Optimal control of nonholonomic motion planning for a free-falling cat

The nonholonomic motion planning of a free-falling cat is investigated. Nonholonomicity arises in a free-falling cat subject to nonintegrable angle velocity constraints or nonintegrable conservation laws. When the total angular momentum is zero, the motion equation of a free-falling cat is established based on the model of two symmetric rigid bodies and conservation of angular momentum. The control of system can be converted to the problem of nonholonomic motion planning for a free-falling cat. Based on Ritz approximation theory, the Gauss-Newton method for motion planning by a falling cat is proposed. The effectiveness of the numerical algorithm is demonstrated through simulation on model of a free-falling cat.

Effects of Degrees of Motion Freedom on Free-Fall of A Sphere in Fluid

Free-fall of a sphere in fluid is investigated at a Galileo number of 204 by direct numerical simulations(DNS). We mainly focus on the effects of different degrees-of-freedom(DOFs) of the sphere motion during free-fall. The characteristics of free-fall are compared with those of flow past a fixed sphere. Additional numerical tests are conducted with constraints placed on the translational or rotational DOFs of the sphere motion to analyze different DOFs of sphere motion. The transverse motion contributes significantly to the characteristics of free-fall; it results in the retardation of the vortex shedding, leading to the decrease of the Strouhal number. In addition, the transversal sphere motion exhibits the tendency to promote the sphere rotation. On the contrary, the effects of the sphere rotation and vertical oscillations during free-fall are negligible.

An investigation using high-precision CCD laser displacement sensor to measure body surface motion induced by heartbeat

The aim of this study was to measure the motion of the body surface induced by heartbeat by using a high-precision laser sensor in order to provide a reference for other research on medical remote sensing techniques that are unconstrained and non-contact. Body surface motions at some points on the chest and on the dorsal region were measured for eight men with a laser displacement sensor. For comparison, an electrocardiograph was also used to monitor the heartbeat. As a result, we confirmed cyclic motion of about 0.1 mm in amplitude everywhere on the body surface, not only from the front of the body but also from the back and the neck. In contrast, which part on the body was most suitable for measurement had to be taken into account because a difference in motion amplitudes was observed in different parts on the body. The amplitude of the motions also depended on the conditions of the body surface as well as underneath the skin. These results show the possibility of acquiring information about heartbeats from anywhere on the body by using an unconscious sensing technique, and the potential for the technique to monitor the condition of the body and personal physical characteristics.

MOTION TYPES AND CHAOS OF MULTI-BODY SYSTEMS VIBRATING WITH IMPACTS

In this paper,the limit sets theory for an autonomous dynamical system is generalized to a multi-body system vibrating with impacts.We discover that if every motion of the system is bounded,it has only four different types:periodic motion 7 t,non-periodic recurrent motion γ2,and non-Poisson stable mo- tions γ3 and γ4 approaching γ1 and γ2, respectively.γ2 is the source of chaos.It is very interesting that cha- otic motions seem stochastic but possess the character of recurrence.By way of example,we discuss chaotic motions of a small ball bouncing vertically on a massive vibrating table.The result obtained by us is different from that obtained by Holmes.

Monolithic Coupling of the Pressure and Rigid Body Motion Equations in Computational Marine Hydrodynamics

In Fluid Structure Interaction(FSI) problems encountered in marine hydrodynamics, the pressure field and the velocity of the rigid body are tightly coupled. This coupling is traditionally resolved in a partitioned manner by solving the rigid body motion equations once per nonlinear correction loop, updating the position of the body and solving the fluid flow equations in the new configuration. The partitioned approach requires a large number of nonlinear iteration loops per time–step. In order to enhance the coupling, a monolithic approach is proposed in Finite Volume(FV) framework,where the pressure equation and the rigid body motion equations are solved in a single linear system. The coupling is resolved by solving the rigid body motion equations once per linear solver iteration of the pressure equation, where updated pressure field is used to calculate new forces acting on the body, and by introducing the updated rigid body boundary velocity in to the pressure equation. In this paper the monolithic coupling is validated on a simple 2D heave decay case. Additionally, the method is compared to the traditional partitioned approach(i.e. "strongly coupled" approach) in terms of computational efficiency and accuracy. The comparison is performed on a seakeeping case in regular head waves, and it shows that the monolithic approach achieves similar accuracy with fewer nonlinear correctors per time–step. Hence, significant savings in computational time can be achieved while retaining the same level of accuracy.

Numerical Investigation of Heave and Pitch Motion Effects on Green Water Loading for a Floating Body

In this paper,the influence of heave and pitch motions on green water impact on the deck is numerically investigated.The vessel motions are determined using a potential theory based method and provided as input to finite volume based CFD computations of green water phenomenon.A dynamic mesh approach is adopted to determine instantaneous body positioning in the fluid domain.Detailed validation studies with published experimental results for 2D and 3D fixed vessel cases are initially performed to validate the present numerical approach before studying the moving vessel problem.The results show that inclusion of heave and pitch motion changes the disturbed wave field near the bow which influences the free surface as well as the impact loading due to green water.The effect of wave steepness on green water impact is also investigated and it is seen that the present numerical method is capable of capturing green water load.It is observed that the effects of vessel motions on green water load are not negligible and one should consider this effect too.The incorporation of vessel motions in the vertical plane affects the green water loading on the deck.

Spine Stereotactic Body Radiation Therapy Residual Setup Errors and Intra-Fraction Motion Using the Stereotactic X-Ray Image Guidance Verification System

Purpose: To determine the precision of our institution’s current immobilization devices for spine SBRT, ultimately leading to recommendations for appropriate planning margins. Methods: We identified 12 patients (25 treatments) with spinal metastasis treated with spine Stereotactic Body Radiation Therapy (SBRT). The Body-FIX system was used as immobilization device for thoracic (T) and lumbar (L) spine lesions. The head and shoulder mask system was used as immobilization device for cervical (C) spine lesions. Initial patient setup used the infrared positioning system with body markers. Stereotactic X-ray imaging was then performed and correction was made if the initial setup error exceeded predetermined institutional tolerances, 1.5 mm for translation and 2° for rotation. Three additional sets of verification X-rays were obtained pre-, mid-, and post-treatment for all treatments. Results: Intrafraction motion regardless of immobilization technique was found to be 1.28 ± 0.57 mm. The mean and standard deviation of the variances along each direction were as follows: Superior-inferior, 0.56 ± 0.39 mm and 0.77 ± 0.52 mm, (p = 0.25);Anterior-posterior, 0.57 ± 0.43 mm and 1.14 ± 0.61 mm, (p = 0.01);Left-right, 0.48 ± 0.34 mm and 0.74 ± 0.40 mm, (p = 0.09) respectively. There was a significantly greater difference in the average 3D variance of the BodyFIX as compared to the head and shoulder mask immobilization system, 1.04 ± 0.46 mm and 1.71 ± 0.52 mm;(p = 0.003) respectively. Conclusions: Overall, our institution’s image guidance system using stereotactic X-ray imaging verification provides acceptable localization accuracy as previously defined in the literature. We observed a greater intrafraction motion for the head and shoulder mask as compared with the BodyFIX immobilization system, which may be a result of greater C-spine mobility and/or the suboptimal mask immobilization. Thus, better immobilization techniques for C-spine SBRT are needed to reduce setup error and intrafraction motion. We are currently exploring alternative C-spine immobilization techniques to improve set up accuracy and decrease intrafraction motion during treatment.

ON UNILATERALLY CONSTRAINED MOTIONS OF RIGID BODIES SYSTEMS

In this paper , the unilaterally constrained motions of a large class of rigid bodiessystems are studied both locally and globally. The main conclusion is that locally,such a system bahaves like a particle in a Riemannian manifold with boundary;globally.under the assumption of energy conservation, the system behaves like a billiards system over a Riemannina manifold with boundary

Mathematical Modelling of Response Amplitude Operator for Roll Motion of a Floating Body：Analysis in Frequency Domain with Numerical Validation

This paper investigates mathematical modelling of response amplitude operator （RAO） or transfer function using the frequency-based analysis for uncoupled roll motion of a floating body under the influence of small amplitude regular waves. The hydrodynamic coefficients are computed using strip theory formulation by integrating over the length of the floating body. Considering sinusoidal wave with frequency （ω ） varying between 0.3 rad/s and 1.2 rad/s acts on beam to the floating body for zero forward speed, analytical expressions of RAO in frequency domain is obtained. Using the normalization procedure and frequency based analysis, group based classifications are obtained and accordingly governing equations are formulated for each case. After applying the fourth order Runge-Kutta method numerical solutions are obtained and relative importance of the hydrodynamic coefficients is analyzed. To illustrate the roll amplitude effects numerical experiments have been carried out for a Panamax container ship under the action of sinusoidal wave with a fixed wave height. The effect of viscous damping on RAO is evaluated and the model is validated using convergence, consistency and stability analysis. This modelling approach could be useful to model floating body dynamics for higher degrees of freedom and to validate the result.

A Robust Incremental Algorithm for Predicting the Motion of Rigid Body in a Time-Varying Environment

A configuration point consists of the position and orientation of a rigid body which are fully described by the position of the frame’s origin and the orientation of its axes, relative to the reference frame. We describe an algorithm to robustly predict futuristic configurations of a moving target in a time-varying environment. We use the Kalman filter for tracking and motion prediction purposes because it is a very effective and useful estimator. It implements a predictor-corrector type estimator that is optimal in the sense that it minimizes the estimated error covariance. The target motion is unconstrained. The proposed algorithm may be viewed as a seed for a range of applications, one of which is robot motion planning in a time-changing environment. A significant feature of the proposed algorithm (when compared to similar ones) is its ability to embark the prediction process from the first time step;no need to wait for few time steps as in the autoregressive-based systems. Simulation results supports our claims and demonstrate the superiority of the proposed model.

面向大范围手势捕捉的Leap Motion数据结构体优化

无标记人手和虚拟环境交互是实现沉浸式虚拟装配的关键,多Leap Motion数据融合是扩展捕捉范围的有效途径。然而,多Leap Motion系统的数据量冗杂,增加了基于局域网传输的网络负荷,使得手势反应迟滞,影响了沉浸感和装配效率。建立了Leap Motion数据结构体优化模型,获得了各类数据的权重,提出了优化方案,优化后数据量降低了36%,针对5个Leap Motion系统进行测试。结果表明:优化后系统的数据传输速度和融合效果得到大幅提升,满足了多Leap Motion实时手工装配的需求。

Experimental Study of Nonlinear Behaviors of A Free-Floating Body in Waves

Nonlinear behaviors of a free-floating body in waves were experimentally investigated in the present study. The experiments were carried out for 6 different wave heights and 6 different wave periods to cover a relatively wide range of wave nonlinearities. A charge-coupled device （CCD） camera was used to capture the real-time motion of the floating body. The measurement data show that the sway, heave and roll motions of the floating body are all harmonic oscillations while the equilibrium position of the sway motion drifts in the wave direction. The drift speed is proportional to wave steepness when the size of the floating body is comparable to the wavelength, while it is proportional to the square of wave steepness when the floating body is relatively small. In addition, the drift motion leads to a slightly longer oscillation period of the floating body than the wave period of nonlinear wave and the discrepancy increases with the increment of wave steepness.

Modeling and Motion Simulation for A Flying-Wing Underwater Glider with A Symmetrical Airfoil

The flying-wing underwater glider (UG), shaped as a blended wing body, is a new type of underwater vehicle and still requires further research. The shape layout and the configuration of the internal actuators of the flying-wing UG are different from those of "legacy gliders" which have revolving bodies, and these two factors strongly affect the dynamic performance of the vehicle. Considering these differences, we propose a new configuration of the internal actuators for the flying-wing UG and treat the flying-wing UG as a multi-body system when establishing its dynamic model. In this paper, a detailed dynamic model is presented using the Newton-Euler method for the flying-wing UG. Based on the full dynamic model, the effect of the internal actuators on the steady gliding motion of vehicle is studied theoretically, and the relationship between the state parameters of the steady gliding motion and the controlled variables is obtained by solving a set of equilibrium equations. Finally, the behaviors of two classical motion modes of the glider are analyzed based on the simulation. The simulation results demonstrate that the motion performance of the proposed flying-wing UG is satisfactory.

Bionic Attitude Transformation Combined with Closed Motion for a Free Floating Space Robot

In order to realize the small error attitude transformation of a free floating space robot,a new method of three degrees of freedom（ DOF） attitude transformation was proposed for the space robot using a bionic joint. A general kinematic model of the space robot was established based on the law of linear and angular momentum conservation. A combinational joint model was established combined with bionic joint and closed motion. The attitude transformation of planar,two DOF and three DOF is analyzed and simulated by the model,and it is verified that the feasibility of attitude transformation in three DOF space. Finally,the specific scheme of disturbance elimination in attitude transformation is presented and simulation results are obtained.Therefore,the range of application field of the bionic joint model has been expanded.

Motion visualization and estimation for flapping wing systems

Studies of fluid-structure interactions associated with flexible structures such as flapping wings require the capture and quantification of large motions of bodies that may be opaque. As a case study, motion capture of a free flying Manduca sexta, also known as hawkmoth, is considered by using three synchronized high-speed cameras. A solid finite element (FE) representation is used as a reference body and successive snapshots in time of the displacement fields are reconstructed via an optimization procedure. One of the original aspects of this work is the formulation of an objective function and the use of shadow matching and strain-energy regularization. With this objective function, the authors penalize the projection differences between silhouettes of the captured images and the FE representation of the deformed body. The process and procedures undertaken to go from high-speed videography to motion estimation are discussed, and snapshots of representative results are presented. Finally, the captured free-flight motion is also characterized and quantified.

Lung Stereotactic Body Radiotherapy Using an Abdominal Compression System, “Air-Bag System”

We investigated respiratory tumor motion in lung stereotactic body radiotherapy (SBRT) with use of the “Air-Bag System”. 114 patients underwent four-dimensional (4D) computed tomography (CT) from October 2010 to April 2012. Gross tumor volume (GTV) was 8.1 ± 11.0 cc (range 0.3 - 77.5 cc). The tumor site was the upper and middle lobes in 62 cases, and lower lobe in 52 cases. The Air-Bag SystemTM consists of an inelastic air bag connected to a second smaller elastic air bag. The inelastic air bag is placed between the patient’s body surface and a HipFix and is secured by pressure adjustment via the elastic air bag. To assess respiratory tumor motion, the centroid of the tumor position is measured in the left-right, anterior-posterior, and caudal-cranial directions using the iPlan RT DoseTM treatment planning system. Respiratory tumor motion vector for patients with upper/middle and lower lobe tumors was 3.0 ± 2.2 mm (range, 0.4 - 11.7 mm) and 6.5 ± 4.6 mm (range, 0.4 - 22.0 mm) respectively, with this difference being significant (p < 0.05). Mean respiratory tumor motion for all patients was 0.9 ± 0.6 mm (range, 0.1 - 3.6 mm) in the left-right direction, 1.5 ± 1.1 mm (range, 0.1 - 5.7 mm) in the anterior-posterior direction, 4.1 ± 4.0 mm (range, 0.1 - 21.4 mm) in the caudal-cranial direction, and 4.7 ± 4.0 mm (range, 0.4 - 22.0 mm) overall. The Air-Bag System is expected to be provided an effective reduction in the motion of lung tumors.

Amended influence matrix method for removal of rigid motion in the interior BVP for plane elasticity

A conventional complex variable boundary integral equation （CVBIE） in plane elasticity is provided. After using the Somigliana identity between a particular fundamental stress field and a physical stress field, an additional integral equality is obtained. By adding both sides of this integral equality to both sides of the conventional CVBIE, the amended boundary integral equation （BIE） is obtained. The method based on the discretization of the amended BIE is called the amended influence matrix method. With this method, for the Neumann boundary value problem （BVP） of an interior region, a unique solution for the displacement can be obtained. Several numerical examples are provided to prove the efficiency of the suggested method.

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.

Motion estimation of elastic articulated objects from image contours

A new method of elastic articulated objects (human bodies) modeling was presented based on a new conic curve. The model includes 3D object deformable curves which can represent the deformation of human occluding contours. The deformation of human occluding contour can be represented by adjusting only four deformation parameters for each limb. Then, the 3D deformation parameters are determined by corresponding 2D contours from a sequence of stereo images. The algorithm presented in this paper includes deformable conic curve parameters determination and the plane, 3D conic curve lying on, parameter determination.