Improving horizontal plane locomotion via leg angle control

The lateral leg spring model has been shown to accurately represent horizontal plane locomotion characteristics of sprawled posture insects such as the cockroach Blaberus discoidalis. While passively stable periodic gaits result from employing a constant leg touch-down angle for this model, utilizing a similar protocol for a point mass model of locomotion in three dimensions produces only unstable periodic gaits. In this work, we return to the horizontal plane model and develop a simple control law that prescribes variations in the leg touch-down angle in response to external perturbations. The resulting control law applies control once per stance phase, at the instant of leg touch-down, and depends upon previous leg angles defined in the body reference frame. As a result, our control action is consistent with the neural activity evidenced by B. discoidalis during locomotion over flat and rough terrain, and utilizes variables easily sensed by insect mechanoreceptors. Application of control in the lateral leg spring model is shown to improve stability of periodic gaits, enable stabilization of previously unstable periodic gaits, and maintain or improve the basin of stability of periodic gaits. The magnitude of leg touch-down angle variations utilized during stabilization appear consistent with the natural variations evidenced by single legs during locomotion over flat terrain.     

Anticipatory postural adjustments associated with lateral and rotational perturbations during standing.

We studied the role of different leg and trunk muscle groups in the generation of anticipatory postural adjustments (APAs) prior to lateral and rotational perturbations associated with predictable and self-triggered postural perturbations during standing. Postural perturbations were induced by a variety of manipulations including catching and releasing a load with the right hand extended either in front of the body or to the right side, performing bilateral fast shoulder movements in different directions, and applying brief force pulses with a hand against the wall. Perturbations in a frontal plane ("lateral perturbations") were associated with significant asymmetries in APAs seen in the right and left distal (soleus and tibialis anterior) muscles; these asymmetries dependent on the direction of the perturbation. Rotational perturbations about the vertical axis of the body generated by fast movements of the two shoulders in the opposite directions were also associated with direction-dependent asymmetries in the APAs in soleus muscles. However, rotational perturbations generated by an off-body-midline force pulse application were accompanied by direction-dependent asymmetries in proximal muscle groups, but not in the distal muscles. We conclude that muscles controlling the ankle joint play an important role in the compensation of lateral and rotational perturbations. The abundance of muscles participating in maintaining vertical posture allows the control system to use different task-dependent strategies during the generation of APAs in anticipation of rotational perturbation.     

Trunk muscle contributions of to L4–5 joint rotational stiffness following sudden trunk lateral bend perturbations

The purpose of this research was to investigate the contributions of individual muscles to joint rotational stiffness and total joint rotational stiffness about the lumbar spine’s L_4–5 joint prior to, and following, sudden dynamic lateral perturbations to the trunk. Kinematic and surface EMG data were collected while subjects maintained a kneeling posture on a robotic platform, while restrained so that motions caused by the perturbation were transferred to the pelvis, causing motion of the trunk and head. The robotic platform caused sudden inertial trunk lateral perturbations to the right or left, with or without timing and direction knowledge. An EMG-driven model of the lumbar spine was used to calculate the muscle forces and contributions to joint rotational stiffness during the perturbations. Data showed 95% and 106% increases in total joint rotational stiffness_, about the lateral bend and axial twist axes, when subjects had knowledge of the timing of the perturbation. Also, the contralateral muscles exhibited a significantly larger total joint rotational stiffness about the lateral bend axis, and earlier surface EMG responses, than the ipsilateral muscles. The results indicate that, when the timing of the perturbation was unknown, subjects relied more on delayed muscle forces following the perturbation to stiffen the L_4–5 joint.     

Contribution of muscle short-range stiffness to initial changes in joint kinetics and kinematics during perturbations to standing balance: A simulation study

Simulating realistic musculoskeletal dynamics is critical to understanding neural control of muscle activity evoked in sensorimotor feedback responses that have inherent neural transmission delays. Thus, the initial mechanical response of muscles to perturbations in the absence of any change in muscle activity determines which corrective neural responses are required to stabilize body posture. Muscle short-range stiffness, a history-dependent property of muscle that causes a rapid and transient rise in muscle force upon stretch, likely affects musculoskeletal dynamics in the initial mechanical response to perturbations. Here we identified the contributions of short-range stiffness to joint torques and angles in the initial mechanical response to support surface translations using dynamic simulation. We developed a dynamic model of muscle short-range stiffness to augment a Hill-type muscle model. Our simulations show that short-range stiffness can provide stability against external perturbations during the neuromechanical response delay. Assuming constant muscle activation during the initial mechanical response, including muscle short-range stiffness was necessary to account for the rapid rise in experimental sagittal plane knee and hip joint torques that occurs simultaneously with very small changes in joint angles and reduced root mean square errors between simulated and experimental torques by 56% and 47%, respectively. Moreover, forward simulations lacking short-range stiffness produced unreasonably large joint angle changes during the initial response. Using muscle models accounting for short-range stiffness along with other aspects of history-dependent muscle dynamics may be important to advance our ability to simulate inherently unstable human movements based on principles of neural control and biomechanics.     

Relating reflex gain modulation in posture control to underlying neural network properties using a neuromusculoskeletal model

During posture control, reflexive feedback allows humans to efficiently compensate for unpredictable mechanical disturbances. Although reflexes are involuntary, humans can adapt their reflexive settings to the characteristics of the disturbances. Reflex modulation is commonly studied by determining reflex gains: a set of parameters that quantify the contributions of Ia, Ib and II afferents to mechanical joint behavior. Many mechanisms, like presynaptic inhibition and fusimotor drive, can account for reflex gain modulations. The goal of this study was to investigate the effects of underlying neural and sensory mechanisms on mechanical joint behavior. A neuromusculoskeletal model was built, in which a pair of muscles actuated a limb, while being controlled by a model of 2,298 spiking neurons in six pairs of spinal populations. Identical to experiments, the endpoint of the limb was disturbed with force perturbations. System identification was used to quantify the control behavior with reflex gains. A sensitivity analysis was then performed on the neuromusculoskeletal model, determining the influence of the neural, sensory and synaptic parameters on the joint dynamics. The results showed that the lumped reflex gains positively correlate to their most direct neural substrates: the velocity gain with Ia afferent velocity feedback, the positional gain with muscle stretch over II afferents and the force feedback gain with Ib afferent feedback. However, position feedback and force feedback gains show strong interactions with other neural and sensory properties. These results give important insights in the effects of neural properties on joint dynamics and in the identifiability of reflex gains in experiments.     

Force-Controlled Balance Perturbations Associated with Falls in Older People: A Prospective Cohort Study

Balance recovery from an unpredictable postural perturbation can be a challenging task for many older people and poor recovery could contribute to their risk of falls. This study examined associations between responses to unpredictable perturbations and fall risk in older people. 242 older adults (80.0±4.4 years) underwent assessments of stepping responses to multi-directional force-controlled waist-pull perturbations. Participants returned monthly falls calendars for the subsequent 12 months. Future falls were associated with lower force thresholds for stepping in the posterior and lateral but not anterior directions. Those with lower posterior force thresholds for stepping were 68% more likely to fall at home than those with higher force thresholds for stepping. These results suggest that amount of force that can be withstood following an unpredictable balance perturbation predicts future falls in community-dwelling older adults. Perturbations in the posterior direction best discriminated between future fallers and non-fallers.     

Functional recovery following manipulation of muscles and sense organs in the stick insect leg

We studied functional recovery of leg posture and walking behaviour in the femur-tibia joint control system of stick insects. Leg extensions in resting animals and during walking are produced by different parts of a single extensor muscle. (a) Ablation of the muscle part responsible for fast movements prevented leg extension during the swing phase. Resting posture remained unaffected. Within a few post-operative days, extension movements recovered, provided that sensory feedback was available. Extension movements were now driven by the muscle part which in intact animals controls the resting posture only. (b) Selective ablation of this (slow) muscle part affected the resting posture, while walking was unaffected. The resting posture partly recovered during subsequent days. To test the range of functional recovery and underlying mechanisms, we additionally transected muscle motor innervation, or we inverted or ablated sensory feedback. We found that recovery was based on both muscular and neuronal mechanisms. The latter required appropriate sensory feedback for the process of recovery, but not for the maintenance of the recovered state. Our results thus indicate the existence of a sensory template that guides recovery. Recovery was limited to a behavioural range that occurs naturally in intact animals, though in different behavioural contexts.     

Neural network models of velocity storage in the horizontal vestibulo-ocular reflex

The vestibulo-ocular reflex (VOR) produces compensatory eye movements by utilizing head rotational velocity signals from the semicircular canals to control contractions of the extraocular muscles. In mammals, the time course of horizontal VOR is longer than that of the canal signals driving it, revealing the presence of a central integrator known as velocity storage. Although the neurons mediating VOR have been described neurophysiologically, their properties, and the mechanism of velocity storage itself, remain unexplained. Recent models of integration in VOR are based on systems of linear elements, interconnected in arbitrary ways. The present study extends this work by modeling horizontal VOR as a learning network composed of nonlinear model neurons. Network architectures are based on the VOR arc (canal afferents, vestibular nucleus (VN) neurons and extraocular motoneurons) and have both forward and lateral connections. The networks learn to produce velocity storage integration by forming lateral (commissural) inhibitory feedback loops between VN neurons. These loops overlap and interact in a complex way, forming both fast and slow VN pathways. The networks exhibit some of the nonlinear properties of the actual VOR, such as dependency of decay rate and phase lag upon input magnitude, and skewing of the response to higher magnitude sinusoidal inputs. Model VN neurons resemble their real counterparts. Both have increased time constant and gain, and decreased spontaneous rate as compared to canal afferents. Also, both model and real VN neurons exhibit rectification and skew. The results suggest that lateral inhibitory interactions produce velocity storage and also determine the properties of neurons mediating VOR. The neural network models demonstrate how commissural inhibition may be organized along the VOR pathway.     

A Simple State-Determined Model Reproduces Entrainment and Phase-Locking of Human Walking

Theoretical studies and robotic experiments have shown that asymptotically stable periodic walking may emerge from nonlinear limit-cycle oscillators in the neuro-mechanical periphery. We recently reported entrainment of human gait to periodic mechanical perturbations with two essential features: 1) entrainment occurred only when the perturbation period was close to the original (preferred) walking period, and 2) entrainment was always accompanied by phase locking so that the perturbation occurred at the end of the double-stance phase. In this study, we show that a highly-simplified state-determined walking model can reproduce several salient nonlinear limit-cycle behaviors of human walking: 1) periodic gait that is 2) asymptotically stable; 3) entrainment to periodic mechanical perturbations only when the perturbation period is close to the model''s unperturbed period; and 4) phase-locking to locate the perturbation at the end of double stance. Importantly, this model requires neither supra-spinal control nor an intrinsic self-sustaining neural oscillator such as a rhythmic central pattern generator. Our results suggest that several prominent limit-cycle features of human walking may stem from simple afferent feedback processes without significant involvement of supra-spinal control or a self-sustaining oscillatory neural network.     

Nuchal ligament reconstructions in diplodocid sauropods support horizontal neck feeding postures

Historically, sauropods have been largely perceived as having vertical, ‘S’-curved necks which were hypothesised to allow them to feed from the canopy of trees. Within the past two decades, this popular perception has been questioned, resulting in a debate over neck posture. The osteological differences between sauropods with horizontal neck posture (Diplodocus), and less horizontally inclined necks (Brachiosaurus) suggest differing life and feeding styles. One differing vertebral feature between these polarised bauplans is the bifurcated neural spine. Regardless of the spine condition, sauropods with and without bifurcated spines have been reconstructed exhibiting the same neck posture. Corroborating histology and morphology in extant taxa highlights the presence of modified vertebral ligaments associated with bifurcated spines. Using these extant taxa to better understand the biomechanics of bifurcated spines, this study proposes alternative soft tissue reconstructions. Previous depictions had the bifurcation trough entirely open or harbouring pneumatic diverticula or muscles; conversely this study proposes that the apices of the bifurcated spines were the anchoring points for a split nuchal ligament, and that the trough of bifurcation was predominantly filled with interspinal ligaments. Ligaments provide energy-efficient elastic rebound, and a paired ligament in the cervical series would aid in prolonged, lateral movement in a horizontal plane (i.e. feeding).     

Visual position stabilization in the hummingbird hawk moth, Macroglossum stellatarum L. I. Behavioural analysis

Optomotor responses of freely flying hawk moths, Macroglossum stellatarum, were characterized while the animals were hovering in front of and feeding on a dummy flower. Compensatory translational and rotational movements of the hawk moth were elicited by vertical grating patterns moving horizontally, mimicking imposed rotational and translational displacements of the animal in the horizontal plane. Oscillatory translational and rotational pattern motion leads to compensatory responses that peak in the frequency range between 2 Hz and 4 Hz. The control systems mediating the translational and rotational components of the optomotor response do not seem to influence each other. The system mediating translational responses is more sensitive in the fronto-lateral part of the visual field than in the lateral part; the opposite is true for the rotational system. The sensitivity of the translational system does not change along the vertical, whereas the rotational system is much more sensitive to motion in the dorsal than in the ventral part of the visual field. These sensitivity gradients may reflect an adaptation to the specific requirements of position stabilization in front of flowers during feeding. Accepted: 13 August 1997     

Dragondrop: a novel passive mechanism for aerial righting in the dragonfly

Dragonflies perform dramatic aerial manoeuvres when chasing targets but glide for periods during cruising flights. This makes dragonflies a great system to explore the role of passive stabilizing mechanisms that do not compromise manoeuvrability. We challenged dragonflies by dropping them from selected inverted attitudes and collected 6-degrees-of-freedom aerial recovery kinematics via custom motion capture techniques. From these kinematic data, we performed rigid-body inverse dynamics to reconstruct the forces and torques involved in righting behaviour. We found that inverted dragonflies typically recover themselves with the shortest rotation from the initial body inclination. Additionally, they exhibited a strong tendency to pitch-up with their head leading out of the manoeuvre, despite the lower moment of inertia in the roll axis. Surprisingly, anaesthetized dragonflies could also complete aerial righting reliably. Such passive righting disappeared in recently dead dragonflies but could be partially recovered by waxing their wings to the anaesthetised posture. Our kinematics data, inverse dynamics model and wind-tunnel experiments suggest that the dragonfly''s long abdomen and wing posture generate a rotational tendency and passive attitude recovery mechanism during falling. This work demonstrates an aerodynamically stable body configuration in a flying insect and raises new questions in sensorimotor control for small flying systems.     

Control of posture, depth, and swimming trajectories of fishes

Perturbations vary in period and amplitude, and responses tounavoidable perturbations depend on response time and scale.Disturbances due to unavoidable perturbations occur in threetranslational planes and three rotational axes during forwardsand backwards swimming. Stability depends on hydrodynamic dampingand correcting forces, which may be generated by propulsors(powered) or by control surfaces moving with the body (trimming).Hydrostatic forces affecting body orientation (posture) resultin negative metacentric heights amplifying rolling disturbances.The ability to counteract perturbations and correct disturbancesis greater for fishes with more slender bodies, which appearsto affect habitat choices. Postural control problems are greatestat low speeds, and are avoided by some fishes by sitting onthe bottom. In currents, body form and behavior affect lift,drag, weight, and friction and hence speeds to which posturecan be controlled. Self-correcting and regulated damping andtrimming mechanisms are most important in stabilizing swimmingtrajectories. Body resistance, fin trajectory, multiple propulsors,and long-based fins damp self-generated locomotor disturbances.Powered control using the tail evolved early in chordates, andis retained by most groups, although fishes, especially acanthopterygians,make greater use of appendages. As with most areas of stability,little is known of control costs. Costs and benefits of low-densityinclusions and hydrodynamic mechanisms for depth control varywith habits and habitats. Control may make substantial contributionsto energy budgets.     

Kelvin-Helmholtz instability in a bounded plasma flow

Kelvin-Helmholtz instability in a three-layer plane geometry is investigated theoretically. It is shown that, in a three-layer system (in contrast to the traditionally considered case in which instability develops at the boundary between two plasma flows), instability can develop at an arbitrary ratio of the plasma flow velocity to the ion-acoustic velocity. Perturbations with wavelengths on the order of the flow thickness or longer can increase even at a zero temperature. The system can also be unstable against long-wavelength perturbations if the flow velocity at one of the boundaries is lower than the sum of the Alfvén velocities in the flow and the ambient plasma. The possibility of applying the results obtained to interpret the experimental data acquired in the framework of the CLUSTER multisatellite project is discussed. It follows from these data that, in many cases, the propagation of an accelerated particle flow in the plasma-sheet boundary layer of the Earth’s magnetotail is accompanied by the generation of magnetic field oscillations propagating with a velocity on the order of the local Alfvén velocity.     

Instantaneous kinematic phase reflects neuromechanical response to lateral perturbations of running cockroaches

Instantaneous kinematic phase calculation allows the development of reduced-order oscillator models useful in generating hypotheses of neuromechanical control. When perturbed, changes in instantaneous kinematic phase and frequency of rhythmic movements can provide details of movement and evidence for neural feedback to a system-level neural oscillator with a time resolution not possible with traditional approaches. We elicited an escape response in cockroaches (Blaberus discoidalis) that ran onto a movable cart accelerated laterally with respect to the animals’ motion causing a perturbation. The specific impulse imposed on animals (0.50 $\pm $ 0.04 m s $^{-1}$ ; mean, SD) was nearly twice their forward speed (0.25 $\pm $ 0.06 m s $^{-1})$ . Instantaneous residual phase computed from kinematic phase remained constant for 110 ms after the onset of perturbation, but then decreased representing a decrease in stride frequency. Results from direct muscle action potential recordings supported kinematic phase results in showing that recovery begins with self-stabilizing mechanical feedback followed by neural feedback to an abstracted neural oscillator or central pattern generator. Trials fell into two classes of forward velocity changes, while exhibiting statistically indistinguishable frequency changes. Animals pulled away from the side with front and hind legs of the tripod in stance recovered heading within 300 ms, whereas animals that only had a middle leg of the tripod resisting the pull did not recover within this period. Animals with eight or more legs might be more robust to lateral perturbations than hexapods.     

Whole Body Mechanics of Stealthy Walking in Cats

The metabolic cost associated with locomotion represents a significant part of an animal''s metabolic energy budget. Therefore understanding the ways in which animals manage the energy required for locomotion by controlling muscular effort is critical to understanding limb design and the evolution of locomotor behavior. The assumption that energetic economy is the most important target of natural selection underlies many analyses of steady animal locomotion, leading to the prediction that animals will choose gaits and postures that maximize energetic efficiency. Many quadrupedal animals, particularly those that specialize in long distance steady locomotion, do in fact reduce the muscular contribution required for walking by adopting pendulum-like center of mass movements that facilitate exchange between kinetic energy (KE) and potential energy (PE) [1]–[4]. However, animals that are not specialized for long distance steady locomotion may face a more complex set of requirements, some of which may conflict with the efficient exchange of mechanical energy. For example, the “stealthy” walking style of cats may demand slow movements performed with the center of mass close to the ground. Force plate and video data show that domestic cats (Felis catus, Linnaeus, 1758) have lower mechanical energy recovery than mammals specialized for distance. A strong negative correlation was found between mechanical energy recovery and diagonality in the footfalls and there was also a negative correlation between limb compression and diagonality of footfalls such that more crouched postures tended to have greater diagonality. These data show a previously unrecognized mechanical relationship in which crouched postures are associated with changes in footfall pattern which are in turn related to reduced mechanical energy recovery. Low energy recovery was not associated with decreased vertical oscillations of the center of mass as theoretically predicted, but rather with posture and footfall pattern on the phase relationship between potential and kinetic energy. An important implication of these results is the possibility of a tradeoff between stealthy walking and economy of locomotion. This potential tradeoff highlights the complex and conflicting pressures that may govern the locomotor choices that animals make.     

A potential link between lateral semicircular canal orientation,head posture,and dietary habits in extant rhinos (Perissodactyla,Rhinocerotidae)

Extant rhinoceroses share the characteristic nasal horn, although the number and size of horns varies among the five species. Although all species are herbivores, their dietary preferences, occipital shapes, and common head postures vary. Traditionally, to predict the “usual” head posture (the most used head posture of animals during normal unstressed activities, i.e., standing) of rhinos, the occipital shape was used. While a backward inclined occiput implies a downward hanging head (often found in grazers), a forward inclined occiput is related to the horizontal head posture in browsing rhinos. In this study, the lateral semicircular canal (LSC) of the bony labyrinth was virtually reconstructed from µCT‐images in order to investigate a possible link between LSC orientation and head posture in extant rhinoceroses. The usual head posture was formerly reconstructed for several non‐rhinoceros taxa with the assumption that the LSC of the inner ear is held horizontal (parallel to the ground) during normal activity of the living animal. The current analysis of the LSC orientation resulted in a downward inclined usual head posture for the grazing white rhinoceros and a nearly horizontal head posture in the browsing Javan rhinoceros. The other three browsing or mixed feeding species show subhorizontal (closer to horizontal than a downgrade inclination) head postures. The results show that anatomical and behavioral aspects, like occipital shape, presence and size of horns/tusk‐like lower incisors, as well as feeding and feeding height preferences influence the usual head posture. Because quantitative behavioral data are lacking for the usual head postures of the extant rhinos, the here described relationship between the LSC orientation and the resulting head posture linked to feeding preferences gives new insights. The results show, that the inner ear provides additional information to interpret usual head postures linked to feeding preferences that can easily be adapted to fossil rhinoceroses.     

The contribution of the lateral semicircular canal to the short latency vestibular evoked potentials in cat

Short latency vestibular evoked potentials (VsEPs) to angular acceleration impulses (maximal intensity 20,000°/sec², rise time 1.5–3 msec) were recorded by skin electrodes in cats before and after various surgical procedures. Under general anesthesia, the animals underwent unilateral labyrinthectomy and the VsEPs in response to stimulation of the remaining inner ear in the plane of the lateral semicircular canal (SCC) with the head flexed 20°–25° were recorded as a baseline. The lateral SCC was then selectively obliterated near its ampulla. This induced major changes in the VsEPs recorded in response to stimulation of the remaining inner ear in this plane: the first 2 VsEP waves were absent, and only longer latency, smaller amplitude waves were present in response to both clockwise and counterclockwise stimulation. On the other hand, obliteration of the anterior and posterior SCCs and, in addition, destruction of both maculae were without major effects on the first 2 VsEP waves in response to excitatory stimulation. The results confirm that when the head is flexed 20°–25° and stimulated with angular acceleration impulses in the horizontal plane, the major site of initiation of the VsEPs in cats and probably in man is the crista ampullaris of the lateral SCC.     

Numerical analysis of maximal bat performance in baseball

Metal baseball bats have been experimentally demonstrated to produce higher ball exit velocity (BEV) than wooden bats. In the United States, all bats are subject to BEV tests using hitting machines that rotate the bat in a horizontal plane. In this paper, a model of bat-ball impact was developed based on 3-D translational and rotational kinematics of a swing performed by high-level players. The model was designed to simulate the maximal performance of specific models of a wooden bat and a metal bat when swung by a player, and included material properties and kinematics specific to each bat. Impact dynamics were quantified using the finite element method (ANSYS/LSDYNA, version 6.1). Maximum BEV from both a metal (61.5 m/s) and a wooden (50.9 m/s) bat exceeded the 43.1 m/s threshold by which bats are certified as appropriate for commercial sale. The lower BEV from the wooden bat was attributed to a lower pre-impact bat linear velocity, and a more oblique impact that resulted in a greater proportion of BEV being lost to lateral and vertical motion. The results demonstrate the importance of factoring bat linear velocity and spatial orientation into tests of maximal bat performance, and have implications for the design of metal baseball bats.