experiments validate Duffing model and the effectiveness of control methods. Abstract Unwanted vibrations caused by the commanded motions lower the positioning accuracy and degrade the control performance of flexible link manipulators. Much work has been devoted to the dynamics and control of flexible link manipulators. However, there are few studies dedicated to the flexible link manipulators having Duffing oscillator dynamics. This paper develops a new model for a flexible single-link manipulator by assuming large mechanical impedance in the drives or large inertia of the motor hub and by considering the flexibility of the single-link manipulator. The derived model includes an infinite number of uncoupled Duffing oscillators by ignoring the modal coupling effects. Two new methods are presented for controlling the vibrations of the flexible manipulator governed by Duffing oscillators. One is designed for the single-mode Duffing oscillator, and the other is for the multi-mode Duffing oscillators. A comparison of these two methods is made using the results of numerical simulations and experimental measurements. Experimental investigations are also performed on a flexible single-link manipulator to validate the dynamic behavior of Duffing oscillators and the effectiveness of the new control methods. [ABSTRACT FROM AUTHOR]

Unwanted vibrations caused by the commanded motions degrade positioning accuracy and safety in flexible link manipulators. There are an infinite number of vibration modes in a single-link flexible manipulator. The contribution of the first mode is fundamental, but the high modes might also have some impacts on the overall system dynamics. A continuous function is designed to control the vibrations of the total modes by smoothing the driving commands. Comparison between the new continuous function and input shaper, which is a series of impulses, is also explored and evaluated. Numerous simulations and experiments for a wide range of working conditions and modeling errors are performed to validate the effectiveness of the new continuous function. [ABSTRACT FROM AUTHOR]

• Planar dynamic model of an underwater soft-link manipulator is derived. • Equations for estimating frequency and mode shape are proposed. • A control method is presented to control coupled vibrations. • Experiments validate effectiveness of dynamic model and control method. Underwater soft-link manipulators can be applied in offshore and marine industries. However, the soft-body link may interact with the fluid flow in this type of coupled liquid-link system. Both frequencies and mode shapes of the coupled system differ from those of uncoupled link vibrations and water flow due to the liquid-link interaction. Therefore, the dynamic model of underwater soft-body manipulators that account for liquid-link interaction is required to comprehend and control. Although significant work has been focused on the underwater manipulator and the soft manipulator, no significant dynamic modeling, control study, and experimental validation have been directed at the liquid-link interaction in underwater soft-body manipulators. A dynamic model of underwater soft-link manipulators undergoing planar motions is presented in this article. The analyses of frequencies and mode shapes for the liquid-link interaction are also described. Meanwhile, a control method is designed to mitigate coupled vibrations in underwater soft-link manipulators. Simulated and experimental results validate the utility of the dynamic model and control method. [ABSTRACT FROM AUTHOR]

Operating cranes is challenging because payloads experience large and dangerous oscillations, especially when the system is suffering from wind disturbances and the large-size payload is modeled as a distributed-mass model. The payload oscillations induced by both intentional motions commanded by the human operator and by the external wind disturbances make the dynamics more complicated. This paper presents a novel combined control architecture to limit oscillations of the distributed-mass payload caused by both human-operator commands and wind disturbances. While a smoothed command suppressed operator-induced oscillations, a wind-rejection command eliminated the payload swing resulting from the wind gusts. Through simulations, a large range of system parameters and motions are analyzed to investigate the dynamic behavior of bridge cranes with distributed-mass beams and wind disturbances by using the new control scheme. Experimental results obtained from a small-scale bridge crane validate the simulated dynamic behavior and the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

• A dynamic model of bridge cranes transporting heterogeneous loads is derived. • The frequency analyses of swing and twisting for eccentric loads is described. • A DP smoother is presented for controlling eccentric-load dynamics. • Experiments validate the dynamic behavior and control effectiveness. Industrial cranes transporting bulky loads are widely used in many engineering applications. However, heterogeneous loads give rise to eccentricity between the mass center and centroid of the load. Natural frequencies of the swing and twisting under eccentric-load mechanisms differ from those under uniform-load configurations. Therefore, load swing and twisting dynamic models that account for eccentricity are required to adequately understand and accurately control such cranes. Although significant work has been directed at the uniform-load dynamics of industrial cranes, little attention has been focused on the eccentric-load dynamics. This article presents a dynamic model of bridge cranes transporting heterogeneous loads. The frequency analyses of double-pendulum swing and twisting for eccentric loads is described. Additionally, a control method is designed using a simplified spherical pendulum with load-twisting dynamics and eccentric-load dynamics. Simulated and experimental results obtained from a small-scale bridge crane transporting a heterogeneous bar verify the utility of the analytical model and validate the effectiveness and robustness of the proposed control method. [ABSTRACT FROM AUTHOR]

While significant work has been directed at suppressing the 2-D slosh, less success has been achieved with reducing the 3-D slosh in a moving rectangular container. Control of the 3-D slosh in a moving rectangular liquid container is very challenging because there are two fundamental modes and an infinite number of high modes. The dynamics of the 3-D slosh in a moving rectangular container are derived. The theoretic analysis shows that both the two fundamental and high modes have large impacts on the sloshing dynamics. A command smoothing technique is designed to suppress slosh for the two fundamental and high modes. Comparing with the combined input shaper and the low-pass filter scheme, the presented smoother provides more robustness to variations in the sloshing frequency. Simulations over a large range of various working conditions and system parameters are conducted to analyze the liquid sloshing dynamics and the robustness of the method. Experimental results obtained from a moving rectangular liquid container validate the simulated sloshing dynamics behavior and the effectiveness of the method. [ABSTRACT FROM PUBLISHER]

Motion-induced oscillations of crane payloads seriously degrade their effectiveness and safety. Significant progress has been achieved with reducing payload oscillations on a single-pendulum crane with a point-mass payload attached to the end of the cable. However, large payloads and the actual configuration of the hoisting mechanism may transform the crane to a double-pendulum system with a distributed-mass payload. The manipulation task can be more challenging because of the complicated dynamics. The dynamics of bridge cranes transporting distributed-mass beams are derived. A command-smoothing scheme is presented to suppress the complex payload oscillations. Simulations of a large range of motions are used to analyze the dynamic behavior of the cranes and the robustness of the method. Experimental results obtained from a small-scale double-pendulum bridge crane transporting a distributed-mass beam validate the simulated dynamic behavior and the effectiveness of the method. [ABSTRACT FROM AUTHOR]

Motion-induced oscillations of crane payloads seriously degrade their effectiveness and safety. For the transport of a large object, the payload is modeled as a distributed-mass model, and is typically attached to the hook by four rigging cables. The manipulation task can be more challenging because of the payload swing toward the driving direction and the payload twisting about the rigging cables. The dynamics of bridge cranes transporting distributed-mass payloads are derived. A control scheme is designed for suppressing both the payload swing and twisting. Simulations of a large range of motions and various system parameters are used to analyze the dynamic behavior and the robustness of the control scheme. Experimental results obtained from a bridge crane transporting distributed-mass crate validate the simulated dynamic behavior and the effectiveness of the control scheme. [ABSTRACT FROM PUBLISHER]

Control of a moving liquid container is challenging because of unwanted transient and residual slosh. Although significant progress has been achieved at eliminating the fundamental sloshing mode, less success has been achieved with designing a controller to suppress slosh for an infinite number of modes. This study presented two methods to reduce an infinite number of sloshing modes in a moving liquid container. The first method is command smoothing to eliminate slosh by using the first-mode frequency. The second one is a combined input-shaping and command-smoothing architecture. The input shaper reduces slosh for the first mode, while the command smoother suppresses slosh for the third and higher modes. Both the command smoothing and the combined control scheme eliminate the transient and residual slosh to a very low level. However, the rise time of the combined controller is shorter than that of the command smoother. Simulations of a large range of motions are used to analyze liquid sloshing dynamics by using the proposed methods. Experimental results obtained from a moving container validate the simulated dynamic behavior and the effectiveness of the methods. [ABSTRACT FROM PUBLISHER]

Operating cranes is challenging because payloads can experience large and dangerous oscillations. The oscillations are induced by both intentional motions commanded by the human operator and by external disturbances. Although significant progress has been achieved by using command shaping to reduce operator‐induced vibration, less success has been achieved on reducing oscillations induced by external disturbances, such as wind. The disturbance‐rejection task is more challenging because it requires accurate sensing of the crane payload. This study presents a combined command shaping and feedback control architecture. The input shaper eliminates the payload oscillation caused by human‐operator commands, and the feedback controller reduces the effect of wind gusts. Simulations of a large range of motions are used to analyse the dynamic behaviour of boom cranes using the proposed controller. Experimental results obtained from a small‐scale boom crane validate the simulated dynamic behaviour and the effectiveness of the controller. [ABSTRACT FROM AUTHOR]

• Model of tower cranes carrying slender payloads is derived. • Equation for estimating the twisting frequency is presented. • A discontinuous piecewise smoother is proposed for controlling swing and twisting. • Experiments validate dynamic behaviour and the control effectiveness. Tower cranes suspending slender payloads are widely used in the construction site. Both the payload swing and twisting degrade the efficient and safe operation. However, the twisting dynamics is more complicated than the swing dynamics. Although numerical analysis of the twisting dynamics has been reported, little attention has been directed at the analytical analysis of the twisting dynamics. A new dynamic model including swing and twisting has been derived in this article. The analytical analysis of the twisting dynamics from the new model has been described. The closed-form solution for estimating frequencies of the payload twisting have been presented. In addition, a new control method is proposed for suppressing swing and twisting in tower cranes transporting slender payloads. The control method has good robustness to variation in working conditions and system parameters, and good performance in rise time. Numerous simulations and experiments demonstrated the key dynamic behavior of the payload twisting and effectiveness of the control method. [ABSTRACT FROM AUTHOR]