Singularities of optimal control problems on some 6-D lie groups

This paper considers the motion planning problem for oriented vehicles travelling at unit speed in a 3-D space. A Lie group formulation arises naturally and the vehicles are modeled as kinematic control systems with drift defined on the orthonormal frame bundles of particular Riemannian manifolds, specifically, the 3-D space forms Euclidean space E-3, the sphere S-3, and the hyperboloid H'. The corresponding frame bundles are equal to the Euclidean group of motions SE(3), the rotation group SO(4), and the Lorentz group SO (1, 3). The maximum principle of optimal control shifts the emphasis for these systems to the associated Hamiltonian formalism. For an integrable case, the extremal curves are explicitly expressed in terms of elliptic functions. In this paper, a study at the singularities of the extremal curves are given, which correspond to critical points of these elliptic functions. The extremal curves are characterized as the intersections of invariant surfaces and are illustrated graphically at the singular points. It. is then shown that the projections, of the extremals onto the base space, called elastica, at these singular points, are curves of constant curvature and torsion, which in turn implies that the oriented vehicles trace helices.

Tracking and mean structure of easterly waves over the Intra-Americas Sea

Easterly waves (EWs) are prominent features of the intertropical convergence zone (ITCZ), found in both the Atlantic and Pacific during the Northern Hemisphere summer and fall, where they commonly serve as precursors to hurricanes over both basins.Alarge proportion of Atlantic EWs are known to form over Africa, but the origin of EWs over the Caribbean and east Pacific in particular has not been established in detail. In this study reanalyses are used to examine the coherence of the large-scale wave signatures and to obtain track statistics and energy conversion terms for EWs across this region. Regression analysis demonstrates that some EW kinematic structures readily propagate between the Atlantic and east Pacific, with the highest correlations observed across Costa Rica and Panama. Track statistics are consistent with this analysis and suggest that some individual waves are maintained as they pass from the Atlantic into the east Pacific, whereas others are generated locally in the Caribbean and east Pacific. Vortex anomalies associated with the waves are observed on the leeward side of the Sierra Madre, propagating northwestward along the coast, consistent with previous modeling studies of the interactions between zonal flow and EWs with model topography similar to the Sierra Madre. An energetics analysis additionally indicates that the Caribbean low-level jet and its extension into the east Pacific—known as the Papagayo jet—are a source of energy for EWs in the region. Two case studies support these statistics, as well as demonstrate the modulation of EW track and storm development location by the MJO.

On the structure of Langmuir turbulence

The Stokes drift induced by surface waves distorts turbulence in the wind-driven mixed layer of the ocean, leading to the development of streamwise vortices, or Langmuir circulations, on a wide range of scales. We investigate the structure of the resulting Langmuir turbulence, and contrast it with the structure of shear turbulence, using rapid distortion theory (RDT) and kinematic simulation of turbulence. Firstly, these linear models show clearly why elongated streamwise vortices are produced in Langmuir turbulence, when Stokes drift tilts and stretches vertical vorticity into horizontal vorticity, whereas elongated streaky structures in streamwise velocity fluctuations (u) are produced in shear turbulence, because there is a cancellation in the streamwise vorticity equation and instead it is vertical vorticity that is amplified. Secondly, we develop scaling arguments, illustrated by analysing data from LES, that indicate that Langmuir turbulence is generated when the deformation of the turbulence by mean shear is much weaker than the deformation by the Stokes drift. These scalings motivate a quantitative RDT model of Langmuir turbulence that accounts for deformation of turbulence by Stokes drift and blocking by the air–sea interface that is shown to yield profiles of the velocity variances in good agreement with LES. The physical picture that emerges, at least in the LES, is as follows. Early in the life cycle of a Langmuir eddy initial turbulent disturbances of vertical vorticity are amplified algebraically by the Stokes drift into elongated streamwise vortices, the Langmuir eddies. The turbulence is thus in a near two-component state, with suppressed and . Near the surface, over a depth of order the integral length scale of the turbulence, the vertical velocity (w) is brought to zero by blocking of the air–sea interface. Since the turbulence is nearly two-component, this vertical energy is transferred into the spanwise fluctuations, considerably enhancing at the interface. After a time of order half the eddy decorrelation time the nonlinear processes, such as distortion by the strain field of the surrounding eddies, arrest the deformation and the Langmuir eddy decays. Presumably, Langmuir turbulence then consists of a statistically steady state of such Langmuir eddies. The analysis then provides a dynamical connection between the flow structures in LES of Langmuir turbulence and the dominant balance between Stokes production and dissipation in the turbulent kinetic energy budget, found by previous authors.

Complete robot-eye calibration without special calibration objects

A robot mounted camera is useful in many machine vision tasks as it allows control over view direction and position. In this paper we report a technique for calibrating both the robot and the camera using only a single corresponding point. All existing head-eye calibration systems we have encountered rely on using pre-calibrated robots, pre- calibrated cameras, special calibration objects or combinations of these. Our method avoids using large scale non-linear optimizations by recovering the parameters in small dependent groups. This is done by performing a series of planned, but initially uncalibrated robot movements. Many of the kinematic parameters are obtained using only camera views in which the calibration feature is at, or near the image center, thus avoiding errors which could be introduced by lens distortion. The calibration is shown to be both stable and accurate. The robotic system we use consists of camera with pan-tilt capability mounted on a Cartesian robot, providing a total of 5 degrees of freedom.

Initiation of deep convection at marginal instability in an ensemble of mesoscale models: a case-study from COPS

The present study investigates the initiation of precipitating deep convection in an ensemble of convection-resolving mesoscale models. Results of eight different model runs from five non-hydrostatic models are compared for a case of the Convective and Orographically-induced Precipitation Study (COPS). An isolated convective cell initiated east of the Black Forest crest in southwest Germany, although convective available potential energy was only moderate and convective inhibition was high. Measurements revealed that, due to the absence of synoptic forcing, convection was initiated by local processes related to the orography. In particular, the lifting by low-level convergence in the planetary boundary layer is assumed to be the dominant process on that day. The models used different configurations as well as different initial and boundary conditions. By comparing the different model performance with each other and with measurements, the processes which need to be well represented to initiate convection at the right place and time are discussed. Besides an accurate specification of the thermodynamic and kinematic fields, the results highlight the role of boundary-layer convergence features for quantitative precipitation forecasts in mountainous terrain.

Action observation and robotic agents: learning and anthropomorphism

The ‘action observation network’ (AON), which is thought to translate observed actions into motor codes required for their execution, is biologically tuned: it responds more to observation of human, than non-human, movement. This biological specificity has been taken to support the hypothesis that the AON underlies various social functions, such as theory of mind and action understanding, and that, when it is active during observation of non-human agents like humanoid robots, it is a sign of ascription of human mental states to these agents. This review will outline evidence for biological tuning in the AON, examining the features which generate it, and concluding that there is evidence for tuning to both the form and kinematic profile of observed movements, and little evidence for tuning to belief about stimulus identity. It will propose that a likely reason for biological tuning is that human actions, relative to non-biological movements, have been observed more frequently while executing corresponding actions. If the associative hypothesis of the AON is correct, and the network indeed supports social functioning, sensorimotor experience with non-human agents may help us to predict, and therefore interpret, their movements.

Effects of utterance length on lip kinematics in aphasia

Most existing models of language production and speech motor control do not explicitly address how language requirements affect speech motor functions, as these domains are usually treated as separate and independent from one another. This investigation compared lip movements during bilabial closure between five individuals with mild aphasia and five age and gender-matched control speakers when the linguistic characteristics of the stimuli were varied by increasing the number of syllables. Upper and lower lip movement data were collected for mono-, bi- and tri-syllabic nonword sequences using an AG 100 EMMA system. Each task was performed under both normal and fast rate conditions. Single articulator kinematic parameters (peak velocity, amplitude, duration,and cyclic spatio-temporal index) were measured to characterize lip movements. Results revealed that compared to control speakers, individuals with aphasia showed significantly longer movement duration and lower movement stability for longer items (bi- and tri-syllables). Moreover, utterance length affected the lip kinematics, in that the monosyllables had smaller peak velocities, smaller amplitudes and shorter durations compared to bi- and trisyllables, and movement stability was lowest for the trisyllables. In addition, the rate-induced changes (smaller amplitude and shorter duration with increased rate) were most prominent for the short items (i.e., monosyllables). These findings provide further support for the notion that linguistic changes have an impact on the characteristics of speech movements, and that individuals with aphasia are more affected by such changes than control speakers.

Speech motor control in fluent and dysfluent speech production of an individual with apraxia of speech and Broca’s aphasia

Apraxia of speech (AOS) is typically described as a motor-speech disorder with clinically well-defined symptoms, but without a clear understanding of the underlying problems in motor control. A number of studies have compared the speech of subjects with AOS to the fluent speech of controls, but only a few have included speech movement data and if so, this was primarily restricted to the study of single articulators. If AOS reflects a basic neuromotor dysfunction, this should somehow be evident in the production of both dysfluent and perceptually fluent speech. The current study compared motor control strategies for the production of perceptually fluent speech between a young woman with apraxia of speech (AOS) and Broca’s aphasia and a group of age-matched control speakers using concepts and tools from articulation-based theories. In addition, to examine the potential role of specific movement variables on gestural coordination, a second part of this study involved a comparison of fluent and dysfluent speech samples from the speaker with AOS. Movement data from the lips, jaw and tongue were acquired using the AG-100 EMMA system during the reiterated production of multisyllabic nonwords. The findings indicated that although in general kinematic parameters of fluent speech were similar in the subject with AOS and Broca’s aphasia to those of the age-matched controls, speech task-related differences were observed in upper lip movements and lip coordination. The comparison between fluent and dysfluent speech characteristics suggested that fluent speech was achieved through the use of specific motor control strategies, highlighting the potential association between the stability of coordinative patterns and movement range, as described in Coordination Dynamics theory.

Preliminary observations on the presence of sustained tendon strain and eccentric contractions of the wrist extensors during a common manual task: implications for lateral epicondylitis

Lateral epicondylitis (LE) is hypothesized to occur as a result of repetitive, strenuous and abnormal postural activities of the elbow and wrist. There is still a lack of understanding of how wrist and forearm positions contribute to this condition during common manual tasks. In this study the wrist kinematics and the wrist extensors’ musculotendon patterns were investigated during a manual task believed to elicit LE symptoms in susceptible subjects. A 42-year-old right-handed male, with no history of LE, performed a repetitive movement involving pushing and turning a spring-loaded mechanism. Motion capture data were acquired for the upper limb and an inverse kinematic and dynamic analysis was subsequently carried out. Results illustrated the presence of eccentric contractions sustained by the extensor carpi radialis longus (ECRL), together with an almost constant level of tendon strain of both extensor carpi radialis brevis (ECRB) and extensor digitorum communis lateral (EDCL) branch. It is believed that these factors may partly contribute to the onset of LE as they are both responsible for the creation of microtears at the tendons’ origins. The methodology of this study can be used to explore muscle actions during movements that might cause or exacerbate LE.

Viscous coupling of shear-free turbulence across nearly flat fluid interfaces

The interactions between shear-free turbulence in two regions (denoted as + and − on either side of a nearly flat horizontal interface are shown here to be controlled by several mechanisms, which depend on the magnitudes of the ratios of the densities, ρ+/ρ−, and kinematic viscosities of the fluids, μ+/μ−, and the root mean square (r.m.s.) velocities of the turbulence, u0+/u0−, above and below the interface. This study focuses on gas–liquid interfaces so that ρ+/ρ− ≪ 1 and also on where turbulence is generated either above or below the interface so that u0+/u0− is either very large or very small. It is assumed that vertical buoyancy forces across the interface are much larger than internal forces so that the interface is nearly flat, and coupling between turbulence on either side of the interface is determined by viscous stresses. A formal linearized rapid-distortion analysis with viscous effects is developed by extending the previous study by Hunt & Graham (J. Fluid Mech., vol. 84, 1978, pp. 209–235) of shear-free turbulence near rigid plane boundaries. The physical processes accounted for in our model include both the blocking effect of the interface on normal components of the turbulence and the viscous coupling of the horizontal field across thin interfacial viscous boundary layers. The horizontal divergence in the perturbation velocity field in the viscous layer drives weak inviscid irrotational velocity fluctuations outside the viscous boundary layers in a mechanism analogous to Ekman pumping. The analysis shows the following. (i) The blocking effects are similar to those near rigid boundaries on each side of the interface, but through the action of the thin viscous layers above and below the interface, the horizontal and vertical velocity components differ from those near a rigid surface and are correlated or anti-correlated respectively. (ii) Because of the growth of the viscous layers on either side of the interface, the ratio uI/u0, where uI is the r.m.s. of the interfacial velocity fluctuations and u0 the r.m.s. of the homogeneous turbulence far from the interface, does not vary with time. If the turbulence is driven in the lower layer with ρ+/ρ− ≪ 1 and u0+/u0− ≪ 1, then uI/u0− ~ 1 when Re (=u0−L−/ν−) ≫ 1 and R = (ρ−/ρ+)(v−/v+)1/2 ≫ 1. If the turbulence is driven in the upper layer with ρ+/ρ− ≪ 1 and u0+/u0− ≫ 1, then uI/u0+ ~ 1/(1 + R). (iii) Nonlinear effects become significant over periods greater than Lagrangian time scales. When turbulence is generated in the lower layer, and the Reynolds number is high enough, motions in the upper viscous layer are turbulent. The horizontal vorticity tends to decrease, and the vertical vorticity of the eddies dominates their asymptotic structure. When turbulence is generated in the upper layer, and the Reynolds number is less than about 106–107, the fluctuations in the viscous layer do not become turbulent. Nonlinear processes at the interface increase the ratio uI/u0+ for sheared or shear-free turbulence in the gas above its linear value of uI/u0+ ~ 1/(1 + R) to (ρ+/ρ−)1/2 ~ 1/30 for air–water interfaces. This estimate agrees with the direct numerical simulation results from Lombardi, De Angelis & Bannerjee (Phys. Fluids, vol. 8, no. 6, 1996, pp. 1643–1665). Because the linear viscous–inertial coupling mechanism is still significant, the eddy motions on either side of the interface have a similar horizontal structure, although their vertical structure differs.

Speech-like and non-speech lip kinematics and coordination in aphasia

Background and aims: In addition to the well-known linguistic processing impairments in aphasia, oro-motor skills and articulatory implementation of speech segments are reported to be compromised to some degree in most types of aphasia. This study aimed to identify differences in the characteristics and coordination of lip movements in the production of a bilabial closure gesture between speech-like and nonspeech tasks in individuals with aphasia and healthy control subjects. Method and procedure: Upper and lower lip movement data were collected for a speech-like and a nonspeech task using an AG 100 EMMA system from five individuals with aphasia and five age and gender matched control subjects. Each task was produced at two rate conditions (normal and fast), and in a familiar and a less-familiar manner. Single articulator kinematic parameters (peak velocity, amplitude, duration, and cyclic spatio-temporal index) and multi-articulator coordination indices (average relative phase and variability of relative phase) were measured to characterize lip movements. Outcome and results: The results showed that when the two lips had similar task goals (bilabial closure) in speech-like versus nonspeech task, kinematic and coordination characteristics were not found to be different. However, when changes in rate were imposed on the bilabial gesture, only speech-like task showed functional adaptations, indicated by a greater decrease in amplitude and duration at fast rates. In terms of group differences, individuals with aphasia showed smaller amplitudes and longer movement durations for upper lip, higher spatio-temporal variability for both lips, and higher variability in lip coordination than the control speakers. Rate was an important factor in distinguishing the two groups, and individuals with aphasia were limited in implementing the rate changes. Conclusion and implications: The findings support the notion of subtle but robust differences in motor control characteristics between individuals with aphasia and the control participants, even in the context of producing bilabial closing gestures for a relatively simple speech-like task. The findings also highlight the functional differences between speech-like and nonspeech tasks, despite a common movement coordination goal for bilabial closure.

To eat or not to eat? Kinematics and muscle activity of reach-to-grasp movements are influenced by the action goal, but observers do not detect these differences

Recent evidence suggests that the mirror neuron system responds to the goals of actions, even when the end of the movement is hidden from view. To investigate whether this predictive ability might be based on the detection of early differences between actions with different outcomes, we used electromyography (EMG) and motion tracking to assess whether two actions with different goals (grasp to eat and grasp to place) differed from each other in their initial reaching phases. In a second experiment, we then tested whether observers could detect early differences and predict the outcome of these movements, based on seeing only part of the actions. Experiment 1 revealed early kinematic differences between the two movements, with grasp-to-eat movements characterised by an earlier peak acceleration, and different grasp position, compared to grasp-to-place movements. There were also significant differences in forearm muscle activity in the reaching phase of the two actions. The behavioural data arising from Experiments 2a and 2b indicated that observers are not able to predict whether an object is going to be brought to the mouth or placed until after the grasp has been completed. This suggests that the early kinematic differences are either not visible to observers, or that they are not used to predict the end-goals of actions. These data are discussed in the context of the mirror neuron system

Extensivity of two-dimensional turbulence

This study is concerned with how the attractor dimension of the two-dimensional Navier–Stokes equations depends on characteristic length scales, including the system integral length scale, the forcing length scale, and the dissipation length scale. Upper bounds on the attractor dimension derived by Constantin, Foias and Temam are analysed. It is shown that the optimal attractor-dimension estimate grows linearly with the domain area (suggestive of extensive chaos), for a sufficiently large domain, if the kinematic viscosity and the amplitude and length scale of the forcing are held fixed. For sufficiently small domain area, a slightly “super-extensive” estimate becomes optimal. In the extensive regime, the attractor-dimension estimate is given by the ratio of the domain area to the square of the dissipation length scale defined, on physical grounds, in terms of the average rate of shear. This dissipation length scale (which is not necessarily the scale at which the energy or enstrophy dissipation takes place) can be identified with the dimension correlation length scale, the square of which is interpreted, according to the concept of extensive chaos, as the area of a subsystem with one degree of freedom. Furthermore, these length scales can be identified with a “minimum length scale” of the flow, which is rigorously deduced from the concept of determining nodes.

A closer look at chaotic advection in the stratosphere: part II: statistical diagnostics

Statistical diagnostics of mixing and transport are computed for a numerical model of forced shallow-water flow on the sphere and a middle-atmosphere general circulation model. In particular, particle dispersion statistics, transport fluxes, Liapunov exponents (probability density functions and ensemble averages), and tracer concentration statistics are considered. It is shown that the behavior of the diagnostics is in accord with that of kinematic chaotic advection models so long as stochasticity is sufficiently weak. Comparisons with random-strain theory are made.

Modelling the rheology of sea ice as a collection of diamond-shaped floes

In polar oceans, seawater freezes to form a layer of sea ice of several metres thickness that can cover up to 8% of the Earth’s surface. The modelled sea ice cover state is described by thickness and orientational distribution of interlocking, anisotropic diamond-shaped ice floes delineated by slip lines, as supported by observation. The purpose of this study is to develop a set of equations describing the mean-field sea ice stresses that result from interactions between the ice floes and the evolution of the ice floe orientation, which are simple enough to be incorporated into a climate model. The sea ice stress caused by a deformation of the ice cover is determined by employing an existing kinematic model of ice floe motion, which enables us to calculate the forces acting on the ice floes due to crushing into and sliding past each other, and then by averaging over all possible floe orientations. We describe the orientational floe distribution with a structure tensor and propose an evolution equation for this tensor that accounts for rigid body rotation of the floes, their apparent re-orientation due to new slip line formation, and change of shape of the floes due to freezing and melting. The form of the evolution equation proposed is motivated by laboratory observations of sea ice failure under controlled conditions. Finally, we present simulations of the evolution of sea ice stress and floe orientation for several imposed flow types. Although evidence to test the simulations against is lacking, the simulations seem physically reasonable.