Second-order Motion Research Articles

Fiddler crabs (Afruca tangeri) detect second-order motion in both intensity and polarization

Motion vision is vital for a wide range of animal behaviors. Fiddler crabs, for example, rely heavily on motion to detect the movement of avian predators. They are known to detect first-order motion using both intensity (defined by spatiotemporal correlations in luminance) and polarization information (defined separately as spatiotemporal correlations in the degree and/or angle of polarization). However, little is known about their ability to detect second-order motion, another important form of motion information; defined separately by spatiotemporal correlations in higher-order image properties. In this work we used behavioral experiments to test how fiddler crabs (Afruca tangeri) responded to both second-order intensity and polarization stimuli. Fiddler crabs responded to a number of different intensity based second-order stimuli. Furthermore, the crabs also responded to second-order polarization stimuli, a behaviorally relevant stimulus applicable to an unpolarized flying bird when viewed against a polarized sky. The detection of second-order motion in polarization is, to the best of our knowledge, the first demonstration of this ability in any animal. This discovery therefore opens a new dimension in our understanding of how animals use polarization vision for target detection and the broader importance of second-order motion detection for animal behavior.

In vivo cardiac diffusion tensor imaging on an MR system featuring ultrahigh performance gradients with 200 mT/m maximum gradient strength.

Our aim is to assess the potential of an MR system with ultrahigh performance gradients (200 mT/m maximum gradient strength) to address two interrelated challenges in cardiac DTI: low SNR and sensitivity to bulk motion. Imaging was performed in 20 healthy volunteers, two patients, and one swine post-myocardial infarction. The impact of maximum gradient strength was assessed with spin echo cardiac DTI featuring second-order motion compensation and varying maximum system gradient strengths (40, 80, 200 mT/m). Motion compensation requirements at 200 mT/m were assessed with sequences featuring zeroth-, first-, and second-order motion compensation. SNR, mean diffusivity, fractional anisotropy, helix angle transmurality, and secondary eigenvector angle in the left ventricle were compared. Increasing maximum system gradient strength from 40 and 80 mT/m to 200 mT/m increased SNR of b = 500 s/mm2 images by 150% and 40% due to reductions in TE. Observed improvements in DTI metrics included reduction in variance in mean diffusivity and helix angle transmurality across healthy volunteers, improved visualization of myocardial borders and delineation of suspected scar. Whereas second-order motion compensation acquisitions were robust to motion-induced signal dropout, zeroth- and first-order motion compensation acquisitions suffered from severe signal loss and localized signal voids, respectively. Ultrahigh performance gradients (200 mT/m) enable high SNR DWIs of the heart and resultant improvements in diffusion tensor metrics. Despite reduced diffusion-encoding duration, second-order motion compensation is required to overcome sensitivity to cardiac motion.

Acquisition of second-order motion perception by learning to recognize the motion of objects made by non-diffusive materials

Acquisition of second-order motion perception by learning to recognize the motion of objects made by non-diffusive materials

Investigation of Low-Frequency Pitch Motion Characteristics for KRISO Standard Offshore Structure (K-Semi) Moored with a Truncation Mooring System

In this study, a model test was carried out to evaluate the station-keeping performance of Korea Research Institute of the Ships and Ocean Engineering (KRISO) standard semi-submersible, K-Semi in the Deep Ocean Engineering Basin (DOEB). The test was performed using a 1/50 scaled model with 12 mooring lines. The water depth was set to 3.2 m using a moveable bottom structure and truncated mooring lines. The dynamic behavior of the K-Semi was examined using a free decay test and regular wave as well as irregular wave tests of 1800. Large surge, heave and pitch due to drift motion from second-order effect were observed. The reason for the excessive low-frequency pitch motion is attributed to the restoring force and moment related to the mooring system as excessive surge occurred. The numerical model of K-Semi with the truncated mooring system was tuned and calibrated using model test results such as free decay and regular wave tests. Through numerical analysis, the motion characteristics of the K-Semi were compared with irregular model test results. In the case of a semi-submersible using a mooring system, it is observed that excessive pitch motion due to vertical restoring force and moment may occur when large horizontal displacement occurs. The effect of low-frequency pitch motion related to surge motion is an important factor in upwell estimation as well as second-order motion in referred DNV-GL OTG13.

The effect of impaired velocity signals on goal-directed eye and hand movements

Information about position and velocity is essential to predict where moving targets will be in the future, and to accurately move towards them. But how are the two signals combined over time to complete goal-directed movements? We show that when velocity information is impaired due to using second-order motion stimuli, saccades directed towards moving targets land at positions where targets were ~ 100 ms before saccade initiation, but hand movements are accurate. Importantly, the longer latencies of hand movements allow for additional time to process the sensory information available. When increasing the period of time one sees the moving target before making the saccade, saccades become accurate. In line with that, hand movements with short latencies show higher curvature, indicating corrections based on an update of incoming sensory information. These results suggest that movements are controlled by an independent and evolving combination of sensory information about the target’s position and velocity.

Zebrafish optomotor response to second-order motion illustrates that age-related changes in motion detection depend on the activated motion system

Various aspects of visual functioning, including motion perception, change with age. Yet, there is a lack of comprehensive understanding of age-related alterations at different stages of motion processing and in each motion system. To understand the effects of aging on second-order motion processing, we investigated optomotor responses (OMR) in younger and older wild-type (AB-strain) and acetylcholinesterase (achesb55/+) mutant zebrafish. The mutant fish with decreased levels of acetylcholinesterase have been shown to have delayed age-related cognitive decline. Compared to previous results on first-order motion, we found distinct changes in OMR to second-order motion. The polarity of OMR was dependent on age, such that second-order stimulation led to mainly negative OMR in the younger group while older zebrafish had positive responses. Hence, these findings revealed an overall aging effect on the detection of second-order motion. Moreover, neither the genotype of zebrafish nor the spatial frequency of motion significantly changed the response magnitude. Our findings support the view that age-related changes in motion detection depend on the activated motion system.

Cardiac q-space trajectory imaging by motion-compensated tensor-valued diffusion encoding in human heart in vivo.

Tensor-valued diffusion encoding can probe more specific features of tissue microstructure than what is available by conventional diffusion weighting. In this work, we investigate the technical feasibility of tensor-valued diffusion encoding at high b-values with q-space trajectory imaging (QTI) analysis, in the human heart in vivo. Ten healthy volunteers were scanned on a 3T scanner. We designed time-optimal gradient waveforms for tensor-valued diffusion encoding (linear and planar) with second-order motion compensation. Data were analyzed with QTI. Normal values and repeatability were investigated for the mean diffusivity (MD), fractional anisotropy (FA), microscopic FA (μFA), isotropic, anisotropic and total mean kurtosis (MKi, MKa, and MKt), and orientation coherence (Cc ). A phantom, consisting of two fiber blocks at adjustable angles, was used to evaluate sensitivity of parameters to orientation dispersion and diffusion time. QTI data in the left ventricular myocardium were MD=1.62 ± 0.07 μm2 /ms, FA=0.31 ± 0.03, μFA=0.43 ± 0.07, MKa=0.20 ± 0.07, MKi=0.13 ± 0.03, MKt=0.33 ± 0.09, and Cc =0.56 ± 0.22 (mean ± SD across subjects). Phantom experiments showed that FA depends on orientation dispersion, whereas μFA was insensitive to this effect. We demonstrated the first tensor-valued diffusion encoding and QTI analysis in the heart in vivo, along with first measurements of myocardial μFA, MKi, MKa, and Cc . The methodology is technically feasible and provides promising novel biomarkers for myocardial tissue characterization.

Second-order approximation pseudo-rigid model of circular arc flexure hinge

The paper presents a novel pseudo-rigid model for describing the elasto-kinematic behaviour of circular arc flexure hinge subjected to a pure moment. The model is based on the kinematic study of flexure hinge large deflection using second-order motion invariants (polodes and inflection circle), which accurately describes the relative motion between the connected bodies. The proposed pseudo-rigid model has a single degree of freedom. It is an epicyclic arrangement with two rolling without slipping external circles with the same radius and a torsional spring with constant stiffness. Analytical formulas for computing the radius and the location of the two rolling circles and the rotational spring stiffness are deduced. The proposed model has been compared with analytical formulas and structural finite element models in different configurations. The results show very good accordance even for large deflections, confirming the model's effectiveness.

Transient Stability of Hybrid Power Systems Dominated by Different Types of Grid-Forming Devices

This paper investigates the transient stability of power systems co-dominated by different types of grid-forming (GFM) devices. Synchronous generators (SGs and VSGs) and droop-controlled inverters are typical GFM devices in modern power systems. SGs/VSGs are able to provide inertia while droop-controlled inverters are generally inertialess. The transient stability of power systems dominated by homogeneous GFM devices has been extensively studied. Regarding the hybrid system jointly dominated by heterogeneous GFM devices, the transient stability is rarely reported. This paper aims to fill this gap. It is found that the synchronization behavior of the hybrid system can be described by a second-order motion equation, resembling the swing equation of SGs. Moreover, two significant differences from conventional power systems are discovered. The first is that the droop control dramatically enhances the damping effect, greatly affecting the transient stability region. The second is that the frequency state variable exhibits a jump at the moment of fault disturbances, thus impacting the post-fault initial-state location and stability assessment. The underlying mechanism behind the two new characteristics is clarified and the impact on the transient stability performance is analyzed and verified. The findings provide new insights into transient stability of power systems hosting heterogeneous devices.

Robust Tracking Control for Electrohydraulic System Using an Internal Model-Based Sliding Surface

Abstract An electrohydraulic system, which is widely applied in practice, is a highly nonlinear system with uncertainty. In order to improve the control performance, the nonlinearity and uncertainty should be taken into consideration. In this context, a lot of researches have been carried out, and most of them need the derivatives of the tracking error to construct their controllers. However, the accurate values of the derivatives are difficult to be obtained in practice. What's more, without considering the characteristics of the reference signal, the direct applications of these control methods in the periodic motion tracking problem of electrohydraulic systems are difficult to achieve satisfactory control performances. Therefore, a novel internal model principle (IMP)-based sliding mode control (SMC) is proposed in the paper. First, an ideal driving force for the second-order piston motion dynamics is designed based on the IMP with the measurement of piston position. And then, the deviation between the ideal and measured driving force is selected as the sliding mode variable. At last, the SMC is formed to guarantee the actual driving force can converge to the ideal one in finite time. As the main contribution of this paper, the proposed IMP-based SMC does not need the derivatives of the tracking error and can achieve a better performance by eliminating the reference frequency related component in the tracking error. To verify the control performance of the proposed method, a 20 Hz sinusoidal reference tracking scenario is considered, and the finite-time exact differentiator (FTD)-based SMC and the FTD-based high-order SMC (HOSMC) are selected as comparison methods. A group of simulations are performed on an electrohydraulic system used in the controlled trajectory rapid compression and expansion machine (CT-RCEM). The simulation results show that the 20 Hz component in the tracking error is eliminated under the proposed controller, but the 20 Hz error components are still remaining as 2.58 mm and 0.64 mm under the FTD-based SMC and the FTD-based HOSMC, respectively.

Temperature measurement of intracranial cerebrospinal fluid using second-order motion compensation diffusion tensor imaging

To reduce the determination errors of CSF pulsation in diffusion-weighted image (DWI) thermometry, we investigated whether applying second-order motion compensation diffusion tensor imaging (2nd-MC DTI) and fractional anisotropy (FA) processing improves the measurement of intracranial cerebrospinal fluid (CSF) temperature. In a phantom study, we investigated the relationship between temperature and FA in artificial CSF (ACSF) to determine the threshold for FA processing. The calculated temperatures of ACSF were compared with those of water. In a human study, 18 healthy volunteers were scanned using conventional DTI (c-DTI) and 2nd-MC DTI on a 3.0 T magnetic resonance imaging (MRI) system. A temperature map was created using diffusion coefficients from each DWI with/without FA processing. The temperatures of intracranial CSF were compared between each DTI image using Welch’s analysis of variance and Games–Howell’s multiple comparisons. In the phantom study, FA did not exceed 0.1 at any temperature. Consequently, pixels exceeding the threshold of 0.1 were removed from the temperature map. Intracranial CSF temperatures significantly differed between the four methods (p < 0.0001). The lowest temperature was 2nd-MC DTI with FA processing (mean, 35.62 °C), followed in order by c-DTI with FA processing (mean, 36.16 °C), 2nd-MC DTI (mean, 37.08 °C), and c-DTI (mean, 39.08 °C; p < 0.01 for each). Because the calculated temperature of ACSF was estimated to be lower than that of water, the temperature of 2nd-DTI with FA processing was considered reasonable. The method of 2nd-MC DTI with FA processing enabled determining intracranial CSF temperature with a reduction in CSF pulsation.

Influence of mental workload on motion perception: A direct comparison of luminance-based and contrast-based stimuli

In order to study the impact of increased mental workload on motion detection, twenty-four observers performed a motion discrimination task in which they had to detect odd moving patches. Two types of moving patches were used, namely luminance-based and contrast-based patches. For both types of patches, the motion discrimination task was performed with and without an additional N-Back task aimed at increasing the mental workload. The dual task decreased discrimination performance for both types of patches, but the difference was significantly larger for contrast-based patches, i.e., for second-order motion stimuli, both as an absolute and relative increment. This suggests that motion discrimination requires larger cognitive resources for contrast-based than for luminance-based stimuli, thereby hinting at the higher complexity of the cognitive mechanisms underlying second-order motion detection.

Nonlinear dynamics of a floating offshore wind turbine platform via statistical quadratization — Mooring, wave and current interaction

This paper applies the method of statistical quadratization to investigate the first and second-order responses of a floating offshore wind turbine platform due to forces from a catenary mooring system, and wave–current coupled interaction. The hydrodynamics are based on the generalized Morison’s equation, while the catenary mooring system is based on a quasi-static approach. The method of statistical quadratization replaces the nonlinearities using equivalent linear and quadratic terms by minimizing the difference between the nonlinear model and the approximated model in a mean-square sense. In this regard, an iterative scheme is applied, in which the equivalent polynomial coefficients are calculated based on the non-Gaussian distribution generated by means of Gram–Charlier expansions. The dynamics are solved using the Volterra theory, and described in terms of transfer functions, which can be directly integrated into the central moments of the distribution. The results demonstrate an excellent agreement with nonlinear time-domain simulations in terms of spectral response and probability distribution. Sensitivity studies are performed to show the contribution of the second-order motion over several environmental conditions. Despite the excellent accuracy, the main advantage of the statistical quadratization is the low computational cost, which is approximately two orders of magnitude faster than nonlinear time-domain simulations.

Nonlinear hydrodynamics of freely floating symmetric bodies in waves by three-dimensional fully nonlinear potential-flow numerical wave tank

This study estimated the nonlinear hydrodynamic performance of freely floating structures in nonlinear water waves. For this, a three-dimensional, fully nonlinear numerical wave tank (NWT) was developed based on potential theory and the boundary element method (BEM). The fully nonlinear NWT evaluates the hydrodynamic force acting on the instantaneous body position and free-surface elevation based on the mixed Eulerian and Lagrangian (MEL) method and acceleration-potential approach. The instantaneous nonlinear free surface was traced at each time step, and the far-field outgoing wave condition was satisfied by placing an artificial free-surface damping zone. In addition, the least square gradient reconstruction method, thin-plate spline method, and modified inverse distance weighting method were adopted to re-grid the calculation nodes and evaluate the spatial derivatives of the physical quantities robustly. The developed NWT was used to evaluate the first-order and second-order motion RAOs and excitation forces of a freely floating vertical cylinder. The results were compared systematically with previously published results using perturbation theory. Moreover, the heave-to-pitch Mathieu-instability phenomena on a deep-draft floating cylinder were demonstrated by the fully nonlinear NWT simulations. The results agreed well with the corresponding experimental observations.

Effects of smooth pursuit and second-order stimuli on visual motion prediction.

The purpose of this study was to determine whether smooth pursuit eye movements affect visual motion prediction using a time‐to‐contact task where observers anticipate the exact instant that a partially occluded target would coincide with a stationary object. Moreover, we attempted to clarify the influence of second‐order motion on visual motion prediction during smooth pursuit. One target object moved to another stationary object (6 deg apart) at constant velocity of 3, 4, and 5 deg/s, and then the two objects disappeared 500 ms after the onset of target motion. The observers estimated the moment the moving object would overlap the stationary object and pressed a button. For the pursuit condition, both a Gaussian window and a random dots texture moved in the same direction at the same speed for the first‐order motion, whereas a Gaussian window moved over a static background composed of random dots texture for the second‐order motion. The results showed that the constant error of the time‐to‐contact shifted to a later response for the pursuit condition compared to the fixation condition, regardless of the object velocity. In addition, during smooth pursuit, the constant error for the second‐order motion shifted to an earlier response compared to the first‐order motion when the object velocity was 3 deg/s, whereas no significant difference was found at 4 and 5 deg/s. Therefore, our results suggest that visual motion prediction using a time‐to‐contact task is affected by both eye movements and motion configuration such as second‐order motion.

Motion characteristics of a barge-type floating vertical-axis wind turbine with moonpools

The studies on floating offshore wind turbines have been increasing over recent decades due to the growing investments of industries in marine renewable energy. Compared with horizontal-axis wind turbines, research on vertical-axis wind turbines is relatively few, though the latter may have advantages over the former in some aspects, for example, potentially lower cost of energy. In this paper, the characteristics of the motion responses of a barge-type floating system with four moonpools and a vertical-axis wind turbine are experimentally and numerically investigated. The focus is on the gyroscopic effects of turbine rotations on the motion responses of the floating system under different wave conditions. Physical model tests are conducted in a wave tank, where a 2-MW-class turbine is modelled in the 1:100 scale. It is found that the first-order sway and roll motion amplitudes near the resonant frequencies are reduced by the turbine rotations, whereas the first-order heave motion of the floating system is hardly influenced. The second-order motion responses and mooring tether tensions may be significantly amplified with the increasing rotating speed of turbine. The maximum ratio of the second-order response amplitude of roll motion to the first-order roll amplitude is up to 17% in the experiments of this study. A radiation and diffraction code based on linear potential flow theory is used to predict the motion responses and mooring forces. The comparisons with experimental data suggest that the viscous damping of water resonance in moonpools and the gyroscopic effects of turbine rotations should be taken into account in predictions.

Adaptively Robust Control Policy Synthesis Through Riemannian Motion Policies

Riemannian Motion Policies (RMPs) have recently been introduced as an online motion planning and policy synthesis framework that designs second-order motion policies defined on robot task spaces, and combines them into one global policy trading off between various motion objectives. Until now RMPs have only been applied either through direct joint-space acceleration control or inverse dynamics control assuming perfect knowledge of the system dynamics. It is unclear how RMPs can be implemented in the presence of dynamics modeling uncertainty and external disturbance. We address this by augmenting the existing RMP framework with a novel robust control Lyapunov function (RCLF) based inverse dynamics controller. This combination produces a fast, reactive, online motion planning and control framework that is also robust to system dynamics parameter uncertainty and external disturbance. We also propose a robust gain adaptation law that can automatically compensate for parameter uncertainty and external disturbance. We provide stability guarantees for the proposed RCLF controller with the gain adaptation law. Additionally, performance of the combined RMP-RCLF system is demonstrated on a 7-degree of freedom (DoF) robot manipulator arm in simulation.

Properties of smooth pursuit and visual motion reaction time to second-order motion stimuli.

A large number of psychophysical and neurophysiological studies have demonstrated that smooth pursuit eye movements are tightly related to visual motion perception. This could be due to the fact that visual motion sensitive cortical areas such as meddle temporal (MT), medial superior temporal (MST) areas are involved in motion perception as well as pursuit initiation. Although the directional-discrimination and perceived target velocity tasks are used to evaluate visual motion perception, it is still uncertain whether the speed of visual motion perception, which is determined by visuomotor reaction time (RT) to a small target, is related to pursuit initiation. Therefore, we attempted to determine the relationship between pursuit latency/acceleration and the visual motion RT which was measured to the visual motion stimuli that moved leftward or rightward. The participants were instructed to fixate on a stationary target and press one of the buttons corresponding to the direction of target motion as soon as possible once the target starts to move. We applied five different visual motion stimuli including first- and second-order motion for smooth pursuit and visual motion RT tasks. It is well known that second-order motion induces lower retinal image motion, which elicits weaker responses in MT and MST compared to first-order motion stimuli. Our results showed that pursuit initiation including latency and initial eye acceleration were suppressed by second-order motion. In addition, second-order motion caused a delay in visual motion RT. The better performances in both pursuit initiation and visual motion RT were observed for first-order motion, whereas second-order (theta motion) induced remarkable deficits in both variables. Furthermore, significant Pearson’s correlation and within-subjects correlation coefficients were obtained between visual motion RT and pursuit latency/acceleration. Our findings support the suggestion that there is a common neuronal pathway involved in both pursuit initiation and the speed of visual motion perception.

Free-breathing diffusion tensor MRI of the whole left ventricle using second-order motion compensation and multitasking respiratory motion correction.

We aimed to develop a novel free-breathing cardiac diffusion tensor MRI (DT-MRI) approach, M2-MT-MOCO, capable of whole left ventricular coverage that leverages second-order motion compensation (M2) diffusion encoding and multitasking (MT) framework to efficiently correct for respiratory motion (MOCO). Imaging was performed in 16 healthy volunteers and 3 heart failure patients with symptomatic dyspnea. The healthy volunteers were scanned to compare the accuracy of interleaved multislice coverage of the entire left ventricle with a single-slice acquisition and the accuracy of the free-breathing conventional MOCO and MT-MOCO approaches with reference breath-hold DT-MRI. Mean diffusivity (MD), fractional anisotropy (FA), helix angle transmurality (HAT), and intrascan repeatability were quantified and compared. In all subjects, free-breathing M2-MT-MOCO DT-MRI yielded DWI of the entire left ventricle without bulk motion-induced signal loss. No significant differences were seen in the global values of MD, FA, and HAT in the multislice and single-slice acquisitions. Furthermore, global quantification of MD, FA, and HAT were also not significantly different between the MT-MOCO and breath-hold, whereas conventional MOCO yielded significant differences in MD, FA, and HAT with MT-MOCO and FA with breath-hold. In heart failure patients, M2-MT-MOCO DT-MRI was feasible yielding higher MD, lower FA, and lower HAT compared with healthy volunteers. Substantial agreement was found between repeated scans across all subjects for MT-MOCO. M2-MT-MOCO enables free-breathing DT-MRI of the entire left ventricle in 10 min, while preserving quantification of myocardial microstructure compared to breath-held and single-slice acquisitions and is feasible in heart failure patients.

Second-order motion descriptors for efficient action recognition

Human action recognition from realistic video data constitutes a challenging and relevant research area. Leading the state of the art we can find those methods based on convolutional neural networks (CNNs), and specially two-stream CNNs. In this family of deep architectures, the appearance channel learns from the RGB images and the motion channel learns from a motion representation, usually, the optical flow. Given that action recognition requires the extraction of complex motion patterns descriptors in image sequences, we introduce a new set of second-order motion representations capable of capturing both: geometrical and kinematic properties of the motion (curl, div, curvature, and acceleration). Besides, we present a new and effective strategy capable of reducing training times without sacrificing the performance when using the I3D two-stream CNN and robust to the weakness of a single channel. The experiments presented in this paper were carried out over two of the most challenging datasets for action recognition: UCF101 and HMDB51. Reported results show an improvement in accuracy over the UCF101 dataset where an accuracy of 98.45% is achieved when the curvature and acceleration are combined as a motion representation. For the HMDB51, our approach shows a competitive performance, achieving an accuracy of 80.19%. In both datasets, our approach shows a considerable reduction in time for the preprocessing and training phases. Preprocessing time is reduced to a sixth of the time while the training procedure for the motion stream can be performed in a third of the time usually employed.