Off-Design Operation and Cavitation Detection in Centrifugal Pumps Using Vibration and Motor Stator Current Analyses.

Centrifugal pumps are essential in many industrial processes. An accurate operation diagnosis of centrifugal pumps is crucial to ensure their reliable operation and extend their useful life. In real industry applications, many centrifugal pumps lack flowmeters and accurate pressure sensors, and therefore, it is not possible to determine whether the pump is operating near its best efficiency point (BEP). This paper investigates the detection of off-design operation and cavitation for centrifugal pumps with accelerometers and current sensors. To this end, a centrifugal pump was tested under off-design conditions and various levels of cavitation. A three-axis accelerometer and three Hall-effect current sensors were used to collect vibration and stator current signals simultaneously under each state. Both kinds of signals were evaluated for their effectiveness in operation diagnosis. Signal processing methods, including wavelet threshold function, variational mode decomposition (VMD), Park vector modulus transformation, and a marginal spectrum were introduced for feature extraction. Seven families of machine learning-based classification algorithms were evaluated for their performance when used for off-design and cavitation identification. The obtained results, using both types of signals, prove the effectiveness of both approaches and the advantages of combining them in achieving the most reliable operation diagnosis results for centrifugal pumps.

The comparative transient prediction on hydrodynamic characteristics and flow field properties of pump-jets with accelerating and decelerating ducts.

Pump-jet holds a pivotal position in various marine applications, underscoring the need for comprehending their transient behavior for the purpose of design enhancement and performance refinement. This paper employs Reynolds-averaged Navier-Stokes equations method in conjunction with Detached Eddy Simulation model. The study delves into the ramifications of accelerating and decelerating ducts, distinguished by camber f and attack angles α, on transient hydrodynamic characteristics. The hydrodynamic characteristics are investigated numerically, after the validation of the numerical methodology by comparing simulation outcomes against experimental results. Subsequently, the study delves into propulsion characteristics, followed by an exploration of time-domain and frequency-domain data transformed through fast Fourier transform to analyze thrust fluctuations and pulsating pressures. Additionally, a detailed examination of pressure distribution and velocity field is provided, aiming to dissect the mechanisms through the variations in f and α influence the flow field. Findings suggest that the outlet velocity of accelerating ducts significantly surpasses the inlet velocity, a behavior contrasted by decelerating ducts. Notably, the patterns of accelerating and decelerating ducts resulting from alterations in f exhibit consistent characteristics with those brought about by changes in α. However, several opposite characteristics surface in transient flow field due to the distinct modifications in the duct profile. Furthermore, by considering vorticity magnitude distribution and vortices, a comparative analysis elucidates the effects of varying f and α on rotor and stator trailing vortices. This contributes to understanding the flow instability mechanism under differing duct configurations. It is evident that changes in f and α exert significant influence on both performance and flow field.

CRISPR-Cas9 Editing of the HBG1 and HBG2 Promoters to Treat Sickle Cell Disease.

BACKGROUND: Sickle cell disease is caused by a defect in the ß-globin subunit of adult hemoglobin. Sickle hemoglobin polymerizes under hypoxic conditions, producing deformed red cells that hemolyze and cause vaso-occlusion that results in progressive organ damage and early death. Elevated fetal hemoglobin levels in red cells protect against complications of sickle cell disease. OTQ923, a clustered regularly interspaced short palindromic repeats (CRISPR)-Cas9-edited CD34+ hematopoietic stem- and progenitor-cell (HSPC) product, has a targeted disruption of the HBG1 and HBG2 (γ-globin) gene promoters that increases fetal hemoglobin expression in red-cell progeny. METHODS: We performed a tiling CRISPR-Cas9 screen of the HBG1 and HBG2 promoters by electroporating CD34+ cells obtained from healthy donors with Cas9 complexed with one of 72 guide RNAs, and we assessed the fraction of fetal hemoglobin-immunostaining erythroblasts (F cells) in erythroid-differentiated progeny. The gRNA resulting in the highest level of F cells (gRNA-68) was selected for clinical development. We enrolled participants with severe sickle cell disease in a multicenter, phase 1-2 clinical study to assess the safety and adverse-effect profile of OTQ923. RESULTS: In preclinical experiments, CD34+ HSPCs (obtained from healthy donors and persons with sickle cell disease) edited with CRISPR-Cas9 and gRNA-68 had sustained on-target editing with no off-target mutations and produced high levels of fetal hemoglobin after in vitro differentiation or xenotransplantation into immunodeficient mice. In the study, three participants received autologous OTQ923 after myeloablative conditioning and were followed for 6 to 18 months. At the end of the follow-up period, all the participants had engraftment and stable induction of fetal hemoglobin (fetal hemoglobin as a percentage of total hemoglobin, 19.0 to 26.8%), with fetal hemoglobin broadly distributed in red cells (F cells as a percentage of red cells, 69.7 to 87.8%). Manifestations of sickle cell disease decreased during the follow-up period. CONCLUSIONS: CRISPR-Cas9 disruption of the HBG1 and HBG2 gene promoters was an effective strategy for induction of fetal hemoglobin. Infusion of autologous OTQ923 into three participants with severe sickle cell disease resulted in sustained induction of red-cell fetal hemoglobin and clinical improvement in disease severity. (Funded by Novartis Pharmaceuticals; ClinicalTrials.gov number, NCT04443907.).

Small hydropower generation using pump as turbine; a smart solution for the development of Pakistan's energy.

Energy supply that is sustainable, effective, and economical has a strong association with socio-economic growth, particularly in developing countries such as Pakistan. Due to the ever-increasing gap between supply and demand, Pakistan has become an energy-deficient nation, with most people having no-to-limited access to power. Pakistan has been suffering from power shortages and an energy crisis because of its strong reliance on fossil-fuels to provide expensive electricity. Therefore, this paper offers a novel concept for developing Pakistan's energy by producing small-hydropower using Pump-As-Turbine (PAT), which is a form of Renewable-energy with lower environmental-impact and has not been used in Pakistan previously. PATs have shown several advantages over traditional hydro-turbines, such as minimum expenses, low-complexity, short delivery time, ease of spare parts, easy installation, availability in a large number of standard sizes, and massive production for broad-range of heads and flow rates. According to technical standards, any sort of pump could be used as PAT, including radial, mixed, single-stage, multi-stage etc. for power generation, which are capable of producing 5kW-1000kW of power, depending on their usage. However, Pakistan has shown little to no interest in exploring small/micro hydropower generation (PATs technology). Thus, this study offers public awareness and forward thinking regarding the use of advanced SHPs and draws the interests of legislators and different investors via solid recommendations about the cost-effective and environmental-friendly technology (PAT).

Microneedle Patch Loaded with Exosomes Containing MicroRNA-29b Prevents Cardiac Fibrosis after Myocardial Infarction.

Myocardial infarction (MI) is a cardiovascular disease that poses a serious threat to human health. Uncontrolled and excessive cardiac fibrosis after MI has been recognized as a primary contributor to mortality by heart failure. Thus, prevention of fibrosis or alleviation of fibrosis progression is important for cardiac repair. To this end, a biocompatible microneedle (MN) patch based on gelatin is fabricated to load exosomes containing microRNA-29b (miR-29b) mimics with antifibrotic activity to prevent excessive cardiac fibrosis after MI. Exosomes are isolated from human umbilical cord mesenchymal stem cells and loaded with miR-29b mimics via electroporation, which can be internalized effectively in cardiac fibroblasts to upregulate the expression of miR-29b and downregulate the expression of fibrosis-related proteins. After being implanted in the infarcted heart of a mouse MI model, the MN patch can increase the retention of loaded exosomes in the infarcted myocardium, leading to alleviation of inflammation, reduction of the infarct size, inhibition of fibrosis, and improvement of cardiac function. This design explored the MN patch as a suitable platform to deliver exosomes containing antifibrotic biomolecules locally for the prevention of cardiac fibrosis, showing the potential for MI treatment in clinical applications.

Efficient phosphate elimination from aqueous media by La/Fe bimetallic modified bentonite: Adsorption behavior and inner mechanism.

Nowadays, eutrophication problem in surface waterbodies has attracted specific attention. Herein, we reported facile synthesis and application of La/Fe engineered bentonite (LFB) for efficient phosphate elimination. Results indicated that bimetallic modified LFB composite could achieve efficient phosphate removal at pH 2-6, and satisfactory selectivity was implied by stable phosphate capturing within the interference of competing species (Cl-, NO3-, HCO3-, SO42-, F- and HA). Pseudo-second-order model could satisfactorily depict the kinetic behavior at different initial concentrations, indicating chemisorption of phosphate on LFB surface. Isotherm study suggested that phosphate adsorption behavior could be fitted well with Sips isotherm equation, indicating that both homogeneous monolayer adsorption and heterogeneous multilayer coverage of phosphate on LFB surface occurred within the investigated conditions. Adsorption thermodynamics implied the spontaneous and endothermic feature of phosphate loading on LFB composite. Characterization analysis confirmed successful La and Fe loading on bentonite, and electrostatic attraction and ligand exchange were the main adsorption mechanism. The high adsorption capacity, cost-effective feature and strong affinity towards phosphate demonstrated certain potential of as-prepared LFB composite for phosphate separation from eutrophic water.

sEMG-based technology for silent voice recognition.

Silent speech recognition (SSR) is a system that implements speech communication when a sound signal is not available using surface electromyography (sEMG)-based speech recognition. Researchers have used surface electrodes to record the electrically-activated potential of human articulation muscles to recognize speech content. SSR can be used for pilot-assisted speech recognition, communication of individuals with speech impairment, private communication, and other fields. In this feasibility study, we collected sEMG data for ten single Mandarin numeric words. After reducing power frequency interference and power supply noise from the sEMG signal, short-term energy (STE) was used for voice activity detection (VAD). The power spectrum features were extracted and fed into the classifier for final identification results. We used the Hold-out method to divide the data into training and test sets on a 7-3 scale, with an average accuracy of 92.3% and a maximum of 100% using a support vector machine (SVM) classifier. Experimental results showed that the proposed method has development potential, and is effective in identifying isolated words from the sEMG signal of the articulation muscles.

Response surface optimization of product yields and biofuel quality during fast hydrothermal liquefaction of a highly CO2-tolerant microalgae.

The effects of biochemical components and processing variables (e.g., temperatures, solid-liquid ratio, ethanol concentration, and time) during fast hydrothermal liquefaction of a highly CO2-tolerant microalgae (Micractinium sp.) on the product yields and biofuel quality were explored using response surface methodology coupled with central composite design. Results showed that the maximum bio-oil yield (51.4 %) was obtained at 321 °C for 49 min at ethanol concentration of 75 % and solid-liquid ratio of 15.3 %. Among different studied parameters, ethanol concentration showed the highest significant impact on the bio-oil yield due to the low P-value and high F-value in ANOVA analysis. Furthermore, the chemical compositions of bio-oils were determined, which showed that the increase of ethanol concentration in the solvent not only increased the bio-oil yield but also promoted the bio-oil quality by reduction of carboxylic acids and nitrogen-containing compounds with simultaneous enhancement of esters in the bio-oil. The present results show that fast hydrothermal liquefaction is a promising approach to convert the microalgae into high quality biofuels rich in esters.

Removal of levofloxacin by an oleaginous microalgae Chromochloris zofingiensis in the heterotrophic mode of cultivation: Removal performance and mechanism.

Microalgae-based technology is an environmental-friendly and cost-effective method for treating antibiotics-contaminated wastewater. This work investigated the removal of levofloxacin (LEV) by an oleaginous microalgae Chromochloris zofingiensis under photoautotrophic and heterotrophic conditions. The results showed that the significantly higher biomass production, accumulation of extracellular polymeric substance and LEV removal efficiency were achieved in heterotrophic C. zofingiensis compared with the photoautotrophic ones. The removal efficiencies under the heterotrophic condition were 97%, 88% and 76% at 1, 10, and 100 mg/L LEV, respectively. HPLC-MS/MS and RNA-Seq analyses suggested that LEV could be bioaccumulated and biodegraded by heterotrophic C. zofingiensis through the reactions of defluorination, hydroxylation, demethylation, ring cleavage, oxidation, dehydrogenation, denitrification, and decarboxylation. The chemical composition of the algal biomass obtained after LEV treatment indicated the potential of this alga for removing LEV from wastewaters and simultaneously producing biodiesel, astaxanthin, and other products. Collectively, this research shows that the heterotrophic C. zofingiensis can be identified as a promising candidate for removing LEV in wastewater remediation.

Dissipativity-Based Disturbance Attenuation Control for T-S Fuzzy Markov Jumping Systems With Nonlinear Multisource Uncertainties and Partly Unknown Transition Probabilities.

This article is concerned with the dissipativity-based disturbance attenuation control for a class of Takagi-Sugeno (T-S) fuzzy Markov jump systems (FMJSs) suffering from nonlinear multisource disturbances. The considered system possesses nonlinear and stochastic jumping disturbances generated by multiple sources, constituting the main challenge to control design and dissipativity analysis. By proposing an adaptive fuzzy disturbance observer and a hybrid feedback controller, a novel fuzzy disturbance attenuation control structure has been constructed. In terms of strict linear matrix inequalities (LMIs), a new sufficient condition is established to guarantee the (Z, Y, X)-ε- dissipative and stochastic exponentially stability of the closed-loop FMJSs. Furthermore, for the concerned FMJSs with partly unknown transition probabilities, the sufficient conditions are also derived and the gains of controller or observer can be computed immediately. Finally, a numerical example is provided to verify the effectiveness of the proposed theory.

A depthwise separable dense convolutional network with convolution block attention module for COVID-19 diagnosis on CT scans.

Coronavirus disease 2019 (COVID-19) has caused more than 3 million deaths and infected more than 170 million individuals all over the world. Rapid identification of patients with COVID-19 is the key to control transmission and prevent depletion of hospitals. Several networks have been proposed to assist radiologists in diagnosing COVID-19 based on CT scans. However, CTs used in these studies are unavailable for other researchers to do deeper extensions due to privacy concerns. Furthermore, these networks are too heavy-weighted to satisfy the general trend applying on a computationally limited platform. In this paper, we aim to solve these two problems. Firstly, we establish an available dataset COVID-CTx, which contains 828 CT scans positive for COVID-19 across 324 patient cases from three open access data repositories. To our knowledge, it has the largest number of publicly available COVID-19 positive cases compared to other public datasets. Secondly, we propose a light-weighted hybrid neural network: Depthwise Separable Dense Convolutional Network with Convolution Block Attention Module (AM-SdenseNet). AM-SdenseNet synergistically integrates Convolutional Block Attention Module with depthwise separable convolutions to learn powerful feature representations while reducing the parameters to overcome the overfitting problem. Through experiments, we demonstrate the superior performance of our proposed AM-SdenseNet compared with several state-of-the-art baselines. The excellent performance of AM-SdenseNet can improve the speed and accuracy of COVID-19 diagnosis, which is extremely useful to control the spreading of infection.

Responses of macroinvertebrate functional traits to riverbed structure of typical debris flow gullies in the upper reaches of the Yangtze River, China.

Debris flow is a typical natural disaster in mountainous areas. Its occurrence has serious impacts on the ecological environment and the life, property safety of local people. The structure of mountain riverbed plays an important role in maintaining the ecological stability of debris flow gullies (DFGs) and improving the ecological condition. However, the effects of hydro-geomorphological processes induced by riverbed structure on local macroinvertebrates have not been well examined. A functional approach was applied to macroinvertebrate data collected in a field survey at sites with different riverbed structure to investigate the response of macroinvertebrate functional traits and environment factors to riverbed structure-induced processes. Riverbed structure was quantitatively calculated by concavity-convexity degree. The results showed that (a) Macroinvertebrates were mainly composed of individuals with the ability of avoiding risks and recovering quickly in DFGs. (b) The environmental factors affecting macroinvertebrates (i.e., average particle size, velocity, flow rate, water depth, and gradient) had a great relationship with riverbed structure. (c) Only 3 (trophic habit, attachment and drift) of the 10 benthic functional traits in the study area had a good correlation with riverbed structure. This study thus found that riverbed structure, as a complex of various environmental factors directly or indirectly affected the community structure and functional traits of macroinvertebrates in DFGs. Besides, it was more suitable for macroinvertebrates of different species to live, and more conducive to the maintenance of ecological stability when the concavity-convexity degree value was about 0.075. Because 5 environmental factors affecting macroinvertebrates were moderate when the degree of concavity was about 0.075. These results can provide scientific basis for ecological conservation and management in DFGs where eco-environment is very fragile.

Research on the Single-Value Indicators for Centrifugal Pump Based on Vibration Signals.

Off-design operation conditions might not only seriously affect the internal flow status of a centrifugal pump, but also result in additional energy loss and potential mechanical damage. Therefore, early-stage monitoring and predication on off-design operation conditions for centrifugal pumps have become essential. Single-value indicators have favorable factors such as a smaller amount of calculation and easier identification. As a result, industries prefer the more straightforward approach: obtaining single-value indicators directly from the signals which could be easier compared with accepted standards. The possibility of applying the single-value indicators of vibration into operation condition monitoring for a centrifugal pump is studied theoretically and experimentally, which shows that the statistical features of vibration might be suitable for hydraulic instability detection for a centrifugal pump.

Evaluation of ergosterol composition and esterification rate in fungi isolated from mangrove soil, long-term storage of broken spores, and two soils.

Ergosterol is an important fungal-specific biomarker, but its use for fungal biomass estimation is still varied. It is important to distinguish between free and esterified ergosterols, which are mainly located on the plasma membrane and the cytosolic lipid particles, respectively. The present study analyzes free and esterified ergosterol contents in: (1) the fifty-nine strains of culturable fungi isolated from mangrove soil, (2) the broken spores of the fungus Ganoderma lucidum stored in capsule for more than 12 years, and (3) the mangrove soil and nearby campus wood soil samples by high performance liquid chromatography (HPLC). The results show that the contents of free and esterified ergosterols varied greatly in fifty-nine strains of fungi after 5 days of growth, indicating the diversity of ergosterol composition in fungi. The average contents of free and total ergosterols from the fifty-nine strains of fungi are 4.4 ± 1.5 mg/g and 6.1 ± 1.9 mg/g dry mycelia, respectively, with an average ergosterol esterification rate of 27.4%. The present study suggests that the fungi might be divided into two classes, one is fungi with high esterification rates (e.g., more than 27%) such as Nectria spp. and Fusarium spp., and the other is fungi with low esterification rates (e.g., less than 27%) such as Penicillium spp. and Trichoderma spp. Moreover, the ergosterol esterification rate in the spores of G. lucidum is 91.4% with a very small amount of free ergosterol (0.015 mg/g), compared with 41.9% with a higher level of free ergosterol (0.499 mg/g) reported in our previous study in 2007, indicating that free ergosterol degrades more rapidly than esterified ergosterol. In addition, the ergosterol esterification rates in mangrove soil and nearby campus wood soil samples range from 0 to 39.0%, compared with 80% in an old soil organic matter reported in a previous study, indicating the potential relationship between aging degree of fungi or soil and esterification rate. The present study proposes that both free and esterified ergosterols should be analyzed for fungal biomass estimation. When the ergosterol esterification rates in soils are higher, free ergosterol might be a better marker for fungal biomass. It is speculated that the ergosterol esterification rate in soils might contain some important information, such as the age of old-growth forests over time scales of centuries to millennia, besides the senescence degree of fungal mycelia in soils. KEY POINTS: • Fungi might be divided into two classes depending on ergosterol esterification rates. • Ergosterol esterification rate of broken spores stored for long time raised evidently. • Both free and esterified ergosterols should be analyzed for fungal biomass estimate. • Free ergosterol is a better marker for fungal biomass with a high esterification rate.

Novel Accordion-Inspired Foldable Pneumatic Actuators for Knee Assistive Devices.

Despite that various soft bending actuators have been presented in recent years, their widespread application in knee assistive devices is still hindered by their uncomfortable geometry, limited torque output, control complexity, and high cost to enhance the knee joint during various human movements. Inspired by accordion bellows, we proposed a novel design of foldable pneumatic bending actuators (FPBAs) in this study, which were fabricated with the thermoplastic polyurethane fabric materials. FPBAs could produce torque by the inflation or interactive compression of their interconnect air chambers with no airflow restriction occurring at any bending angle. General mechanical equations for FPBAs were derived to characterize their output torque as functions of their geometry and internal air pressure. To evaluate the feasibility of FPBAs, a specific prototype with rectangular chambers was constructed and tested by mechanical experiments. A knee exosuit equipped with the prototype was also designed, and five subjects were recruited to perform static postures in knee rehabilitation training with and without the assistance of the knee exosuit. Subjects' persistence time and knee extensors' surface electromyography signals were recorded and compared, which verified the assisting effects of the knee exosuit. Besides knee assistive devices, the FPBAs could also be applied to other soft robots thanks to their competitive advantages, such as flexibility, large torque output, low-pressure input, simple fabrication process, light weight, and low cost.

Study on the method of compensation for the heading effect of the rate offset frequency laser inertial measurement unit.

For the rate offset frequency laser inertial measurement unit (IMU), the errors of its three attitude angles, laser gyroscope, and accelerometer are coupled, which will affect the initial alignment result of the IMU and will make the measurement results of the IMU at different positions and angles deviate from the truth value. Meanwhile, with the increase of tilt angle, the heading effect becomes more obvious, and the error value is distributed positively cosine with the heading angle. In order to ensure the adaptability of the IMU to various operating conditions, it is necessary to compensate for the heading effect. The contribution of each error source of IMU to the heading effect is theoretically studied in this paper. We present a new method for compensating for the heading effect of the rate offset frequency laser IMU, in which the normal drift error of the vertical direction laser gyroscope and the zero bias error of the accelerometer under the turntable coordinate system are compensated. Based on the above method, simulation analysis and test verification are carried out. The experimental results show that the compensation method has a remarkable effect. In the case of two horizontal attitude angles tilted 0.0873 rad and 5 min initial alignment, the error of the rate offset frequency laser IMU reduced from 5.02E-04 rad $({3}\sigma)$(3σ) to 1.45E-04 rad $({3}\sigma)$(3σ), and the accuracy increased by 71%. High-precision initial alignment is achieved, which can meet the requirements of high-precision engineering applications.

Detection of surface defects in film-coated metals and measurement of coating thickness.

A novel sensor based on the interdigitated structure is presented to detect surface defects in film-coated metals and measure coating thickness. The detection and measurement are based on monitoring the shift of resonance frequency which is caused by the perturbation of electromagnetic field around the interdigitated structure. A 200-µm-wide defect was successfully detected in the experiment. In addition, the numerical simulations show that the designed sensor can detect a 50-µm-wide defect with a 220 MHz shift in the resonance frequency. The sensor is sensitive, inexpensive, portable, and can detect both defects and measure coating thickness.

Artificial potential field based robust adaptive control for spacecraft rendezvous and docking under motion constraint.

This paper studied the robust safety control problem for spacecraft proximity maneuvers in the presence of parametric uncertainties, external disturbances, and motion constraint. First, a cardioid-based curve is utilized to describe motion constraint, and two artificial potential fields are established to describe the collision-avoidance requirement. Then, by combining artificial potential field with the backstepping methodology, a robust safety control strategy is designed for close-range proximity operations with time-varying nonconvex motion constraint. Compared with the existing works, the presented control scheme can guarantee the convergence of relative pose errors, and ensure no collision happens between the two spacecraft during the rendezvous and proximity process. Finally, simulation results are provided to illustrate the feasibility of the presented control approach.

A numerical coupling method for particle tracking in electromagnetic fields.

With the arrival of the information age, the electromagnetic energy in space increases constantly, resulting in the influence of electromagnetic waves on the charged aerosol particles in the environment which should be taken into account. Here, a numerical coupling method based on temporal and spatial scales is proposed to solve the difficulty in obtaining the trajectory of particles under the action of high-frequency electromagnetic waves. In the temporal scale, two constant forces with linear relationship are used to equilibrate the electromagnetic field forces under different conditions, however the above-mentioned equivalent method has the space limitation; in addition, on the spatial scale, the model with larger geometry should be divided into multiple basic modules spatially, the domain division method is adopted and due to the above method it can be used well in the basic module. Verified the correctness through the comparison of the results, and compared with the traditional method, the above method greatly reduces the computational complexity. Some interesting results were obtained by calculating the modulated waves with the above method, which indicate that special forms of electromagnetic waves will significantly affect the motion of particles.

Extended state observer based output control for spacecraft rendezvous and docking with actuator saturation.

This paper investigates the relative position tracking and attitude synchronization problem of a chaser spacecraft rendezvous and docking with an uncontrolled tumbling target in the presence of external disturbances and actuator saturation. By combining the extended state observer technique with backstepping control methodology, a robust output-feedback control strategy with no precise motion information of the tumbling target is proposed. Moreover, a particular Nussbaum-type function is introduced to compensate for the nonlinear terms arising for actuator saturation. Within the Lyapunov framework, it is then shown that the proposed control strategy can guarantee the relative position and attitude errors converge into small regions containing the origin. Finally, numerical simulations are carried out to verify the effectiveness of the designed control strategy.