Modeling and Fuzzy Decoupling Control of an Underwater Vehicle-Manipulator System
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This paper presents the detailed modeling and simulation of the dynamic coupling between an autonomous underwater vehicle (AUV) and a manipulator. The modeling processes are described with the incorporation of the most dominating hydrodynamic effects such as added mass, lift and drag forces. The hydrodynamic coefficients are derived using strip theory and are adjusted according to dynamical similarity. A fuzzy decoupling controller (FDC) is proposed for an autonomous underwater vehicle-manipulator system (UVMS) which consists of two subsystems, an underwater vehicle and a manipulator. The proposed controller uses a fuzzy algorithm (FA) to adaptively tune the gain matrix of the error function (EF). The EF is described by the integral sliding surface function. This technique allows the off-diagonal elements developed for decoupling the system to be incorporated in the gain matrix. Tracing the FA and EF back to the principle of feedback linearization, one further obtains evidence about the decoupling and stability of the system. Moreover, a desired trajectory with the consideration of the dynamic coupling of the AUV is designed to reduce the thruster forces and manipulator's torques. This technique provides high performance in terms of tracking error norms and expended energy norms. A major contribution of this study is that it adopts the off-diagonal elements to exploit the dynamic coupling between the degrees of freedom of the subsystem and the dynamic coupling between the two subsystems. Simulation results demonstrate the effectiveness and robustness of the proposed technique in the presence of parameter uncertainties and external disturbances.Keywords:
Linearization
Decoupling (probability)
Robustness
Underactuation
Visual Servoing
Epipolar geometry
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For underactuated marine vessels, the dimension of the configuration space exceeds that of the control input space. This article describes underactuated marine vessels and the control challenges they pose. In particular, there are two main approaches to design control systems for underactuated marine vessels. The first approach reduces the number of degrees of freedom (DOF) that it seeks to control such that the number of DOF equals the number of independent control inputs. The control problem is then a fully actuated control problem – something that simplifies the control design problem significantly – but special attention then has to be given to the inherent internal dynamics that has to be carefully analyzed. The other approach to design control systems for underactuated marine vessels seeks to control all DOF using only the limited number of control inputs available. The control problem is then an underactuated control problem and is quite challenging to solve. In this article, it is shown how line-of-sight methods can solve the underactuated control problems that arise from path following and maneuvering control of underactuated marine vessels.
Underactuation
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As most of the ships are belongs to underactuated mechanical systems, the motion control problems of underactuated ships attract many research concerns. In this paper, the point stabilization and path tracking control of underactuated ships are surveyed, where the techniques for point stabilization of underactuated ship under second-order nonholonomic constraints are explained, and three types of control strategies for path tracking are presented, that is, simplified-state, partial-state and full-state depended control. Furthermore, the straight-line and curved-path tracking are investigated in details. Finally, the research perspectives of motion control of underactuated ships are discussed.
Underactuation
Nonholonomic system
Tracking (education)
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Abstract The inclusion of linearized moist physics can increase the accuracy of 4D‐Var data assimilation and adjoint‐based sensitivity analysis. Moist processes such as convection can exhibit nonlinear behaviour. As a result, representation of these processes in a linear way requires much care; a straightforward linearization may yield a poor approximation to the behaviour of perturbations of interest and could contain numerical instability. Here, an extensive numerical study of the Jacobian of the relaxed Arakawa–Schubert ( RAS ) convection scheme is shown. A Jacobian based on perturbations at individual model levels can be used to understand the physical behaviour of the RAS scheme, predict how sensitive that behaviour is to the prognostic variables and determine the stability of a linearization of the scheme. The linearity of the scheme is also considered by making structured perturbations, constructed from the principle components of the model variables. Based on the behaviour of the Jacobian operator and the results when using structured perturbations, a suitable method for linearizing the RAS scheme is determined. For deep, strong convection, the structures of the RAS Jacobian are reasonably simple, the rate at which finite‐amplitude estimates of the structures change with respect to input perturbations is small and the eigenmodes of the Jacobian are not prohibitively unstable. For deep convection, an exact linearization is therefore suitable. For shallow convection, the RAS scheme can be more sensitive to the input prognostic variables due to the faster time‐scales and proximity to switches. Linearization of the RAS therefore requires some simplifications to smooth the behaviour for shallow convection. It is noted that the physical understanding of the scheme gained from examining the Jacobian provides a useful tool to the developers of nonlinear physical parametrizations.
Linearization
Deep convection
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Underactuation
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Mathematical Tools.- Mathematical Preliminaries.- Modeling and Control Properties of Ocean Vessels.- Modeling of Ocean Vessels.- Control Properties and Previous Work on Control of Ocean Vessels.- Control of Underactuated Ships.- Trajectory-tracking Control of Underactuated Ships.- Simultaneous Stabilization and Trajectory-tracking Control of Underactuated Ships.- Partial-state and Output Feedback Trajectory-tracking Control of Underactuated Ships.- Path-tracking Control of Underactuated Ships.- Way-point Tracking Control of Underactuated Ships.- Path-following of Underactuated Ships Using Serret-Frenet Coordinates.- Path-following of Underactuated Ships Using Polar Coordinates.- Control of Underactuated Underwater Vehicles.- Trajectory-tracking Control of Underactuated Underwater Vehicles.- Path-following of Underactuated Underwater Vehicles.- Control of Other Underactuated Mechanical Systems.- Control of Other Underactuated Mechanical Systems.- Conclusions and Perspectives.
Underactuation
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The velocity Jacobian matrix and the force Jacobian matrix are important index for kinematics, singularity and dynamics analyses of parallel manipulators. A novel computer variation geometric approach is proposed for solving the velocity Jacobian matrix and the force Jacobian matrix of parallel manipulators with linear driving limbs, as well as the determinant of Jacobian matrix. First, basic computer variation geometry techniques and definitions are presented for designing the simulation mechanisms, and several simulation mechanisms of parallel manipulators with linear driving limbs are created. Second, some velocity simulation mechanisms are created and the partial derivatives in Jacobian matrix are solved automatically and visualized dynamically. Based on the results of the computer simulation, the velocity Jacobian matrix and force Jacobian matrix are formed and the determinant of Jacobian matrix is solved. Moreover, the simulation results prove that the computer variation geometry approach is fairly quick and straightforward, and is accurate and repeatable. This project is supported by NSFC No. 50575198.
Matrix (chemical analysis)
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The Jacobian matrix of a dynamical system describes its response to perturbations. Conversely, one can estimate the Jacobian matrix by carefully monitoring how the system responds to environmental noise. We present a closed-form analytical solution for the calculation of a system's Jacobian from a time series. Being able to access the Jacobian enables a broad range of mathematical analyses by which deeper insights into the system can be gained. Here we consider in particular the computation of the leading Jacobian eigenvalue as an early warning signal for critical transitions. To illustrate this approach, we apply it to ecological meta-foodweb models, which are strongly nonlinear dynamical multi-layer networks. Our analysis shows that accurate results can be obtained, although the data demand of the method is still high.
SIGNAL (programming language)
Matrix (chemical analysis)
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