Terminal Angle Research Articles

Identifying the Problem Side with Single-Leg Squat and Hamstrings Flexibility for Non-Specific Chronic Low Back Pain.

Background and Objectives: In patients with non-specific chronic low back pain (LBP), their pain and problem sides can differ. Clinical Pilates assessment provides an approach to identify the problem side, but this approach requires experience and can be subjective. This study aimed to investigate if objective measures of single-leg squat postural control and hamstrings flexibility could identify the problem side in adults with non-specific chronic LBP. Materials and Methods: Forty adults with non-specific chronic LBP were tested on single-leg squat postural control and hamstrings flexibility. The problem side of participants was assessed with the Clinical Pilates method. Paired t-tests were used to compare the postural sway parameters of the single-leg squat and hamstrings flexibility between the problem and non-problem sides. Cohen's kappa was then used to assess the agreement of postural sway and flexibility measures with the Clinical Pilates method. Results: The problem side showed smaller vertical force variance, larger sway path distances, lower peak vertical force, smaller terminal knee flexion angle, longer time to complete the five single-leg squats, and tighter hamstrings as compared to the non-problem side. However, only the overall and anteroposterior sway path distances, terminal knee flexion angle, total squat duration, and hamstrings flexibility yielded moderate to strong agreement with the Clinical Pilates method. Conclusions: Single-leg squat postural sway parameters and hamstrings flexibility can objectively identify the problem side in adults with non-specific chronic LBP.

A DMPC-based three-dimensional cooperative guidance scheme with impact time and impact angle constraints

In this paper, a distributed model predictive control (DMPC)-based three-dimensional (3D) cooperative guidance scheme is proposed for multiple interceptors with controllable thrust and constrained acceleration, to simultaneously attack a maneuvering target at desired terminal angles. The cooperative guidance scheme consists of a fractional power function-based extended state observer (FPESO) for disturbance estimation, and a DMPC controller to generate the control actions. By introducing the assumed state trajectory, the DMPC controller (of each interceptor) can simultaneously employ the zebra optimization algorithm (ZOA) to solve the constrained optimization problem, and generate the real-time guidance commands with no need of any global information. For restricting the uncertain deviation between the assumed state trajectory and the actual one, a compatibility constraint is designed, and the terminal ingredients are developed for coupling and decoupling stage costs, respectively. By applying the above designed constraints and the terminal ingredients, the recursive feasibility of the resulting optimization problem and the closed-loop stability of multi-interceptor system are both ensured. Through numerical simulations, it is verified that the proposed cooperative guidance scheme can achieve cooperative interception with impact time and angle constraints in various scenarios, and has advantageous performance.

Three-dimensional adaptive dynamic surface guidance law for missile with terminal angle and field-of-view constraints

In this paper, an adaptive dynamic surface (DSC) guidance law for missile is designed to intercept the maneuvering target with field-of-view (FOV) and terminal angle constraints in three-dimensional(3D) space, and the missile autopilot dynamics is considered. Firstly, the time-varying transformation function related to line of sight (LOS) is used to replace the FOV constraints, transforming the process-constrained control problem into the output-constrained control problem. Meanwhile, the 3D coupled relative kinematics model considering missile autopilot dynamics and maneuvering target acceleration is established. Secondly, a novel time-varying asymmetric barrier Lyapunov function (TABLF) with dead-zone characteristics is introduced to the adaptive dynamic surface guidance law design process to improve the robustness of parameter debugging. Thirdly, with the help of a nonlinear adaptive filter, the ‘explosion of complexity’ problem can be avoided effectively, which is caused by analytic computation of virtual signal derivatives. Furthermore, aiming at the problem of autopilot dynamic errors, target acceleration disturbances, and unmeasurable parameters in the model, a novel adaptive law is used to evaluate online. Then, the stability of the closed-loop system is rigorously proven using Lyapunov criteria. Ultimately, Numerical simulations with various constraints and comparison studies have been considered to show the feasibility and effectiveness of the proposed missile guidance law.

Rapid and Near-Analytical Planning Method for Entry Trajectory under Time and Full-State Constraints

A rapid trajectory-planning method based on an analytical predictor–corrector design of drag acceleration profile and a bank-reversal logic based on double-stage adaptive adjustment is proposed to solve the entry issue under time and full-state constraints. First, an analytical predictor–corrector algorithm is used to design the profile parameters to satisfy the terminal of altitude, velocity, range, time, and flight-path angle constraints. Subsequently, an adaptive lateral planning algorithm based on heading adjustment and maintenance is proposed to achieve the flight stage adaptive division and determination of the bank-reversal point, thereby satisfying the terminal position and heading angle constraints. Concurrently, a rapid quantification method is proposed for the adjustable capacity boundary of the terminal heading angle. On this basis, a range-and-time correction strategy is designed to achieve high precision and the rapid generation of a three-degree-of-freedom entry trajectory under large-scale lateral maneuvering. The simulation results demonstrated that compared with the existing methods, the proposed method can adaptively divide flight stages, ensuring better multitask applicability and higher computational efficiency.

Design of air-breathing supersonic vehicle guidance law for intercepting the high maneuvering target with impact angle constraint

Abstract To achieve interception vehicles that can intercept high maneuvering targets with impact angle constraint, and improve the strike effectiveness of the vehicle, based on the two-dimensional planar motion model of the vehicle and the target, this article proposes a sliding mode control vehicle guidance law. The stability of the guidance law is verified through the Lyapunov function, and an extended state observer is set to check for disturbances. After simulation verification, the guidance law can intercept the target with predetermined terminal angle constraints and has good tracking performance.

Intelligent diving guidance with terminal angle and velocity constraints via deep reinforcement learning

An adaptive guidance strategy that integrates optimal guidance and deep reinforcement learning to address a highly dynamic terminal guidance problem that entails meeting terminal position, angle, and velocity constraints. The proposed strategy leverages optimal guidance commands to accomplish position and angle control while introducing a deep reinforcement learning-based bias for the velocity constraint. In the training process, a dual-velocity state space is constructed to enhance the adaptability of the strategy to different guidance tasks, while training is optimized using the prediction-correction and expert knowledge to improve the training efficiency and optimality of the strategy. Simulations demonstrate that the proposed guidance strategy can achieve simultaneous control of terminal position, angle and velocity, and adapt to different guidance tasks.

Electrospray plume divergence: Background pressure influence

The influence of background pressure on electrospray plume evolution is observed by simulating the emission and propagation of an electrospray particle population into an electric field at a range of relevant background pressures. Differences in plume evolution from atmospheric pressure to one hundredth of atmospheric pressure are evident from plume characteristics such as (1) the overall domain of the resulting plumes and (2) the terminal angle at a downstream terminus of one standard deviation and three standard deviations of particle number density. Plume divergence and terminal angle are shown to correlate strongly with background pressure for pressures above which plume-background collision rates are significant, consistent with experimental observations of increased plume divergence with increased background pressure. The results suggest a simple expression for the pressure below which a system achieves minimum plume divergence: Pth=kT/7.7299σfld for a system of temperature T, background fluid molecules with cross-section σfl, and plume species of diameter d.

Time-to-go based three-dimensional multi-missile spatio-temporal cooperative guidance law: A novel approach for maneuvering target interception

This research presents a novel approach called 'Time-to-target-based multi-missile spatio-temporal cooperative guidance' This approach enables the simultaneous guidance of multiple missiles, allowing them to intercept a maneuvering target from different terminal intercept angles to maximize damage. The article introduces a finite-time optimal cooperative guidance technique to reduce the load on missile engines in the line-of-sight (LOS) direction. It proposes a time-varying sliding mode guidance scheme, which is parameterized by the remaining flight time, for both longitudinal and lateral LOS directions. The scheme helps prevent excessive initial acceleration in the longitudinal and lateral LOS directions while ensuring intercept angle constraints. The time-varying cooperative guidance law proposed in this study enables the simultaneous interception of a maneuvering target with different terminal intercept angles at the moment of terminal intercept. The numerical simulation results indicate that the multi-missile spatio-temporal cooperative guidance method is effective, superior, and robust. The method enables multiple missiles to achieve the minimum acceptable intercept distance at different terminal intercept angles while optimizing fuel in the LOS direction.

Multi-UAV DMPC Cooperative Guidance with Constraints of Terminal Angle and Obstacle Avoidance

This paper studies the salvo attack problem for multiple unmanned aerial vehicles (UAVs) against a maneuvering target, and a guidance scheme based on distributed model predictive control (DMPC) is presented to achieve cooperative interception with constraints of terminal impact angle and no-fly zone (or obstacle) avoidance. Firstly, for guaranteeing the synchronization of UAVs in calculating their acceleration commands, the assumed predictive trajectories are introduced, whose deviation from the actual state trajectories is limited by the designed compatibility constraints. Secondly, based on the velocity-obstacle model, the obstacle avoidance constraints are presented, and for guaranteeing the convergence of impact time and impact angles, the auxiliary controller and terminal ingredients are developed, which complete the design of DMPC cooperative guidance scheme. Subsequently, the rigorous proof for the convergence of the proposed guidance scheme is provided. Based on the above design, a complete implementation process of the guidance scheme is presented, in which each UAV uses the particle swarm optimization algorithm to solve the preprocessed local optimization problem, and only the shared information among neighbors is utilized for calculation. Finally, the numerical simulations are conducted under diverse cases, which demonstrate the effectiveness of the proposed guidance scheme when solving cooperative interception problems with terminal angle and obstacle avoidance constraints.

Three-dimensional terminal angle constraint guidance law with class [formula omitted] function-based adaptive sliding mode control

This paper investigates the three-dimensional (3-D) interception guidance problem, where the missile is required to intercept the maneuvering target with the desired terminal angles. For the nonlinear relative kinematic model, a class K∞ function-based adaptive sliding mode guidance law is proposed, which ensures that the errors of terminal Line-of-Sight (LOS) angles converge to the small neighborhoods of origin at the time of interception, without relying on information about the target's acceleration. To overcome the challenges of large initial control input and chattering in existing sliding mode guidance laws, two improved control schemes are introduced. The first scheme is to directly impose saturation constraints into the adaptive gain. However, it is important to ensure that the unknown disturbance remains within the prescribed saturation bound. To avoid the limitation, another approach involves introducing auxiliary dynamics to eliminate the reaching phase and slow down the convergence of LOS angles by presetting the convergence time of the sliding mode variables, which helps mitigate excessive initial control inputs. Numerical simulations are conducted using a realistic missile model and considering a 3-DOF point-mass aircraft as the target to evaluate three different guidance laws. The results indicate that the proposed guidance law ensures interception accuracy while substantially reducing the control gain.

Prescribed-Time Chattering-Free Sliding Mode Guidance Law with Terminal Angle Constraint Based on Periodic Delayed Feedback

Prescribed-Time Chattering-Free Sliding Mode Guidance Law with Terminal Angle Constraint Based on Periodic Delayed Feedback

Fried-Breadstick sign: A novel marker for healthy vasculature in magnetic resonance angiography

The Fried-Breadstick sign is characterized as a continuous signal loss at the center of the intracranial internal carotid artery (ICA) on time-of-flight magnetic resonance angiography (TOF-MRA). In this study, we present a novel imaging marker on TOF-MRA and investigate its potential association with ICA-middle cerebral artery (ICA-MCA) atherosclerosis and ischemic stroke. Vessel wall magnetic resonance imaging data were obtained from patients with recent clinical stroke or asymptomatic patients with suspected middle cerebral artery (MCA) atherosclerosis, covering the period from January 2007 to August 2015. We conducted a comparative analysis of ICA stenosis, MCA atherosclerosis and stenosis degree, and the terminal ICA bifurcation angle between ICA-MCAs with and without the Fried-Breadstick sign, involving a total of 1,005 ICA-MCAs from 553 patients. The Fried-Breadstick sign exhibited a higher prevalence in non-to-mild stenotic ICAs (57.5% vs. 9.8% in severely stenotic ICA, P < 0.001) and plaque-free MCAs (53.2% vs. 26.6% in MCAs with plaque, P < 0.001). Factors independently associated with the presence of the Fried-Breadstick sign included MCA stenosis degree (odds ratio [OR]: 0.85/10% increase, 95% confidence interval [CI]: 0.80 – 0.90), ICA stenosis (compared to non-to-mild stenosis, moderate stenosis: OR: 0.39, 95% CI: 0.28 – 0.54, severe stenosis: OR: 0.10, 95% CI: 0.06 – 0.17), and terminal ICA bifurcation angle (OR: 0.86/10° increase, 95% CI: 0.79 – 0.93). In atherosclerotic MCAs without luminal narrowing, the Fried-Breadstick sign was also less frequently observed than in plaque-free MCAs (34.6% vs. 53.2%, P = 0.012). In conclusion, the presence of the Fried-Breadstick sign is associated with healthier ICA-MCAs devoid of stenosis or plaque. The Fried-Breadstick sign may signify healthy ICA-MCA hemodynamics, serving as a potential screening tool for intracranial atherosclerosis without incurring additional cost or risk.

Effects of McConnell and Kinesio taping on kinematic variables during stair descent in patients with patellofemoral pain syndrome.

Studies regarding effects of therapeutic tapings when patients with patellofemoral pain syndrome (PFPS) descend stairs are limited. The purpose of this study was to investigate the effect of McConnell taping (MT) and Kinesio taping (KT) on kinematic variables when patients with PFPS descend stairs. Fifty PFPS patients were randomly assigned to either the MT group or the KT group. Pain and lower extremities joint angles were measured while descending stairs before and after the intervention. All outcomes measured were analyzed using either paired t tests or independent t tests to compare the difference within or between groups, respectively. There was a statistically significant difference in both groups in anterior knee pain scale score (p< 0.05). As a result of analysis of lower extremities joint angles at initial contact, loading response, and terminal stance, there were statistically significant within-group differences in hip, knee flexion, abduction and lateral rotation angles in both groups (p< 0.05). There were statistically significant within-group differences in hip flexion, knee flexion, and dorsiflexion angles in pre-swing (p< 0.05). There was a statistically significant difference between the groups in the following events: (1) knee lateral rotation angle at initial contact; (2) hip flexion angle at loading response; (3) and hip flexion at terminal stance angle (p< 0.05). MT and KT were effective in lowering knee pain and improving lower extremities joint angle when patients with PFPS descend stairs. In the comparison between the groups, the MT group showed significantly reduced anterior knee pain and increased range of motion of the lower extremities joint compared to the KT group.

Usefulness of CineECG method in identification of P-wave morphology variants in an elderly epidemiologic cohort

Abstract Background Biphasic P waves in inferior leads categorizes interatrial block (IAB) into partial or advanced subtypes. P-wave morphology is highly variable, and visual assessment of P-wave morphology is subjective, especially in case of low-amplitude P waves. CineECG is a non-subjective approach which is not sensitive to signal amplitude, and which can also calculate terminal P-wave angle. Purpose To assess the relationship between P-wave morphology in inferior ECG leads, categorization of the IAB subtypes and terminal P-wave angle using CineECG in an elderly epidemiologic cohort. Methods We included participants with sinus rhythm on an ECG collected 2002-2006 in the general-population based Malmö Preventative Project (n=983, age 70±5 years, 38% females). ECGs were digitally processed using the Glasgow algorithm. IAB was defined as a P-wave ≥120 ms and classified regarding as partial (pIAB, P waves affected in none [pIAB-0] or only 1 inferior lead III [p-IAB-1]) or advanced (aIAB, P waves affected in leads III and aVF [aIAB-2] or all 3 inferior leads [aIAB-3, typical aIAB]). All ECGs were also processed using CineECG. The vectorcardiogram was computed from the 12 lead ECG and a generic model of the atria and torso, with average body build and heart orientation. We used the terminal P-wave angle as the variable which describes the direction of the terminal part of P wave in the frontal plane (Figure). Results IAB was documented in 413 (42%) subjects: 344 (35%) had pIAB (199 (20%) with pIAB-0; 145 (15%) with pIAB-1) and 60 (6.5%) had aIAB (45 (5%) with aIAB-2 and 15 (1.5%) with aIAB-3 or typical aIAB). P wave morphology could not be categorized by these definitions in 9 subjects. Terminal P wave angle correlated with P wave morphology (Spearman’s r=0.127, p&amp;lt;0.001) and progressively increased with increase of P wave morphology class from pIAB-0 to aIAB-3 (Figure, Table). Conclusion Morphology variants of IAB can be classified depending on the degree of the terminal P wave angle which correlates with the order and number of bipolar inferior leads. CineECG provides an instrument for 3D quantification of the terminal atrial depolarization direction which can be used to detect IAB in an earlier stage.Figure.Atrial depolarisarion and IAB.

Distributed adaptive cooperative guidance against maneuvering targets with time-varying terminal angle constraint and overload saturation

Distributed adaptive cooperative guidance problem for multiple missiles intercepting a maneuvering target with time-varying terminal angle constraint and overload saturation is investigated in this paper. First of all, an extended state observer (ESO) is designed for each missile which can estimate the line-of-sight (LOS) rate and unknown external disturbances simultaneously. Secondly, a sliding manifold is proposed for each missile which consists of states of the ESO and neighbor terminal angle formation error. Then, a distributed cooperative guidance law is presented which can achieve the terminal angle constrained cooperative guidance. Furthermore, in order to deal with overload saturation, an auxiliary state is designed for the stability of the whole guidance system. Thirdly, the design process of cooperative guidance law is summarized as a guidance algorithm and the stability of the guidance error dynamics is proved via Lyapunov theories. Finally, the validity of the presented cooperative guidance algorithm is demonstrated by a numerical example.

Nonlinear three dimensional all-aspect guidance with terminal impact angle constraints

In this paper, a nonlinear three dimensional all-aspect guidance law, to intercept maneuvering target at pre-specified orientation, is presented. Without decoupling the engagement kinematics into two perpendicular planes, the proposed guidance law is derived in three dimensions directly. More importantly, the proposed strategy is an ‘all-aspect’ guidance law, which allows missile to intercept the target at the desired impact angle, even in the presence of very large initial pointing errors. First, in order to design a guidance law with all-aspect interception capability, the collision conditions analysis process is carefully developed and an additional necessary constraint condition is derived. Then, based on chattering reduction sliding mode control, a nonlinear three dimensional terminal impact angle constrained guidance law is derived considering maneuvering targets. After capturability analysis, an additional sliding mode surface and a switching logic are further designed, so that the all-aspect capability is guaranteed. Finally, numerical simulations are provided to demonstrate the effectiveness of the proposed guidance strategy.

Ballistic Missile Trajectory Design Considering Impact Angle Constraint

The current paper investigates the problem of guiding ballistic re-entry vehicles to the terminal point under the additional terminal constraint of final flight path angle. In this regard, the classical Lambert’s Problem is reformulated to include the final flight path angle constraint. The proposed solution of the modified Lambert’s problem consists of a minimum of two different trajectories starting from the same initial location and intersecting each other at a location, which is determined by applying the desired time of flight and terminal flight path angle constraints. The modified Lambert strategy strategy is shown to satisfy terminal flight path angle constraint along with the time of flight, initial and final location constraints. This scheme requires the ballistic vehicle to perform an additional stage burn during descent in-order to switch from an initial trajectory, using Lambert strategy, to a final trajectory which satisfies the final flight path angle constraint. An additional stage burn is provided such that the position and velocity of the vehicle traveling in the initial trajectory is matched with that required for it to be on the final trajectory. It is also found that the amount of propellant required for the trajectory transfer, is dependent on the total time of flight and the altitude at which the additional stage burn occurs. The optimal values of these two parameters are found using interior-point optimization technique.

Synthesis of Suboptimal Guidance Law for Anti-Tank Guided Missile with Terminal Impact Angle Constraint Based on the SDRE Technique

In this paper, the homing-phase guidance law is proposed against a stationary target in the planar engagement scenario. In this problem, two technical criteria that the guidance law must achieve are: first, zero terminal miss distance, and second, satisfying the desired impact angle constraint at the final time. This guidance law is synthesized as a nonlinear optimal control problem with an infinite-time horizon and is solved using the state-dependent Riccati equation (SDRE) method. To obtain a guidance law with a finite-time horizon, a state weighting matrix based on the time-to-go is utilized in the SDRE control scheme. The synthesized guidance law is applied to a new generation anti-tank guided missile class, with specific thrust and drag parameters. Nonlinear simulations are conducted to demonstrate the fundamental properties, applicability, and effectiveness of the proposed guidance law.

The Concept and Understanding of Synchronous Stability in Power Electronic-Based Power Systems

Synchronous stability in power systems is of essential importance for system safety and operation. For the phase-locked loop (PLL)-based synchronous stability in power electronic-based power systems, which has recently stimulated interest in researchers in the field of electrical power engineering, but is still controversial, this paper divides the topic into two aspects, including the PLL device stability and the system stability. It is found that the PLL device is always stable and the error between the PLL output angle θpll and the terminal voltage angle θt is always finite. Therefore, the synchronization of power electronic-based power systems should be understood as the output synchronization between the electrical rotation vectors (θt or θpll) from each item of grid-tied equipment, rather than the synchronization of the PLL device itself. In addition, it is found that θpll plays an active role in the system synchronization dynamics not only in electromagnetic timescales but also electromechanical timescales and it could be selected as a dominant observable. In this paper, the concept of synchronous stability is well clarified. These findings are well supported by theoretical analyses and MATLAB/Simulink simulations, and thus could provide insights on the synchronous stability mechanism.

Design of finite time cooperative mid-course guidance law for unmanned target drone aircrafts

For cooperative mid-course guidance problem of multiple unmanned target drone aircrafts(UTDA), a novel cooperative guidance law with impact angle constraints is proposed in this study. Firstly, the relative motion equation of UTDAs and target, and the multiple-UTDA cooperative guidance model with impact angle constraints are constructed. Then, the process of cooperative guidance law design is divided into two stages. In the first stage, the acceleration command on the LOS direction is designed based on the fixed-time consensus theory, the speed dimension is introduced which can guarantee the consensus of all UTDAs' impact times in fixed time. In the second stage, an impact-angle-control guidance law is proposed based on the approaches of variable coefficients sliding mode control and finite-time convergence theory to reach the virtual targets, the acceleration command on the direction of perpendicular to the LOS is developed, which can ensure that all the LOS angles converge to the desired terminal LOS angle in finite-time and some mobility when approaching the virtual targets is achieved, and the Lyapunov stability is adopted. Finally, numerical simulations express that the cooperative mid-course guidance law designed in this study can make each UTDA reach the virtual target at the same time with small miss distance and meet the LOS constraint, and demonstrate the effectiveness of the proposed mid-course guidance law.