Linear Impulses Research Articles

Free Gait Generation of Quadruped Robots via Impulse-Based Feasibility Analysis

Online gait adaptation is crucial for improving the dynamic performance of quadruped locomotion systems, while current approaches often adopt the predefined periodic gait pattern. This article proposes a free gait generation algorithm that only takes the robot state as input. Specifically, we introduce the feasible impulse polytope, which takes into account both linear and angular momentum impulses acting on the body in a prediction horizon. This naturally leads us to formulate a leg capability metric related to the effect of take-off and touch-down on the body motion. Then, gait sequence, take-off timing, and touch-down location can be automatically adjusted online as long as a metric threshold is given. To cope with rough terrain, a series of quadratic programming problems are established for online pose optimization under mild assumptions. Furthermore, we fully integrate the proposed algorithms with the robot control and estimation framework for real-time implementation. We first validate our approach with the quadruped robot SCIT-Dog through locomotion with speed changes, on stairs and slopes, and under lateral disturbances. Besides, a push-recovery experiment is established to show the superiority of the proposed approach over the baseline method with prespecified gait patterns. Experiment results verify the ability of the proposed algorithms to achieve autonomous gait transitions in response to various emergencies.

Roles of each leg in impulse generation in professional baseball pitchers: preliminary findings uncover the contribution of the back leg towards whole-body rotation

ABSTRACT This study examined the roles of each leg in generating linear and angular impulses during baseball pitching. Professional pitchers (n = 4) pitched from a force plate instrumented mound, and 6–11 successful fastball pitches were used for analyses. We compared linear and angular impulses across the back and front legs. Linear and angular impulses were calculated from ground reaction force (GRF) and moment about each global axis passing through the centre of mass (COM), respectively. Additionally, we analysed measures that control the moment: (1) GRF magnitude, (2) magnitude of the position vector from COM to the centre of pressure and (3) the angle between (1) and (2). We found that the back leg generated forward linear impulse and the front leg generated backward linear impulse for all pitchers. Surprisingly, we found that the back leg generated significantly greater positive angular impulse about a global leftward axis (from the mound towards first base) than did the front leg in all four pitchers. Furthermore, the back leg’s moment about the leftward axis became positive after the magnitude of forward GRF decreased from its maximum, suggesting that the back leg’s role transitioned from generating forward linear momentum to angular momentum.

Characterization of material properties and deformation in the ANGUS phantom during mild head impacts using MRI

Traumatic brain injury (TBI) is a major health concern affecting both military and civilian populations. Despite notable advances in TBI research in recent years, there remains a significant gap in linking the impulsive loadings from a blast or a blunt impact to the clinical injury patterns observed in TBI. Synthetic head models or phantoms can be used to establish this link as they can be constructed with geometry, anatomy, and material properties that match the human brain, and can be used as an alternative to animal models. This study presents one such phantom called the Anthropomorphic Neurologic Gyrencephalic Unified Standard (ANGUS) phantom, which is an idealized gyrencephalic brain phantom composed of polyacrylamide gel. Here we mechanically characterized the ANGUS phantom using tagged magnetic resonance imaging (MRI) and magnetic resonance elastography (MRE), and then compared the outcomes to data obtained in healthy volunteers. The direct comparison between the phantom's response and the data from a cohort of in vivo human subjects demonstrate that the ANGUS phantom may be an appropriate model for bulk tissue response and gyral dynamics of the human brain under small amplitude linear impulses. However, the phantom's response differs from that of the in vivo human brain under rotational impacts, suggesting avenues for future improvements to the phantom.

Uniform Stability of Complex-Valued Neural Networks of Fractional Order With Linear Impulses and Fixed Time Delays.

As a generation of the real-valued neural network (RVNN), complex-valued neural network (CVNN) is based on the complex-valued (CV) parameters and variables. The fractional-order (FO) CVNN with linear impulses and fixed time delays is discussed. By using the sign function, the Banach fixed point theorem, and two classes of activation functions, some criteria of uniform stability for the solution and existence and uniqueness for equilibrium solution are derived. Finally, three experimental simulations are presented to illustrate the correctness and effectiveness of the obtained results.

Yang-Mills observables: from KMOC to eikonal through EFT

We obtain a conservative Hamiltonian describing the interactions of two charged bodies in Yang-Mills through mathcal{O}left({alpha}^2right) and to all orders in velocity. Our calculation extends a recently-introduced framework based on scattering amplitudes and effective field theory (EFT) to consider color-charged objects. These results are checked against the direct integration of the observables in the Kosower-Maybee-O’Connell (KMOC) formalism. At the order we consider we find that the linear and color impulses in a scattering event can be concisely described in terms of the eikonal phase, thus extending the domain of applicability of a formula originally proposed in the context of spinning particles.

Tidal effects for spinning particles

Expanding on the recent derivation of tidal actions for scalar particles, we present here the action for a tidally deformed spin-1/2 particle. Focusing on operators containing two powers of the Weyl tensor, we combine the Hilbert series with an on-shell amplitude basis to construct the tidal action. With the tidal action in hand, we compute the leading-post-Minkowskian tidal contributions to the spin-1/2–spin-1/2 amplitude, arising at mathcal{O} (G2). Our amplitudes provide evidence that the observed long range spin-universality for the scattering of two point particles extends to the scattering of tidally deformed objects. From the scattering amplitude we find the conservative two-body Hamiltonian, linear and angular impulses, eikonal phase, spin kick, and aligned-spin scattering angle. We present analogous results in the electromagnetic case along the way.

계단과 경사로 하강 동작 중의 발목관절 충격량 비교

The purpose of this study was to compare ankle joint loads (Linear and Angular Impulses) while descending the stairs and ramp. Ten young male subjects participated in this study. Stairs and ramp of identical slope (30 degrees) were custom-made to include force plates in the middle of pathways. Subjects descended the stairs and ramp at a comfortable speed and posture. The stance period was divided into three phases, weight acceptance (WA), single limb stance, and pre-swing. Three-directional impulses and their sum were derived from the reaction forces and moments at the ankle joint. Differences in impulse sums (Both Linear and Angular) between stairs and ramp were significant only in the early (WA) phase, whereas those of stairs were greater than the ramp. All subjects adopted forefoot strike strategy for the stairs and 80% of the subjects adopted rearfoot strike strategy for the ramp. An increase in the GRF and moment arm of the GRF at the ankle joint in case of forefoot strike may have contributed to the increase in the linear and angular impulse in the early phase of stair descent compared to ramp descent. The results are in agreement with the preference of ramp in the elderly.

A System for Simple Robotic Walking Assistance With Linear Impulses at the Center of Mass.

Walking can be simplified as an inverted pendulum motion where both legs generate linear impulses to redirect the center of mass (COM) into every step. In this work, we describe a system to assist walking in a simpler way than exoskeletons by providing linear impulses directly at the COM instead of providing torques at the joints. We developed a novel waist end-effector and high-level controller for an existing cable-robot. The controller allows for the application of cyclic horizontal force profiles with desired magnitudes, timings, and durations based on detection of the step timing. By selecting a lightweight rubber series elastic element with optimal stiffness and carefully tuning the gains of the closed-loop proportional-integral-derivative (PID) controller in a number of single-subject experiments, we were able to reduce the within-step root mean square error between desired and actual forces up to 1.21% of body weight. This level of error is similar or lower compared to the performance of other robotic tethers designed to provide variable or constant forces at the COM. The system can produce force profiles with peaks of up to 15 ± 2% of body weight within a root mean square error (RMSE) of 2.5% body weight. This system could be used to assist patient populations that require levels of assistance that are greater than current exoskeletons and in a way that does not make the user rely on vertical support.

Global asymptotic stability for a periodic delay hematopoiesis model with impulses

In this paper, sufficient conditions for the global asymptotic stability of a broad family of periodic impulsive scalar delay differential equations are obtained. These conditions are applied to a periodic hematopoiesis model with multiple time-dependent delays and linear impulses, in order to establish criteria for the global asymptotic stability of a positive periodic solution. The present results are discussed within the context of recent literature. In conclusion, when compared with previous works, not only sharper stability criteria are obtained here, even for models without impulses, but also the usual constraints imposed on the linear impulses are relaxed.

Skipping has lower knee joint contact forces and higher metabolic cost compared to running

BackgroundThe health benefits of running based exercise programs are plentiful however the high rate of injury in these programs often reduces or eliminates exercise participation. Skipping has shorter steps, reduced vertical ground reaction forces (GRFs), and lower knee extensor torques, compared to running forming the basis of the present hypothesis that skipping would have lower tibio-femoral and patello-femoral joint contact forces. Research questionThe purpose of this study was to compare knee contact forces between skipping and running at the same speed. We also compared metabolic cost of these two gaits to examine the idea that the larger vertical displacement in skipping is a primary factor in its previously reported high metabolic cost. MethodsThe study evaluated joint contact forces through musculoskeletal modeling with GRF and 3D kinematic data and metabolic cost using oxygen consumption data from 20 young, healthy, trained participants as they skipped and ran on an instrumented treadmill at 2.68 m/s. Results: Skipping, compared to running, had substantially lower tibio-femoral and patello-femoral joint contact forces and linear impulses on both per-step and per-kilometer (i.e. lower cumulative loads) bases and also 30% higher metabolic cost. The lower joint loads in skipping were directly associated with its shorter steps and the higher metabolic cost was directly associated to its larger vertical displacement through the stride. SignificanceAs joint loads may predispose individuals to running related injuries, skipping presents an attractive alternative exercise modality with additional increased aerobic benefits.

Relative controllability of delay differential systems with impulses and linear parts defined by permutable matrices

This paper investigates the relative controllability of delay differential systems with linear impulses and linear parts defined by permutable matrices. We use the impulsive delay Grammian matrix to discuss the relatively controllability of impulsive linear delay controlled systems and we use the Krasnoselskii's fixed point theorem to discuss the relatively controllability of impulsive semilinear delay controlled systems. Finally, two examples are presented to illustrate our theoretical results.

Lower extremity joint stiffness during walking distinguishes children with and without autism

How children with Autism Spectrum Disorder (ASD) and peers with typical development (TD) modulate lower extremity stiffness during walking could identify a mechanism for gait differences between groups. We quantified differences in lower extremity joint stiffness and linear impulses, along the vertical and anterior/posterior axes during over-ground walking in children with ASD compared to age- and gender-matched children with TD. Nine age- and gender-matched pairs of children, aged 5–12 years, completed the current study. Joint stiffness and linear impulses were computed in four sub-phases of stance: loading response, mid-stance, terminal stance, and pre-swing. The Model Statistic technique (α = 0.05) was used to test for statistical significance between the matched-pairs for each variable and sub-phase. Furthermore, dependent t-tests (α = 0.05) were utilized, at the group level, to determine whether significant differences existed between sub-phases. Results indicate that children with ASD may exhibit greater stiffness in pre-swing, and thus, produce inefficient propulsive forces during walking. We attribute these differences to sensory processing dysfunction previously observed in children with ASD.

Consecutive postural adjustments (CPAs): A kinetic analysis of variable velocity during a pointing task

This paper examines the postural adjustments that occur after the end of a voluntary movement (consecutive postural adjustments, CPAs). Its aim is to reinforce the theory that CPAs are necessary to counterbalance the destabilizing effect of a voluntary movement. In addition, we compared the main features of CPAs with those of anticipatory postural adjustments (APAs) in order to gather evidence that could afford new insights into postural programming. Nine healthy adults were invited to adopt a sitting position to perform nine pointing movements at decreasing velocities. The antero-posterior component of the reaction forces was measured. Upper limb kinematics were recorded and the kinetics calculated. The main features under study included linear impulses, peak amplitudes and duration of CPAs and APAs. Two main results emerged from our study: the impulse produced after the end of a focal movement (CPAIx) was negative, while the impulse produced before its end (*ASPIx) was positive; their absolute values were not significantly different; when movement velocity increased, CPA impulse and peak amplitude (pCPA) increased significantly, contrary to duration (dCPA). Furthermore, APA impulse, peak amplitude and duration were all increased. These findings on pointing movements strengthen the hypothesis that CPAs play a role of body stabilization and that the postural chain kinetics is programmed according to focal movement velocity. Evidence on CPA obtained from healthy subjects may contribute to the further specification of the differences associated with motor impairment.

Selenium reaction mechanism in manganese electrodeposition process

A difficulty for the electrochemical deposition is the high negative electrolytic potential of the Mn+2/Mn° pair in aqueous solutions producing water reduction at any pH value; to resolve this problem it is necessary to use selenium dioxide (SeO2) as additive. However, there is little information about the selenium mechanism presenting discrepancies. Founded on linear voltammetry, cyclic voltammetry, chronoamperometry test, and impulses of constant potential and thermodynamic analysis, are experimental evidences of the reaction mechanism to explain the selenium action; from here the originality of this work. It is demonstrated that two reactions that occur in the selenium mechanism at −0.3 and −0.6V, the first for the selenium deposition and the second for the selenium dissolution. On the active sites of the cathode the specie of selenium reduced at −0.3V is the ion hydrogen selenite (H2SeO3−), while at −0.6V the deposited selenium is reduced to selenide.

Existence of Positive Periodic Solutions for Scalar Delay Differential Equations with and without Impulses

The paper is concerned with a broad family of scalar periodic delay differential equations with linear impulses, for which the existence of a positive periodic solution is established under very general conditions. The proofs rely on fixed point arguments, employing either the Schauder theorem or Krasnoselskii fixed point theorem in cones. The results are illustrated with applications to an impulsive hematopoiesis model or generalized Nicholson’s equations, among other selected examples from mathematical biology. The method presented here turns out to be very powerful, in the sense that the derived theorems largely generalize and improve other results in recent literature, even for the situation without impulses.

Stability Analysis of Delayed Impulsive Systems and Applications

This paper investigates exponential stability of nonlinear delayed impulsive systems. The effects of impulses with sufficiently small input delays and arbitrary sizes of input delays are thoroughly examined according to whether the continuous dynamics of the systems is stable. Several exponential stability criteria are obtained and are then applied to study constant time-delay systems with linear input impulses. Numerical examples are provided to illustrate the usefulness of the main study results.

Motion of double pendulum colliding with an obstacle of rough surface

The externally excited and damped vibration of the double pendulum in the vertical plane are considered. The pendulum can collide many times during the motion with a motionless obstacle having the rough surface. The double pendulum colliding with this object has been modeled as a piecewise smooth system constrained by the unilateral constraint. In the relatively long time between the collisions, the differential equations govern the motion of the pendulum. When the contact with the obstacle appears, the pendulum exhibits a discontinuous behavior. An important element of the solving algorithm is aimed on the continuous tracking of the position of the pendulum in order to detect the collision with the unilateral constraints and to determine the state vector of the pendulum at the impact time instant. A single collision is described by the Euler’s laws of motion in the integral form. The equations are supplemented by the Poisson’s hypothesis and Coulomb’s law of friction. The friction law is formulated for the instantaneous values of the reaction forces. The values of their impulses depend on the existence of a slip between the contacting bodies. Therefore, the Coulomb law cannot be generalized for the linear impulses of the forces in a simple way. We have applied the Routh method in order to solve the problem. The method has a simple geometrical interpretation in the impulse space. The angular velocities of both pendulum parts as well as the reaction forces at the joints of the system, which change in stepwise manner, have been presented in the paper.

Modification of Impulse Generation During Pirouette Turns With Increased Rotational Demands.

This study determined how dancers regulated angular and linear impulse during the initiation of pirouettes of increased rotation. Skilled dancers (n = 11) performed single and double pirouette turns with each foot supported by a force plate. Linear and angular impulses generated by each leg were quantified and compared between turn types using probability-based statistical methods. As rotational demands increased, dancers increased the net angular impulse generated. The contribution of each leg to net angular impulse in both single and double pirouettes was influenced by stance configuration strategies. Dancers who generated more angular impulse with the push leg than with the turn leg initiated the turn with the center of mass positioned closer to the turn leg than did other dancers. As rotational demands increased, dancers tended to increase the horizontal reaction force magnitude at one or both feet; however, they used subject-specific mechanisms. By coordinating the generation of reaction forces between legs, changes in net horizontal impulse remained minimal, despite impulse regulation at each leg used to achieve more rotations. Knowledge gained regarding how an individual coordinates the generation of linear and angular impulse between both legs as rotational demand increased can help design tools to improve that individual's performance.

Trunk Muscle Activation at the Initiation and Braking of Bilateral Shoulder Flexion Movements of Different Amplitudes.

The aim of this study was to investigate if trunk muscle activation patterns during rapid bilateral shoulder flexions are affected by movement amplitude. Eleven healthy males performed shoulder flexion movements starting from a position with arms along sides (0°) to either 45°, 90° or 180°. EMG was measured bilaterally from transversus abdominis (TrA), obliquus internus (OI) with intra-muscular electrodes, and from rectus abdominis (RA), erector spinae (ES) and deltoideus with surface electrodes. 3D kinematics was recorded and inverse dynamics was used to calculate the reactive linear forces and torque about the shoulders and the linear and angular impulses. The sequencing of trunk muscle onsets at the initiation of arm movements was the same across movement amplitudes with ES as the first muscle activated, followed by TrA, RA and OI. All arm movements induced a flexion angular impulse about the shoulders during acceleration that was reversed during deceleration. Increased movement amplitude led to shortened onset latencies of the abdominal muscles and increased level of activation in TrA and ES. The activation magnitude of TrA was similar in acceleration and deceleration where the other muscles were specific to acceleration or deceleration. The findings show that arm movements need to be standardized when used as a method to evaluate trunk muscle activation patterns and that inclusion of the deceleration of the arms in the analysis allow the study of the relationship between trunk muscle activation and direction of perturbing torque during one and the same arm movement.

The Scaled Reassigned Spectrogram with Perfect Localization for Estimation of Gaussian Functions

The reassignment technique is used to increase localization for signal components in the time-frequency representation. The technique gives perfect localization for infinite linear chirp-signals, impulses and constant frequency signals but not for short non-stationary signals. In this paper, a scaled reassignment is proposed, based on the spectrogram using a Gaussian window. The resulting reassignment gives perfect localization for a Gaussian function when the window length matches the function length. Based on the scaled reassignment, an algorithm that estimates the Gaussian function length is also proposed.