Constant Velocity Research Articles

Training Interventions for Improved Deceleration Ability in Adult Team-Based Field Sports Athletes

Background: Deceleration is a fundamental component of multidirectional speed by which athletes reduce the velocity of their centre of mass to stop or execute changes of direction following acceleration or running at a constant velocity. Enhancing deceleration abilities is crucial for athletes as successfully executing horizontal deceleration has important implications for match outcomes in sports requiring rapid multidirectional movements. However, specific training interventions targeting deceleration are scarce. The purpose of this systematic review and meta-analysis was to examine the effects of training interventions on deceleration performance in adult team-based field and court sports athletes. Methods: A systematic literature search was conducted through electronic databases, SPORTdiscus, PubMed, and Web of Science from inception to February 2022, and re-run in May 2023. The search terms were related to different training interventions and kinetic, kinematic, and performance outcomes related to deceleration performance. Studies were included if they consisted of a randomised controlled trial which investigated the effects of training on deceleration-specific outcome measures in adult team-based field and court sports athletes. Risk of bias was assessed using the revised Cochrane risk-of-bias tool for randomised trials (RoB2). Post-intervention effect sizes (Hedge’s g) were calculated between the intervention and control groups and a meta-analysis was performed using a random effects model. Results: Twelve studies were included, with 29 deceleration-specific outcomes measured in a total of 381 participants. There was inconsistency in methodological designs, including control group types, length and type of interventions and in reported deceleration-specific outcome measures. Across all observations of deceleration performance measures there was a standardised mean difference of -0.04 (95% CI: -0.50, 0.42), favouring control groups, indicating little effect of training on deceleration performance. For secondary outcomes related to deceleration, for kinetics (SMD = -0.29, 95% CI = -0.83, 0.25, I2 = 55%, p < 0.01), joint kinetics (SMD = -0.20, 95% CI = -1.01, 0.61, I2 = 68%, p < 0.01) and muscle activation (SMD = -0.10, 95% CI = -0.44, 0.24, I2 = 19%, p = 0.28) had greater effects for control groups, whereas joint kinematics (SMD = 0.07, 95% CI = -0.11, 0.24, I2 = 0%, p = 0.77), favoured the intervention groups. Conclusion: For the deceleration-specific outcomes reported in the included studies, training was not likely to produce a performance improvement in participants compared to control groups. However, due to methodological inconsistencies between studies and observed high risk of bias, the results should be interpreted with caution. More rigorous research methods should be included in the future to address areas that may introduce potential biases. Future research should address the differences in the type, timing, frequency, and duration of the implemented training interventions for improving deceleration performance, and in the reported deceleration-specific outcome measures. Registration: This systematic review was registered on the Open Science Framework (https://osf.io/cmwbr) (https://doi.org/10.17605/OSF.IO/CMWBR)

Variation in wear scar penetration depths due to impact angle on the erosion wear of advanced aluminum matrix nanocomposites

In present study, developing (Al-Fe-Si) materials with high wear and erosion resistance for aerospace components, such as wing skin and fuselage sections, presents a significant challenge for researchers. This study delves into the reinforcement effects of TiC in aluminum composites, produced via ultrasonic-assisted stir casting. The focus lies on exploring the UASC technique to create composites with varied TiC weight percentages (0 %, 2 %, 4 %, and 6 % by weight) and evaluating their erosion resistance. Experiments varied erodent particle impact angle, velocity, and discharge rate, alongside impingement angles, and maintaining a constant velocity of 151 m/s for 10-minute durations, using solid particles averaging 201 µm in size. Increasing TiC content improved erosion resistance. Optical profilometry revealed a −131 µm maximum wear scar depth at a 45° impingement angle, with significantly higher erosion wear compared to other angles. These findings offer valuable insights for enhancing mechanical system design and durability. Eroded surface failure analysis utilized FE-SEM images to examine composites impacted by erodent forces.

Electromagnetic field coupled circuits and open‐loop control of fast starting processes in induction motors

AbstractTo solve the problems of difficulty in speed measurement and low accuracy of speed measurement of induction motor (IM) during fast starting, the electromagnetic field coupling circuit (EFCC) and open‐loop control of IM considering rapid speed change are proposed. First, the EFCC of IM is established through the stator circuit, air gap magnetic field circuit and rotor circuit, and the stator voltage and electromagnetic torque of the fast starting process are deduced from the air gap magnetic density on the basis of constant slip angular velocity, and then the open‐loop control method based on the EFCC is given. Finally, compared with the open‐loop control based on the TEC, the results of simulation and experiment show that the open‐loop control based on the EFCC can follow the acceleration starting more quickly and the starting current is smaller, which is conducive to reducing the cost of the drive.

A novel method for acoustic emission source location in CFRP-concrete debonding using ΔT mapping and DBSCAN algorithm

Concrete-CFRP composite structures exhibit a stiff behavior, leading to sudden failure. Monitoring the brittle nature of this failure is crucial, and the acoustic emission (AE) technique provides a promising tool for locating and classifying damage. However, the conventional source location methodology assumes that the acoustic wave travels in a straight path with constant velocity. This assumption does not hold true for concrete-CFRP composite structures, where the presence of microcracks and CFRP layers induces anisotropy and defects, altering the wave speed and traveling direction. This, in turn, introduces errors in the source location. To address these challenges, this research presents a novel source location method using ΔT maps and achieving convergence through the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm. The methodology demonstrates significant improvement in AE source location when applied to concrete-CFRP composite specimens in the presence defects with varying magnitudes. Additionally, the proposed method shows effectiveness in monitoring damage progression when applied to single-lap shear tests performed on concrete specimens with attached CFRP laminate.

True triaxial test and DEM simulation of rock mechanical behaviors, meso-cracking mechanism and precursor subject to underground excavation disturbance

Mechanical excavation or blasting generates stress waves that rapidly dissipate in the surrounding high-geostress rock, causing microdynamic disturbances. These disturbances trigger microcracks within the damaged rock, even inducing engineering disasters. However, the fracture behaviors and mechanisms of rockmass subjected to excavation disturbances under three-dimensional geostress remains unclear. Therefore, this study proposed a true triaxial static–dynamic combined loading method to capture the entire process of tunnel excavation damage and the continuous fracturing induced by microdynamic disturbances. True triaxial static–dynamic combined tests and numerical simulations using PFC3D-GBM were employed systematically to analyze the influence of principal stresses σ1, σ2, and σ3 on the disturbances mechanical behaviors of the gabbro. The disturbance failure under true triaxial stress indicated a three-stage pattern of deformation: deceleration, constant velocity, and acceleration. With increased σ1 or decreasing σ2 and σ3, the disturbance bearing capacity of the gabbro significantly decreased. Moreover, an increase in σ1 and σ3 corresponded to an increased proportion of intergranular shear cracks, whereas an increase in σ2 resulted in a notable increase in intragranular tensile cracks. Small-magnitude events tended to disperse during the deceleration and constant-velocity stages, whereas larger-magnitude events were concentrated during the acceleration stage. The AE parameter b-value initially increased and then decreased during disturbance fracture process. The excavation disturbance of the tunnel intensified the depth of the damage zone and the energy released, thereby increasing the risk of a catastrophic deep fracture.

Optimization of heat transfer rate of trihybrid nanofluid Embedded between two horizontal coaxial cylinders by RSM

Heat pipes are heat transfer devices that carry heat from one point to another efficiently. The thermal conductivity and heat transfer performance of the heat pipe can be increased by integrating nanofluids, making them appropriate for applications such as electronics cooling, spacecraft thermal management, and heat recovery systems. The suggested work is being carried out for the approximate solution of tri-hybrid nanofluid (copper (Cu), silver (Ag) and graphene oxide (GO)) flow between two horizontal coaxial cylinders. The inner cylinder is rotating with constant velocity and the outer cylinder is fixed. Moreover, the flow is under the influence of magnetic field. The system of governing partial differential equations is converted into a set of non-linear ordinary differential equations by incorporating the suitable similarity transformation and then solved numerically by employing Runga-Kutta 4th order technique. Response surface methodology (RSM) is also incorporated in order to optimize the heat transfer rate by the various combinations of the physical parameters involved in the study. The study revealed that the temperature of the nanofluid increased by raising the strength of the Reynolds number and melting parameter. From optimization technique RSM it came to know that the heat transfer rate reached its peak value when the strength of the Reynolds number and concentration of the nanoparticle of the fluid is higher than normal.

Savonius-Magnus Hybrid Turbine Design Performance Based on Computational Fluid Dynamics

Savonius turbine is a vertical-axis wind turbine (VAWT), which has the advantage of being able to capture wind from different directions. This turbine is suitable for high turbulent wind areas. The blade on the Savonius turbine used in this study is equipped with a Magnus rotor with dimensions of 120 mm in diameter and 720 mm in height. The main purpose of this study is to determine the torque and pressure generated by turbines with three and four blades. The design was then tested numerically with variations in wind velocity. The simulation model was created using computer-aided design software, namely Autodesk Inventor 2023, and then inputted into computational fluid dynamics (CFD) software, namely Ansys Workbench 2022 R2. Wind velocities were varied by 3, 5, 7, 9, and 11 m/s and simulated using transient time with constant wind velocity. The result of this study is that the largest pressure is generated by a hybrid turbine with four blades at a wind velocity of 11 m/s. The results show that the torque and wind pressure that occurs in three- and four-blade hybrid turbines tend to rise; the faster the wind, the higher the torque and pressure of both hybrid turbines

Third sound detectors in accelerated motion

An accelerated observer moving through empty space sees particles appearing and disappearing, while an observer with a constant velocity does not register any particles. This phenomenon, generally known as the Unruh effect, relies on an initial vacuum state, thereby unifying the experience of all inertial observers. We propose an experiment to probe this observer-dependent detector response, using a laser beam in circular motion as a local detector of superfluid helium-4 surface modes or third sound waves. To assess experimental feasibility, we develop a theoretical framework to include a non-zero temperature initial state. We find that an acceleration-dependent signal persists, independent of the initial temperature. By introducing a signal-to-noise measure we show that observing this signal is within experimental reach.

Investigation of accelerated moving load on dynamic response of FG Timoshenko nanobeam in thermal environment based on nonlocal strain gradient theory

For the first time, this paper investigates the forced vibrations of a functionally graded (FG) nanobeam with an accelerating moving load in a thermal environment. There is no exact coupling solution for the vibrations of nanobeam with an accelerated moving load, so this paper aims to provide a method to obtain an accurate solution for nanoscale structures with an accelerated moving load. The equations of motion are derived using Timoshenko's beam theory and the nonlocal strain gradient theory (NSGT). The Laplace method has been used to solve the coupling and exact differential equations. Then, by inverting Laplace from the coupled equations, an exact solution of the temporal response for FG nanobeam with constant acceleration and initial velocity in a thermal environment was obtained. The natural frequency was compared with previous works for validity and had acceptable results. Finally, the effect of parameters such as changes in acceleration and velocity of moving force, negative acceleration, power law index of FG material, different temperatures, nonlocal parameter, and longitudinal scale parameter on the maximum dynamic displacement of nanobeam is investigated. These results can be used better to design FG nanostructures with accelerated moving loads. Considering the sensitivity of data analysis in nano dimensions, it is necessary to provide an analytical solution method in these dimensions to reduce the error percentage in nano dimensions to zero. which is presented in this work for the first time.

A virtual wind tunnel for deforming airborne wind energy kites

This paper presents a quasi-steady simulation framework for soft-wing kites with suspended control unit employed for airborne wind energy. The kites are subject to actuation-induced and aero-elastic deformation and are described by a coupled aero-structural model in a virtual wind tunnel setup. Key contributions of the present work are a kinetic dynamic relaxation algorithm and a procedure to define a physically consistent initial state. For symmetric actuation, the kite is pitch-statically stable and the simulations converge to a static equilibrium state. Most soft-wing kites are not roll-statically stable and do not find a static equilibrium without a symmetry assumption, as this introduces non-zero roll- and yaw moments. Another important contribution is the introduction of a steady circular flight state that enables convergence without a symmetry assumption. By neglecting gravity, the kite can fly in a perfectly circular turning motion around the wind vector with a constant radius and constant rotational velocity without requiring active control input. In an idealized wind-aligned tether case, the difference in aerodynamic- and centrifugal force application centers makes it impossible to achieve both a force- and moment equilibrium. This was resolved by including an elevation angle that introduces a radial tether force component, which introduces a centrifugal and aerodynamic force difference. Therefore, an operating point with roll equilibrium can be found where the kite finds a static equilibrium, enabling the first quasi-steady simulations of turning flights. Simulated quantifications of soft-wing kite turning behavior, i.e., turning laws, contribute to better kite- and control design.

Improved Transcranial Plane-Wave Imaging With Learned Speed-of-Sound Maps.

Although transcranial ultrasound plane-wave imaging (PWI) has promising clinical application prospects, studies have shown that variable speed-of-sound (SoS) would seriously damage the quality of ultrasound images. The mismatch between the conventional constant velocity assumption and the actual SoS distribution leads to the general blurring of ultrasound images. The optimization scheme for reconstructing transcranial ultrasound image is often solved using iterative methods like full-waveform inversion. These iterative methods are computationally expensive and based on prior magnetic resonance imaging (MRI) or computed tomography (CT) information. In contrast, the multi-stencils fast marching (MSFM) method can produce accurate time travel maps for the skull with heterogeneous acoustic speed. In this study, we first propose a convolutional neural network (CNN) to predict SoS maps of the skull from PWI channel data. Then, use these maps to correct the travel time to reduce transcranial aberration. To validate the performance of the proposed method, numerical, phantom and intact human skull studies were conducted using a linear array transducer (L11-5v, 128 elements, pitch = 0.3 mm). Numerical simulations demonstrate that for point targets, the lateral resolution of MSFM-restored images increased by 65%, and the center position shift decreased by 89%. For the cyst targets, the eccentricity of the fitting ellipse decreased by 75%, and the center position shift decreased by 58%. In the phantom study, the lateral resolution of MSFM-restored images was increased by 49%, and the position shift was reduced by 1.72 mm. This pipeline, termed AutoSoS, thus shows the potential to correct distortions in real-time transcranial ultrasound imaging, as demonstrated by experiments on the intact human skull.

Entangled states dynamics of moving two-level atoms in a thermal field bath

We consider a two-level atom that follows a wordline of constant velocity, while interacting with a massless scalar field in a thermal state through: (i) an Unruh–DeWitt (UDW) coupling, and (ii) a coupling that involves the time derivative of the field. We treat the atom as an open quantum system, with the field playing the role of the environment, and employ a master equation to describe its time evolution. We study the dynamics of entanglement between the moving atom and a (auxiliary) qubit at rest and isolated from the thermal field. We find that in the case of the standard UDW coupling and for high temperatures of the environment the decay of entanglement is delayed due to the atom’s motion. Instead, in the derivative coupling case, the atom’s motion always causes the rapid death of entanglement.

A study of particle dry deposition parameterizations in an atmospheric radioactive preparedness model: Application to the Chernobyl case

Parameterization of dry deposition is key for modelling of atmospheric transport and deposition of radioactive particles. Still, very simple parameterizations are often encountered in radioactive preparedness models such as the SNAP model (SNAP=Severe Nuclear Accident Program) of the Norwegian Meteorological Institute. In SNAP a constant dry deposition velocity (=0.2 cm/s) neglecting aerodynamic and surface resistances, is presently used. Therefore, two new dry depositions schemes (the Emerson scheme and the EMEP (European Monitoring and Evaluation Programme) scheme) have been implemented in SNAP to evaluate the benefits of including aerodynamic and surface resistances codes with respect to model prediction skills. The three dry deposition schemes are evaluated using 137Cs total deposition from soil sample data (n = 540) for a 60 km radial zone out from the Chernobyl Nuclear Power Plant (ChNPP) collected during the months after the accident. The present study capitalizes on high resolution meteorological data (2.5 km horizontal resolution), a detailed land-use data set with 273 sub-classes and the hitherto most comprehensive source term description for the Chernobyl accident. Based on our findings it is recommended to replace the present simple SNAP scheme with the Emerson or EMEP dry deposition scheme.

Advancing Sea Surface Height Retrieval through Global Navigation Satellite System Reflectometry: A Model Interaction Approach with Cyclone Global Navigation Satellite System and FengYun-3E Measurements

The measurement of sea surface height (SSH), which is of great importance in the field of oceanography, can be obtained through the innovative technique of GNSS-R for remote sensing. This research utilizes the dataset from spaceborne GNSS-R platforms, the Cyclone Global Navigation Satellite System (CYGNSS) and FengYun-3E (FY-3E), as the primary source of data for retrieving sea surface height (SSH). The utilization of artificial neural networks (ANNs) allows for the accurate estimation of ocean surface height with a precision of meter-level accuracy throughout the period of 1–17 August 2022. As a traditional machine learning method, an ANN is employed to extract pertinent data features, facilitating the acquisition of precise sea surface height estimations. Additionally, separate models are devised for both GNSS-R platforms, one based on constant velocity (CV) and the other on constant acceleration (CA). The Interactive Multiple Model (IMM) is utilized as the main method to combine the four models and convert the likelihood of each model. The transition between the models allows the filters to effectively adapt to dynamic changes and complex environments. This approach relies on the fundamental notion of the Kalman filter (KF), which showcases robust noise handling capabilities in predicting the SSH, separately. The results demonstrate that the model interaction technology is capable of efficiently filtering and integrating SSH data, yielding a Root Mean Square Error (RMSE) of 1.03 m. This corresponds to a 9.84% enhancement compared to the retrieved height from CYGNSS and a 37.19% enhancement compared to the retrieved height from FY-3E. The model proposed in this paper provides a potential scheme for the GNSS-R data fusion of multiple platforms and multiple models. In the future, more data sources and more models can be added to achieve more accurate adaptive fusion.

Examination of smart battery thermal management system using the counter flow of air and nanofluid for cooling cylindrical rechargeable batteries for better resilience

This paper examines smart thermal management of a battery pack (BTK) with a square arrangement of 16 cylindrical battery cells numerically. The cooling of the battery is carried out simultaneously using laminar airflow in a channel and laminar nanofluids (NFs) flow in the tube inserted between the battery cells. The BTK includes rechargeable lithium-ion cells and a tube placed in the channel. The inlets of air and NFs are counter-flow, and the study is done at constant air velocity for different NFs velocities in the tube from 0.001 to 0.003 m/s and different volume percentages (VOP) of NFs from 1 % to 3 %. The numerical study is performed transiently using the finite element method in 2000 s. The results demonstrate that the use of NFs and air for the thermal management (THMT) of battery cells results in better temperature uniformity on the battery cells, especially in the rows placed at the outlet. An increment iimproveP of nanoparticles improves the heat transfer coefficient (HTRC) between air and NFs flows. Also, enhancing the VOP of NFs increases the temperature of the outlet air and decreases the temperature of the outlet NFs. The average temperature (T-Av) and the maximum temperature (T-Mx) of the BTK are high until the battery is charged. They are reduced when the battery charge is stopped due to the air and NFs flows.

Experimental Heat Transfer Analysis of a New Turbulator in a Concentric Heat Exchanger Tube: A Full Factorial Design Approach

Abstract People have been looking for alternative energy sources because current sources may be depleted. Furthermore, it is critical to utilize available energy sources as effectively as possible. Turbulators are among the topics to consider when it comes to energy efficiency. In practice, turbulators are often used in exchangers to enhance heat transfer. Putting newly constructed turbulators in determined locations of the constant surface temperature heat exchanger, velocity, temperatures, pressure, and flow measurements have been performed in the inlet and outlet. In the case of using different numbers of turbulators, their placement in different locations, their arrangement at different distances, and their use at different Reynolds, the changes in pressure drop, Nusselt number, friction factor, efficiency, exergy loss rate, and NTU were determined with the full-factor experimental design. When the test data were evaluated, it was seen that as the number of turbulators increased, the thermal efficiency, friction factor, and pressure loss also increased. Using turbulators in different numbers, at different positions, at different distances, and with different Reynolds numbers, the effect ratio on the pressure loss, Nusselt number, and friction factor parameters was detected. In the analyses made, the most efficient parameters on heat transfer were determined, respectively, as Reynolds number (64.55%), the position of turbulators (19.73%), the distance between turbulators (6.09%), and the number of turbulators (5.94%).

Pressure propagation mechanism of open-cell aluminium foam within a pipe under hypervelocity impact

Low-density open-cell aluminium (Al) foam exhibits a different deformation mode under hypervelocity impacts compared to being subjected to medium-low speed and quasi-static compression. In this case, material flows between cells in the form of metal jets and propagates forward. This paper establishes the open-cell Al foam model based on Voronoi tessellation. Using numerical methods, one-dimensional hypervelocity constant velocity impact experiments of 1–6 km/s inside a closed pipe are conducted on Al foam with different internal structure parameters (average cell diameter: 2–3.5 mm; ligament width: 0.251–1 mm). Propagation mechanism of pressure waves in foams and the key factors affecting the propagation velocity are investigated. Three zones are divided according to the condition of jet distribution along the impact direction: unaffected zone, jet influence zone, and particle accumulation zone. The variation of the length of different zones with impact velocity is discussed: higher velocities result in longer jet influence zones but shorter particle accumulation zones. Meanwhile, length of zones is closely related to the width of Al foam ligament and cell pore diameter: the larger the diameter of cell pores and the smaller the width of ligaments, the longer the length of the jet influence zone. Time dependence is exhibited in the length of jet influence zone for the large cell pore diameter specimens(≥0.03 cm). Particle pressures are extracted using the one-dimensional averaging method, which propagates forward significantly lower than in dense materials. Dominant factors affecting the pressure wave propagation of open-cell Al foam, i.e., the internal unloading space, are obtained by combining two-dimensional hypervelocity impact simulation experiments with different boundary conditions. A strong correlation between metal jet distribution and particle pressure propagation is observed.

Critical Velocities of Single-layer and Two-layer Composite Tubes of Transversely Isotropic Materials Based on a Potential Function Method in 3-D Elasticity

Abstract Critical velocities of a single-layer tube of a transversely isotropic material and a two-layer composite tube consisting of two perfectly-bonded cylindrical layers of dissimilar transversely isotropic materials are analytically determined using the potential function method of Elliott in three-dimensional (3-D) elasticity. The displacement and stress components in each transversely isotropic layer of the tube subjected to a uniform internal pressure moving at a constant velocity are derived in integral forms by applying the Fourier transform method. The solution includes those for a tube composed of two dissimilar cubic or isotropic materials as special cases. In addition, it is shown that the model for the two-layer composite tube can be reduced to that for the single-layer tube. Closed-form expressions for four critical velocities are derived for the single-layer tube. The lowest critical velocity is obtained from plotting the velocity curve and finding the inflection point for both the single-layer and two-layer composite tubes. To illustrate the newly developed models, two cases are studied as examples – one for a single-layer isotropic steel tube and the other for a two-layer composite tube consisting of an isotropic steel inner layer and a transversely isotropic glass-epoxy outer layer. The numerical values of the lowest critical velocity predicted by the new 3-D elasticity-based models are obtained and compared with those given by existing models based on thin- and thick-shell theories.

Efficacy of a Single-Bout of Auditory Feedback Training on Gait Performance and Kinematics in Healthy Young Adults.

This study investigated the immediate effects of auditory feedback training on gait performance and kinematics in 19 healthy young adults, focusing on bilateral changes, despite unilateral training. Baseline and post-training kinematic measurements, as well as the feedback training were performed on a treadmill with a constant velocity. Significant improvements were seen in step length (trained: 590.7 mm to 611.1 mm, 95%CI [7.609, 24.373]; untrained: 591.1 mm to 628.7 mm, 95%CI [10.698, 30.835]), toe clearance (trained: 13.9 mm to 16.5 mm, 95%CI [1.284, 3.503]; untrained: 11.8 mm to 13.7 mm, 95%CI [1.763, 3.612]), ankle dorsiflexion angle at terminal stance (trained: 8.3 deg to 10.5 deg, 95%CI [1.092, 3.319]; untrained: 9.2 deg to 12.0 deg, 95%CI [1.676, 3.573]), hip flexion angular velocity, (trained: -126.5 deg/s to -131.0 deg/s, 95%CI [-9.054, -2.623]; untrained: -130.2 deg/s to -135.3 deg/s, 95%CI [-10.536, -1.675]), ankle angular velocity at terminal stance (trained: -344.7 deg/s to -359.1 deg/s, 95%CI [-47.540, -14.924]; untrained: -340.3 deg/s to -376.9 deg/s, 95%CI [-37.280, -13.166s]), and gastrocnemius EMG activity (trained: 0.60 to 0.66, 95%CI [0.014, 0.258]; untrained: 0.55 to 0.65, 95%CI [0.049, 0.214]). These findings demonstrate the efficacy of auditory feedback training in enhancing key gait parameters, highlighting the bilateral benefits from unilateral training.

Sequential Optimal Trajectory Planning Scheme for Robotic Manipulators along Specified Path Based on Direct Collocation Method

Robotic manipulators play a pivotal role in modern intelligent manufacturing and unmanned production systems, often tasked with executing specific paths accurately. However, the input of the robotic manipulators is trajectory which is a path with time information. The resulting core technology is trajectory planning methods which are broadly classified into two categories: maximum velocity curve (MVC) methods and multiphase direct collocation (MPDC) methods. This paper concentrates on addressing challenges associated with the latter methods. In MPDC methods, the solving efficiency and accuracy are greatly influenced by the number of discretization nodes. When dealing with systems with complex dynamics, such as robotic manipulators, striking a balance between solving time and path discretization errors becomes crucial. We use a mesh refinement (MR) algorithm to find a suitable number of nodes under the premise of ensuring the path discretization error. So, the actual device can effectively implement the planned solutions. Nonetheless, the conventional application of the MR algorithm requires solving the original problem in each iteration; these processes are extremely time-consuming and may fail to solve when dealing with a complex dynamic system. As a result, we propose a sequential optimal trajectory planning scheme to solve the problem efficiently by dividing the original optimal control (OC) problem into two stages: path planning (PP) and trajectory planning (TP). In the PP stage, we employ a DC method based on arc length and an MR algorithm to identify key nodes along the specified path. This aims to minimize the approximation error introduced during discretization. In the TP stage, the identified key nodes serve as boundary conditions for an MPDC method based on time. This facilitates the generation of an optimal trajectory that maximizes motion performance, considering constant velocity in Cartesian space and dynamic constraints while keeping the path discretization error. Simulation and experiment are conducted with a six-axis robotic manipulator, ROCR6, and show significant potential for a wide range of applications in robotics.