Integrated System for Robust 6-DOF Positioning Utilizing New Closed-Form Visual Motion Estimation Methods in Planar Terrains

Estimating the relative positions and (or) trajectory of a camera from video images is a fundamental problem in motion vision. Of special relevance is the closed-form solution for planar scenes, for processing fly-over imagery from airborne and underwater robotics platforms, automated airplane landing utilizing runway landmarks, photomosaicing, etc. However, the method's robustness can break down in certain scenarios, e.g., due to inherent translation-rotation ambiguity of visual motion with short baselines and narrow field of view. The robustness can be improved by devising methods that compute a smaller set of motion parameters, utilizing other sensors to measure the remaining components. This paper addressed key issues in six degrees of freedom positioning from fly-over imagery by integrating vision with rotational angle sensors. First, we propose and utilize robust closed-form solutions for estimating the motion and orientation of a planar surface from the image flow variations up to first order, given measurements of pitch and roll motions. We also describe a calibration technique to enable the integration of angle sensor and visual measurements. Next, an error analysis enables us to evaluate the impact of inaccurate pitch and roll measurements on the estimates from the new closed-form solutions. Finally, the performance of our new methods and the integrated positioning system are evaluated in various experiments with synthetic and real data     

Maximum theoretical power absorption of connected floating bodies under motion constraints

In this paper, a mathematical model is presented to evaluate the maximum mean power that can be absorbed by a three-dimensional system of connected floating bodies in waves under a weighted global constraint. The constraint imposed on the motion amplitudes of the system can be used to limit the motions of the bodies in order to make sure that the assumption of linear theory for wave–structure interaction remains valid. The absorbed power of a structure can be considered as the difference between excitation and radiated power without consideration of practical power take off. The solutions for the maximum relative capture widths of rigidly connected two rafts have a good agreement with the calculated ones for the same rafts being seen as a single whole structure. Meanwhile, the results of maximum power absorption of two hinged slender rafts in cuboid shape give a good agreement as well with those by using slender-body approximations. Then dynamics of a hinged two rafts are studied and results show how the maximum efficiency is affected by raft width and restricting the motions.     

Accurate measurement of six Degree Of Freedom small-scale ship motion through analysis of one camera images

A new six Degree Of Freedom (6DOF) motion measurement technique for small-scale physical models of floating bodies is presented, based on analysis of image sequence from one camera. The proposed system consists of one camera and one target: the method estimates the 3-D rigid motion following the time evolution of the target of known pattern fixed to the moving body and framed by the camera. In particular, the rotation matrix and the translation vector of the 3-D rigid motion between initial still position and a generic moved position are calculated by assuming the existence of a planar homography between the camera CCD plane and the plane passing through the flat target surface. Geometrical relationship allows one the calculation of wanted 6DOFs for every point of the modeled body. In the paper, the method is mathematically presented in terms of equations of rigid motion with its associate accuracies. The image-based technique is illustrated on some tests carried out in an experimental multipurpose wave basin.     

New Method for Predicting the Motion Responses of A Flexible Joint Multi-Body Floating System to Irregular Waves

A new hybrid method of frequency domain and time domain is developed in this paper to predict the motion responses of a flexibly joint multi-body floating system to irregular waves. The main idea of the method is that the three-dimensional frequency method is used to obtain the hydrodynamic coefficients and the response equations are solved in time domain step by step. All the forces can be obtained at the same time. The motions and nonlinear mooring forces of a box type six-body floating system are predicted. A comparison of the theoretical method-based solutions with experimental results has shown good agreement.     

Hadley and Rossby regimes in a simple model of convection of a rotating fluid

This paper analyzes the properties of solutions to the equations describing the motion of a stratified fluid in the class of velocity and temperature fields linear in coordinates. For an ideal fluid, these equations, on the one hand, are exact for the corresponding hydrodynamic problem and, on the other hand, are identical to the equations of motion for a heavy top. In a conservative case, the equations of motion of a top share common solutions with the equations of geophysical fluid dynamics and reproduce motions similar to those existing in the theory of the large-scale atmospheric circulation. This study considers the effects of viscosity and heat conduction in the fluid, which are, in a sense, similar to the effect of friction in the case of a top. The influence of deflections of the vectors of gravity and external rotation from their standard directions for a plane-parallel atmosphere is also considered. The regimes of motions that are described by the starting equations and approximations commonly used to model the atmospheric general circulation (the quasi-geostrophic approximation) are analyzed. It is shown that these equations correctly describe the Hadley and Rossby circulation regimes and transitions between them that are observed in numerical and laboratory experiments. Particular attention is given to the consistency between different regimes of the exact equations and their quasi-geostrophic approximations, which is manifested for small Rossby numbers and is generally absent for large Rossby numbers. The asymptotic behaviors of the curves of transition between the Hadley and Rossby regimes under the conditions of breaking the external symmetry of flows are obtained. These asymptotics explain the corresponding transition boundaries for the regimes observed in the known experiments in annuluses.     

Application of the extended Melnikov's method for single-degree-of-freedom vessel roll motion

Traditionally, when using Melnikov's method to analyze ship motions, the damping terms are treated as small. This is typically true for roll motion but not always true for other and/or multiple degrees of freedom. In order to apply Melnikov's method to other and/or multiple-degree-of-freedom motions, the small damping assumption must be addressed. In this paper, the extended Melnikov method is used to analyze ship motion without the constraint of small linear damping. Two roll motion models are analyzed here. One is a simple roll model with nonlinear damping and cubic restoring moment. The other is the model with biased restoring moment. Numerical simulations are investigated for both models. The effectiveness and accuracy of this method is demonstrated.     

基于声呐图像的深海采矿车组合定位导航算法

实现高精度的定位导航是深海采矿车完成海底工作任务的基础条件。在采矿车行进过程中,声呐设备生成的图像信息能够反映海底场景的变化,从而体现采矿车本身的运动,由此建立了一种声呐图像里程计,并将其与轮式里程计和USBL测量数据相结合提出了一种深海采矿车组合定位导航算法。首先对多波束前视声呐图像进行预处理,然后使用Canny算法进行特征检测并对特征点云进行配准,再结合声呐成像原理构建了声呐图像里程计运动模型,最后通过轮式里程计运动模型推导预测方程、声呐图像里程计运动模型和USBL测量数据推导更新方程,利用EKF（extended Kalman filter）算法实现基于多传感器融合的定位与姿态估计。海试数据验证了该组合定位算法能实现轮式里程计、声呐里程计和超短基线在速度、位置、艏向角估计、定位速率的精度互补,具有一定的有效性和精确性,该算法为深海采矿车的定位与导航算法研发提供了参考。     

Coupled dynamics of tethered buoy systems

The three-dimensional coupled behavior during the interaction of buoys with their mooring systems is numerically analyzed. A time-domain model was developed to predict the response of a tethered buoy subject to hydrodynamic loadings. External loadings include hydrodynamic forces, tethers tensions, wind loadings and weight. System nonlinearities include large rotational and translational motions, and non-conservative fluid loadings. The mooring problem is formulated as a combined nonlinear initial-value and two-point-boundary-value problem which is directly integrated both in time and space. Buoy equations of motion are derived using small Eulerian angles. Coupling between rotational and translational degrees of freedom is included and coupling between the buoy and cable is effected by adopting the buoy equations of motion as boundary conditions at one end for the mooring problem. Numerical examples are provided to validate the formulation and solution technique; predicted responses of three types of buoy (sphere, spar, and disc) are compared with experimental results.     

Submersible holocamera for detection of particle characteristics and motions in the ocean

A submersible holographic camera has been developed for measuring the particle distributions, characteristics and motions within a sample volume in the ocean. Its main purpose is to provide data on the spatial distribution, size, shape, orientation, inter-particle relationships, turbulence, local shear and relative motion due to swimming and sinking of plankton. This battery powered, modular, self-contained system is remotely operated by a PC through fiber optic links. Data from on-board environmental sensors are used to select locations for recording holograms and relating the images to broader scale physical structures. The holocamera also has a buoyancy control system that allows deployment as a neutrally buoyant drifter or in a slow profiling mode. The instrument is currently configured for in-line holography, but it has been designed to be readily adaptable to off-axis holography. The cylindrical sample volume is 6.3 cm in diameter and its length can be varied from 10 to 68 cm. The light source is a pulsed ruby laser chosen predominantly because zooplankton are typically less sensitive to red light. The laser has independent dual flashlamps for maximum flexibility in selecting delay between exposures. About 300 single or multiple exposure holograms can be recorded during a single deployment. Data such as particle size, shape, orientation, distribution in space and velocity are obtained by reconstructing the holograms, scanning them with a video camera equipped with a microscope objective, digitizing the images and analyzing relevant data. Several recent field tests have demonstrated the system reliability and resolution. Particles with sizes as small as 10 μm and details on cell structures of larger particles in the 3–5 μm range could be identified and used for identifying and categorizing the particles. Sample single and double exposure images, the latter for measuring motion, and sample spatial distributions are provided. Methods for mapping the liquid velocity distribution are addressed briefly. Parameters affecting the image resolution and location in space, such as particle density, distance from the film plane and focus are discussed and demonstrated.     

湍流混合输运通量的数学物理描述基础——高确定性闭合的湍流二阶矩和基本特征量控制方程组

湍流,在海洋动力系统其他类运动的控制方程组中,主要以输运通量剩余项的形式出现,它是最重要的海洋混合运动主体。本文的主要研究目标是,在湍流最新研究成果及其子系统控制方程组基础上,提出高确定性的二阶矩闭合原理,导出闭合的二阶矩和基本特征量控制方程组,建立湍流输运通量的数学物理描述基础。现有的湍流基本特征量方程组,其右端项的闭合办法实际上是非独立的。因此要么在今后的研究中引入独立的闭合办法,要么回归到湍流的现场实验分析研究,给出独立的特征量实验关系,从而有可能得到湍流混合系数的解析估计。     

Maximum wave-power absorption under motion constraints

An expression is derived for the maximum mean power that can be absorbed by a system of oscillating bodies in waves under a global constraint on their motions. The particular case of a single half-immersed sphere is used to show how the ‘point absorber’ result predicting capture widths in excess of unity must be modified. The theory is also applied to the submerged cylinder wave-energy device and curves are presented which show how the maximum efficiency is affected by restricting the motion of the device.     

On the motions of the underwater remotely operated vehicle with the umbilical cable effect

In this paper, a hydrodynamic model is developed to simulate the six degrees of freedom motions of the underwater remotely operated vehicle (ROV) including the umbilical cable effect. The corresponding hydrodynamic forces on the underwater vehicle are obtained by the planar motion mechanism test technique. With the relevant hydrodynamic coefficients, the 4th-order Runge–Kutta numerical method is then adopted to solve the equations of motions of the ROV and the configuration of the umbilical cable. The multi-step shooting method is also suggested to solve the two-end boundary-value problem on the umbilical cable with respect to a set of first-order ordinary differential equation system. All operation simulations for the ROV including forward moving, ascending, descending, sideward moving and turning motions can be analyzed, either with or without umbilical cable effect. The current effect is also taken into consideration. The present results reveal that the umbilical cable indeed significantly affects the motion of the ROV and should not be neglected in the simulation.     

A Novel Dynamics Analysis Method for Spar-Type Floating Offshore Wind Turbine

The dynamic behavior of floating offshore wind turbine (FOWT) is crucial for its design and optimization. A novel dynamics analysis method for the spar-type FOWT system is proposed in this paper based on the theorem of moment of momentum and the Newton’s second law. The full nonlinearity of the equations of motion (EOMs) and the full nonlinear coupling between external loads and the motions are preserved in this method. Compared with the conventional methods, this method is more transparent and it can be applied directly to the large-amplitude rotation cases. An in-house code is developed to implement this method. The capability of in-house code is verified by comparing its simulation results with those predicted by FAST. Based on the in-house code, the dynamic responses of a spar-type FOWT system are investigated under various conditions.     

An efficient algorithm for strapdown accelerometer-based motion measurement

The paper is concerned with the measurement of motion of free floating bodies using accelerometers strapped to a cross-arm mounted on the body. The measurement system has been studied with the help of a formulation involving a set of coupled nonlinear initial-value equations involving the angular acceleration components. A PC-based software using the Bulirsch-Stoer technique has been developed to solve the initial-value problem so as to deduce the body motions from the measured accelerations. Suitable filtering strategy has been employed at every stage of numerical integration. The reliability of the strapdown accelerometer system together with software developed has been validated using a “dry” test. Typical motion measurements have been done in all the six degrees of freedom of a tug model in a wave flume. The method is deemed to be an efficient and cost-effective technique suitable for free floating bodies and for large motions.     

An integrated dynamic model of ocean mining system and fast simulation of its longitudinal reciprocating motion

An integrated dynamic model of China’s deep ocean mining system is developed and the fast simulation analysis of its longitudinal reciprocating motion operation processes is achieved. The seafloor tracked miner is built as a three-dimensional single-body model with six-degree-of-freedom. The track-terrain interaction is modeled by partitioning the track-terrain interface into a certain number of mesh elements with three mutually perpendicular forces, including the normal force, the longitudinal shear force and the lateral shear force, acting on the center point of each mesh element. The hydrodynamic force of the miner is considered and applied. By considering the operational safety and collection efficiency, two new mining paths for the miner on the seafloor are proposed, which can be simulated with the established single-body dynamic model of the miner. The pipeline subsystem is built as a three-dimensional multi-body discrete element model, which is divided into rigid elements linked by flexible connectors. The flexible connector without mass is represented by six spring-damper elements. The external hydrodynamic forces of the ocean current from the longitudinal and lateral directions are both considered and modeled based on the Morison formula and applied to the mass center of each corresponding discrete rigid element. The mining ship is simplified and represented by a general kinematic point, whose heave motion induced by the ocean waves and the longitudinal and lateral towing motions are considered and applied. By integrating the single-body dynamic model of the miner and the multi-body discrete element dynamic model of the pipeline, and defining the kinematic equations of the mining ship, the integrated dynamic model of the total deep ocean mining system is formed. The longitudinal reciprocating motion operation modes of the total mining system, which combine the active straight-line and turning motions of the miner and the ship, and the passive towed motions of the pipeline, are proposed and simulated with the developed 3D dynamic model. Some critical simulation results are obtained and analyzed, such as the motion trajectories of key subsystems, the velocities of the buoyancy modules and the interaction forces between subsystems, which in a way can provide important theoretical basis and useful technical reference for the practical deep ocean mining system analysis, operation and control.     

Flow-Induced Vibration of A Nonlinearly Restrained Curved Pipe Conveying Fluid

Investigated in this study is the flow-induced vibration of a nonlinearly restrained curved pipe conveying fluid. The nonlinear equation of motion is derived by equilibrium of forces on microelement of the system under consideration. The spatial coordinate of the system is discretized by DQM (differential quadrature method). On the basis of the boundary conditions, the dynamic equation is solved by the Newton-Raphson iteration method. The numerical solutions reveal several complex dynamic motions for the variation of the fluid velocity parameter, such as limit cycle motion, buckling and so on. The result obtained also shows that the sub parameter regions corresponding to the several motions may change with the variation of some parameters of the curved pipe. The present study supplies a new reference for investigating the nonlinear dynamic response of some other structures.     

浮基多体系统自激运动响应的时域分析方法

浮基多体系统上部机构作业时不仅存在多体系统内部各物体间的耦合作用 ,还存在浮基与流场间的耦合作用。本文将浮基在流场中引起的辐射势表示为浮基加速度与时域规范化速度势乘积的卷积形式 ,导出流体动压力及静水系泊恢复力与浮基运动的关系。使用多刚体力学的凯恩方法得到系统的动力学方程。最后给出了在时域中数值求解系统运动响应的具体步骤     

Motion response simulation of a twin-hulled semi-submersible

The purpose of the study was to develop a prediction technique to simulate the motion response of a damaged platform under wave, wind and current forces. The equations of motion were obtained using Newton's second law and the numerical solution technique of non-linear equations of motion is explained for intact and damaged cases. The analysis technique employs large displacement non-linear equations of motion. Solutions were obtained in the time-domain to predict the motion characteristics. In this study, analysis procedures were developed to calculate: (a) wave loading on asymmetrical structural configurations; (b) hydrodynamic reaction forces (inertia or moment of inertia, damping and restoring forces) on asymmetrical shapes. During the damage simulation, change in the mass of the structure as well as wave and hydrodynamic reaction forces, were taken into account. The computer program developed for the time-domain simulation is introduced. In order to avoid slowly decaying transient motions of the structure due to wave excitation forces, an exponential ramp function is used. The application of a ramp function enables a quick convergence in the time-domain solution of equations of motion. Results of a numerical motion simulation program and the experimental studies are also presented in order to make comparisons. Comparison of the test results with the numerical simulations shows good agreement for heave, roll and pitch motions. The formulations and the computational procedures given in this paper provide useful tools for the investigation of the non-linear dynamic stability characteristics of floating structures in waves for intact, damaged and post-flooding conditions in six-degrees of freedom.     

波浪与抛石潜堤相互作用的MPS法数值模型研究

为了研究波浪与抛石潜堤相互作用过程中大自由表面变形和堤内渗流等强非线性紊流运动问题,利用改进的MPS法,建立了模拟波浪与抛石潜堤相互作用的MPS法数值计算模型。模型将抛石潜堤假定为均质多孔介质,采用Drew的二相流运动方程描述多孔介质内外的流体运动;通过在动量方程中增加非线性阻力项,并引入亚粒子尺度紊流模型,模拟波浪与可渗结构物相互作用过程中的紊流运动。选取“U”型管中多孔介质内渗流过程和孤立波与可渗潜堤相互作用两个典型的渗流问题,通过将数值计算结果与理论解和实测值的对比分析,对所提出的MPS法紊流渗流模型的模拟精度进行验证。结果表明:基于改进的MPS法构建的垂向二维紊流渗流模型可以很好地再现“U”型管中多孔介质内渗流以及波浪作用下可渗潜堤内外的复杂流场,显著缓解流-固界面处的压力震荡与粒子分布不均匀问题,实现了较高的模拟精度。     

Coupled dynamic analysis of deep-sea mining support vessel with dynamic positioning

Deep-sea mining (DSM) is an advanced concept. A simulation method of coupled vessel/riser/body system in DSM combined with dynamic positioning (DP) is proposed. Based on the three-dimensional potential flow theory, lumped mass method, and Morison’s equations the dynamic models of the production support vessel, riser and slurry pump are established. A proportion integration differentiation (PID) controller with a nonlinear observer and a thrust allocation unit are used to simulate the DP system. Coupled time domain simulation is implemented with the vessel operated in two DP modes. Results of the vessel and pump motions, riser tension, and thruster forces are obtained. It shows that the pump will be lifted by the riser when the vessel is chasing the next set point. Riser tension is influenced by the wave frequency motions of the vessel in positioning mode and low-frequency motions in tracking mode. The proposed simulation scheme is practical to study the DSM operation.