Type Of Pump Research Articles

Disinfectant polyhexamethylene guanidine triggered simultaneous efflux pump antibiotic- and metal-resistance genes propagation during sludge anaerobic digestion

The environmental transmission of antibiotic resistance genes (ARGs) and metal resistance genes (MRGs) exerted devastating threats to global public health, and their interactions with other emerging contaminants (ECs) have raised increasing concern. This study investigated that the abundances of ARGs and MRGs with the predominant type of efflux pump were simultaneously increased (8.4–59.1%) by disinfectant polyhexamethylene guanidine (PHMG) during waste activated sludge (WAS) anaerobic digestion. The aggregation of the same microorganisms (i.e., Hymenobacter and Comamonas) and different host bacteria (i.e., Azoarcus and Thauera) were occurred upon exposure to PHMG, thereby increasing the co-selection and propagation of MRGs and ARGs by vertical gene transfer. Moreover, PHMG enhanced the process of horizontal gene transfer (HGT), facilitating their co-transmission by the same mobile genetic elements (20.2–223.7%). Additionally, PHMG up-regulated the expression of critical genes (i.e., glnB, trpG and gspM) associated with the HGT of ARGs and MRGs (i.e., two-component regulatory system and quorum sensing) and exocytosis system (i.e., bacterial secretion system). Structural equation model analysis further verified that the key driver for the simultaneous enrichment of ARGs and MRGs under PHMG stress was microbial community structure. The study gives new insights into the aggravated environmental risks and mechanisms of ECs in sludge digestion system, providing guidance for subsequent regulation and control of ECs.

Analysis Of Battery LiFePO4 Pack Capacity As An Alternative Energy Source In Water Pump Shimizu PS-135 E

Electrical energy is a basic need for society and is a fairly economical resource that can be used for various activities. Human activities are supported by electrical energy. Electrical energy has important role in supporting all activities such as the industrial, commercial building, transportation and housing sectors. Water pump Shimizu PS-135 E is a type of water pump that is widely used in family activities, its function is to supply water from water sources (reservoirs, wells) for family needs such as bathing and washing. The pump relies continuously use of electrical energy, it means that, if this energy source runs out, the pump will not be able to operate automatically and ultimately. For this reason, in this research, the LiFePO4 type battery is used as an alternative energy source to overcome the above problems. The results of the analysis in this research show that to run the water pump for 1.5 hours a 42,000 mAh 12 Volt LiFePO4 battery is required which is arranged in a 4S - 7P manner and as a battery protector a 60 A Daly type BMS is used. Testing the load on the water pump until the battery cut time showed that the battery drain time was 1.3 hours, the battery condition was 20% with a voltage of 12.89 Volts. AC output voltage 230.4 Volts, current 1.145 A, power (P) = 195 Watts, Power Factor 0.72. The volume of water produced in 1.3 hours (78 minutes) is 2,182 liters.

Deformation investigation of electromagnetic diaphragm pump rubber diaphragm.

A diaphragm pump is a type of volumetric pump that has excellent sealing performance. An electromagnetic diaphragm pump is a kind of widely adopted diaphragm pump that has a simple structure, low power loss, and high cost performance. However, the calculation method of deformation for the electromagnetic diaphragm pump rubber diaphragm is presently lacking. Herein, a calculating method of deformation for the electromagnetic diaphragm pump rubber diaphragm is proposed. By establishing and analyzing a deformation model of the electromagnetic diaphragm pump rubber diaphragm, a theoretical relationship between the deformation of the electromagnetic diaphragm pump rubber diaphragm, the size of the electromagnetic diaphragm pump rubber diaphragm and the pressure of fluid is determined. The experimental results indicate that the biggest difference between the tested axial deformation and the calculated axial deformation of the electromagnetic diaphragm pump rubber diaphragm is 0.04 mm and the calculation results show agreement with the experimental results.

A Study on the Transient Characteristics of the Power-Off Transition Process of a Double-Volute Centrifugal Pump

A double-volute centrifugal pump is a very important pump type; the internal flow field of a centrifugal pump will change drastically during the transition process of power failure, which will affect the safety and stability of the pump’s operation. In this paper, the CFD numerical simulation method is used, and the UDF procedure is developed to realize the continuous update of the impeller speed at each time step. The working parameters, such as the torque and flow rate at the instantaneous moment, are obtained through the sequential iteration of each small step, and a numerical simulation of the power-off transient is carried out on a double-volute centrifugal pump; additionally, the changes in the external characteristic parameters and the internal flow field of the centrifugal pump are analyzed in detail. The results show that the double-volute centrifugal pump experienced four different modes after power failure, namely pump mode, braking mode, turbine mode, and runaway mode, and the absolute values of the runaway speed and runaway flow rate are 1.465 times and 1.21 times the initial values, respectively. Through the analysis of the flow field in different regions, the change processes of the generation, development, and disappearance of the vortex at each position of the centrifugal pump are obtained, and the change and development processes of the internal velocity gradient of the centrifugal pump are obtained. In addition, it is found that the high-speed area located in the second volute runner is larger than that of the first volute runner because the second volute runner is shorter and narrower than the first volute runner.

Project management using the developed AHP–VIKOR method with the fuzzy approach

ABSTRACT There are many factors to consider when designing a sewerage pumping station (SPS), such as sizing the system, pump type, cooperation between pumps, SPS elevation, wastewater discharge location, system venting, correct number of inflows into the pumping station (PS) reservoir, and chemical resistance of the installations. In this study, we developed a multi-criteria-decision-making (MCDM) fuzzy AHP–VIKOR method with the aim to contribute to the improvement and development of MCDM methods. By combining and improving the existing AHP and VIKOR methods with the application of fuzzy logic theory, a novel fuzzy AHP–VIKOR method is for easier and clearer obtaining of optimal solutions. The new method was applied to obtain the findings in the analysis of four complex design solutions for canalisation, treatment, and pumping of atmospheric wastewater in the SPS in Makiš, an urban neighbourhood of Belgrade in Serbia. The analysis was carried out in relation to the stability of the solution by way of considering the use of different methods of MCDM optimisation, while taking into account ways of channelling, treatment, and evacuation of wastewater.

Optimization of Cavitation Performance of High-Speed Centrifugal Pump Based on the Meta-Model of optimal Prognosis

Abstract Using a specific type of high-speed centrifugal pump as an example, this study conducted a parameterized optimization design on geometric parameters of the impeller’s flow path. A response sample space was generated with the flow path geometric parameters as input and pressure increment and cavitation volume as output. Based on the Meta-Model of optimal Prognosis, the optimal surrogate model was fitted, and a global sensitivity analysis was conducted. The results indicated that the impeller’s inlet edge parameter and mid-curve parameter had a significant impact on the pressure increment and cavitation volume of the pump. Using a genetic algorithm, the optimal flow path geometric parameters were obtained, and numerical simulation methods were applied to verify the obtained parameters. The results showed that after optimization, the pressure coefficient of the centrifugal pump increased by 0.035, and the cavitation performance improved by 22.28%. The impeller cavitation area and void volume were significantly reduced, and the flow path pressure distribution and flow state were improved.

Research on complex products assembly sequence planning and its application based on PSO-GA

Abstract A PSO-GA-based method is proposed to improve the efficiency of complex product assembly sequence planning. We minimize total assembly time by optimizing the assembly sequence, considering the number of tool changes and assembly direction changes as evaluation criteria. A genetic algorithm (GA) is introduced into particle swarm optimization (PSO) to solve and verify assembly sequence planning. Finally, the effectiveness and rationality of the hybrid algorithm are verified by taking a certain type of gear pump as an example.

Use of an Absorption Heat Pump to Lift the District Cooling Waste Heat Temperature for the District Heating Supply in Tallinn: a Technical and Economic Analysis

Absorption heat pumps can lift a lower temperature waste heat source to a higher temperature useful output. In that process, it uses less electricity as an input compared to heat pumps with electrical compressors. Therefore, in some cases, it can be used to lift a lower temperature waste heat source to a higher temperature useful output with less electricity consumption. Absorption heat pumps are not very widely spread in district heating, mostly because there aren’t many suitable waste heat sources or conditions needed to run them. Tallinn has a district heating system with an annual generation of more than 2 TWh and a goal to make it an entirely carbon neutral district heating system by 2030. Tallinn has also started to develop a district cooling network, and by the end of 2023, the installed capacity was about 6 MW. District cooling capacity is estimated to grow to around 100 MW in 2030. This paper investigates different types of absorption heat pumps and the possibilities of integrating an absorption heat pump to a district cooling plant with the purpose of using waste heat from the cooling plant for renewable heat generation, that can be used in district heating. Different technical aspects are examined to find a suitable production solution, are presented as results. From an economical point of view, the cost of heat to cover peaks with an absorption heat pump is calculated. The effect of reducing fossil fuel use in the Tallinn district heating network with an absorption heat pump is estimated.

Developing a generalizable pediatric ECMO emergency checklist for clinical specialist: Progress and challenges.

Extracorporeal membrane oxygenation (ECMO) emergencies require skilled clinical specialist (CS) who manage ECMO circuits. While tools for assessing CS skills have been published, there is significant variation in protocols and circuit design. This study aims to further develop these checklists to produce a generalizable ECMO skill assessment with adequate validity evidence to support its use as a summative evaluation tool. An initial survey determined variation in ECMO circuit components and configurations, and the original checklists and simulations were altered through a modified Delphi process. The finalized checklist and simulation were then assessed for validity and reliability. Three trained raters assessed ten simulations from five subjects at two different institutions using two circuit designs. Data analysis was conducted using a fully crossed subject x rater x circuit generalizability (G) and decision (D) study. The G-study coefficient was 0 with 0% variance across subject and circuit. The greatest variance was among raters (28.7%). Significant variance was also associated with the subject and pump type relationship (27%). Despite the rigorous process used to modify the assessment, generalizability was poor. Lack of familiarity with center-specific circuit design played a key role. Future endeavors in ECMO skill assessment should focus either on developing and validating site-specific tools or standardizing circuit designs.

Advanced 2D Computational Fluid Dynamics Model of an External Gear Pump Considering Relief Grooves

The article presents an advanced two-dimensional (2D) computational fluid dynamics (CFD) model of an external gear pump which considers relief grooves. Relief grooves are limiting design features for the flow process of this type of pump, and their influence in existing studies is considered by a three-dimensional (3D) model only. The structural modification proposed by the authors is beyond the possibilities of real implementation, but it gives the possibility to precisely model the pump’s design features. In contrast to the existing studies (using 3D CFD), the proposed advanced 2D model requires significantly fewer computing resources. Numerical experiments were carried out using the 2D model at different pump operating modes depending on the rotation frequency (950–1450 min−1) and pressure load (5–150 bar). The numerical results were validated by a real-world experiment for the same pump operating modes using an existing laboratory experimental setup. An analysis of the CFD model and real experiment results was carried out by determining a quantitative index of match (FIT), which varies in the range of 97.93–99.82%. This proves the performance of the proposed CFD model, which can be further used as a part of more complex hydraulic systems models.

EVALUATION OF THE ENERGY EFFICIENCY OF THE NEW CONSTRUCTIVE SOLUTION OF SUCKER-ROD PUMP

As is known, in our country, oil production is carried out both in the Caspian Sea and in oil fields on land. For the mechanized exploitation of oil fields on land, in most cases used different type of sucker-rod pumps. The main object of the study of the article is a new constructive solution of the pumping unit, the novelty of which is approved by the ownership certificates of the Eurasian Patent Organization and the Intellectual Property Organization of the Republic of Azerbaijan. The main factor characterizing the operation of pumping units is its quality indicators such as metal consumption, reliability, efficiency and energy consumption. When switching from a balanced sucker-rod pumping unit to an unbalanced the efficiency factor decreases from 0.834 to 0.65 and decreases from 0.605 to 0.312. In this case, power losses increase sharply not only in transmissions, but also in energy distribution networks. If the engine is not fully loaded or is not selected correctly, then these energy coefficients decrease even more. The selection of engine power is performed according to the worst conditions, i.e. the cyclic mode of operation of an unbalanced pumping unit. Despite this, it can be said that in almost all oil fields, the power of asynchronous motors is greatly exaggerated, which causes additional losses. In article proposed expressions for determining the optimal power of the electric motor were proposed, taking into account the efficiency factor of the balancing device during the balancing of the proposed new constructive solution of the beamless pumping unit with a combined, movable counter weights and rotary counter weights. This allows to prevent excess energy consumption and reduce energy costs. Which is very important in the era of globalization, when energy prices are rising sharply.

Research of the Meshing Performance of New Concave-convex Ball Teeth

Aiming at the limitations of the existing hydraulic pumps, a new type of bidirectional water-hydraulic internal ball gear pump using concave-convex ball teeth meshing to transfer power is proposed. In this paper, the principle of internal gear pump is utilized to establish the model of internal ball gear pump, and its mechanical properties and dynamic meshing characteristics are numerically investigated by using the finite element method. The results show that (a) the concave-convex ball gears run smoothly without any interference, and (b) increasing the number of gear rows can effectively reduce the maximum stress and meshing impact under a given load and speed. This study provides a basis for the development of high-performance ball gear pumps.

ПОВЫШЕНИЕ ЭКСПЛУАТАЦИОННЫХ ПОКАЗАТЕЛЕЙ ДИЗЕЛЬНОГО ДВИГАТЕЛЯ ВНУТРЕННЕГО СГОРАНИЯ

The current problem of operating automotive equipment at low temperatures associated with the loss of diesel fuel’s properties (reducing the cloud point and crystallization of the fuel) is being considered, resulting in equipment failures due to failure of the power system and direct freezing of the fuel in the tubes, paraffin deposition leading to clogging of fuel filters. Domestic automotive vehicles do not have any effective means of heating diesel fuel, which forces drivers operating equipment in harsh climatic conditions to use their own individual developments. For these purposes, a device has been developed that allows you to heat all the diesel fuel poured into the fuel tank. The drive of the device (fuel priming pump) is proposed to be electric (from a linear electric motor), from the vehicle's on-board network, the type of pump used is piston, double-acting. A comprehensive calculation of the fuel priming pump is presented in order to determine its main characteristics and design dimensions. A schematic diagram of the installation of the developed device and all elements in the diesel engine power system is presented. The implementation of the proposed technical solution was carried out in the power system of the YaMZ-238 diesel engine installed on a load stand under conditions of its operation in low temperatures (the Far North, etc.). The obtained results of tests on a bench engine confirm the relevance of the research and showed that the use of the developed technical solution will allow heating all the diesel fuel poured into the car tank to a temperature of plus 50 °C, thereby eliminating the possibility of its crystallization and cloudiness and, in general, reducing the number of vehicle failures. techniques related to this problem.

Optimized sulfur curing of pulse-damping rubber tubes

In pumping systems present in the industrial field, positive displacement pumps are used due to the high manometric loads and the characteristics of the extracted fluid. However, this type of pump provides a pulsating flow in the system that causes large pressure fluctuations, reducing the useful life of the installations. Because of this problem, pulsation dampers (attenuators) are used in the system in order to promote a more continuous flow and the good functioning of the process. In-line type attenuators feature a flexible tube composed of elastomer, whose viscoelastic behavior causes flow attenuation. The objective of this work is to evaluate whether there is a relationship between the sulfur content present in blends of natural rubber (NR) and synthetic rubber of the Butadiene Styrene (SBR) and the performance of tubular attenuators in a pumping system with pulsating flow. Four NR/SBR rubber blends with different sulfur concentrations in the formulation (0.5; 1.5, 3.0 and 4.5 phr) were tested. The rubbers were characterized using Fourier Transform Infrared Spectroscopy (FTIR) and their mechanical properties were analyzed using mechanical tensile tests. The efficiency of the attenuators was evaluated through bench tests that simulate pumping systems in the field. The results of the mechanical tests showed significant relationships with the performance of the attenuators in experimental tests. In attenuation tests, blends with 1.5; 3.0 and 4.5 phr sulfur had attenuation results of 27.06 %, 9.70 % and 1.61 %, respectively. The 0.5 phr attenuator could not withstand the applied loads due to lack of elastic properties. Thus, it was found that materials with a lower modulus of elasticity had greater efficiency in attenuating the pulsating flow and greater compliance, in which the attenuator that was formulated with 1.5 phr of sulfur showed 25.45 % greater pulsation damping than the stiffer material.

Internal Flow Characteristics of Centrifugal Pumps under Different Startup Combination Schemes

Pump station engineering is a water conservancy project used for long-distance water transfer, irrigation and drainage, and urban living and industrial water supply. Centrifugal pumps are one of the main pump types commonly used in pumping stations, and their operation is of considerable importance for the safety, stability, and efficient operation of pumping stations. This paper takes a large pumping station with seven centrifugal pump units as the research object and combines experimental research and numerical simulation. The axial flow velocity uniformity, average cross-sectional deviation angle, and hydraulic loss of the pump inlet section are evaluated, and the internal flow characteristics of the pump under different startup combination conditions are analyzed based on entropy generation and vorticity. This study also explores the operational performance of the pump station under different startup combination conditions, revealing the mutual influence mechanism between different startup combinations of pump stations and the internal and external characteristics of centrifugal pumps and introducing the optimal startup combination scheme for the pump station system. Research results indicate that the difference in energy loss of centrifugal pumps under different startup combinations is mainly manifested in the impeller and guide vane flow channels. For the two existing inlet flow channel structures in the pump station, the unit effectively operates when the inlet flow channel is tilted to the left. The optimal startup combination method of the pump station under different startup combinations is determined.

Field Validation of a Universally Applicable Condition-Based Maintenance System for Mud Pumps

Summary Although mud pumps are considered to be critical rig equipment, their health monitoring currently still relies on infrequent human observation and monitoring. This approach often fails to detect pump damage at an early stage, resulting in nonproductive time (NPT) and increased well construction costs when initial damage progresses and pumps go down unexpectedly and catastrophically. Automated approaches to condition-based maintenance (CBM) of mud pumps to date have failed due to the lack of a generalized solution applicable to any pump type and/or operating conditions. This paper presents a field-validated universally applicable solution to mud pump CBM. The system uses a sensor package that includes acoustic emission sensors and accelerometers in combination with anomaly detection deep learning data analysis to pinpoint any abnormal behavior of the pump and its components. The deep learning models are trained with undamaged normal state data only, and a damage score characterizing the extent of damage to the mud pump is calculated to identify the earliest signs of damage. The system can then generate alerts to notify the rig crew of the damage level of key mud pump components, prompting proactive maintenance actions. Field tests were conducted while drilling an unconventional shale well in west Texas, USA, and a geothermal well in Japan (i.e., two very different drilling operations) to verify the feasibility and general applicability of the developed pump CBM solution. Sensors were attached to pump modules, and data were collected and analyzed using the deep learning models during drilling operations. During the field tests, different hyperparameters and features were compared to select the most effective ones for identifying damage while at the same time delivering low false positive rates (i.e., false alarms during normal state pump operation). The system required only several hours of normal state data for training with no prior pump information. Moreover, it correctly identified the degradation of the pump, swabs, and valves and produced early alerts several hours (in the range of 0.5–17 hours) before actual pump maintenance action was taken by the rig crew. This generally applicable pump CBM system eliminates the environmental, health, and safety concerns that can occur during human-based observations of mud pump health and avoids unnecessary NPT associated with catastrophic pump failures. The final version of this system will be a fully self-contained magnetically attachable box containing sensors and a processor, generating simple indicators for recommending proactive pump maintenance tasks when needed.

Multi-Objective Optimization with Active–Passive Technology Synergy for Rural Residences in Northern China

Due to the serious problems with energy efficiency, carbon emissions, and thermal comfort of rural residences in northern China, an optimization of active and passive heating technologies for rural residences is necessary. In this paper, an optimization for rural residences in northern China is conducted with four objectives: the whole life cycle carbon emission; the annual energy consumption through heating, ventilation, and air conditioning systems; the annual cost; and thermal comfort. In addition, the optimization model with active–passive heating technology synergy is resolved by NSGA-II genetic algorithm. The active and passive design variables, including the type of air source heat pump, orientation, the type and thickness of envelope insulation, the layer of window glass, the window-to-wall area ratio, as well as sunspace parameters are preferred to obtain the optimal solution. The results indicate that the optimal solution obtained by the ideal point method gives the most outstanding performance. Compared with the prototype, the optimized carbon emissions in severe cold and cold regions decreased by 56.1% and 54.6%, respectively. The annual energy consumption decreased by 59.7% and 62.2%. Finally, the roof insulation thickness is the most sensitive design variable in Pareto-optimal solution sets. This paper offers significant guidance in the application of the optimization method of active–passive technology synergy to the energy-saving design of buildings.

Efek tinggi hisap terhadap kapasistas pompa sentrifugal

Centrifugal pumps are one type of pump commonly used in the industry, particularly in the processing and distribution of clean water. The characteristics of these pumps can be determined by varying the flow rate at a certain height. A study was conducted to investigate the effects of three different pump heights (3.5 m, 4.5 m, and 5.5 m) on the efficiency of a centrifugal pump using water at a temperature of 31℃. The results showed that the maximum overall efficiency was obtained at a height of 4.5 m with a value of 33.22% and a total head of 23.39 m. The pump height was found to have an impact on the pump capacity, with higher pump positions resulting in an increased occurrence of cavitation bubbles in the suction pipe, leading to a decrease in pump performance. Therefore, the placement of centrifugal pumps should be carefully considered, taking into account factors such as height and distance of the suction pipe, to minimize cavitation and achieve optimal pump performance.

Bioavailability Study of Experimental Push–pull Osmotic Pump Tablet of Nifedipine in Dogs

This study aimed to assess the bioavailability of experimental extended-release nifedipine tablets of push-pull osmotic pump type composed of a semipermeable membrane-coated bilayer core tablet containing PEO N10 and PEO 303 in drug layer and push layer, respectively on dogs. A test on dogs was performed using a two-way randomized crossover design with a single oral dose, fasting condition. Plasma samples were obtained at intervals and analyzed for nifedipine by UPLC-MS/MS after liquid-liquid extraction using glibenclamide as the internal standard. The pharmacokinetic parameters were calculated and the bioavailability of nifedipine extended-release tablets was evaluated by comparing the pharmacokinetic parameters between the prepared extended-release tablets of 30 mg NIF and the reference tablets of Adalat LA 30 mg. It was found that the prepared push-pull osmotic pump tablets of 30 mg nifedipine were equivalent in bioavailability to Adalat LA reference tablets of 30 mg nifedipine in experimental dogs according to the regulations of US-FDA and Vietnamese pharmacopeia 5th edition. The main pharmacokinetic parameters of nifedipine test and reference tablets after a single oral administration were as follows: Cmax 26.95 ± 7.82 (ng.mL-1) and 27.20 ± 6.99 (ng.mL-1), Tmax 12.33 ± 3.44 hours and 11.50 ± 3.33 hours, AUC0-96 728.96 ± 328.87 (ng.h.mL-1) and 702.48 ± 404.48 (ng.h.mL-1), AUC0-∞, 741.05 ± 340.39 (ng.h.mL-1) and 710.71 ± 408.76 (ng.h.mL-1), MRT 21.80 ± 5.25 hours and 22.06 ± 5.20 hours, respectively. The 90% confidence intervals for the ratio of Cmax, AUC0-∞, and MRT values for the test and reference products, using logarithmically transformed data were 90.82% - 108.09%, 91.97% - 118.21%, 90.74% -107.62%, respectively. No statistically significant difference was found for the Tmax value.

Force Compensation Control for Electro-Hydraulic Servo System with Pump–Valve Compound Drive via QFT–DTOC

Each joint of a hydraulic-driven legged robot adopts a highly integrated hydraulic drive unit (HDU), which features a high power–weight ratio. However, most HDUs are throttling-valve-controlled cylinder systems, which exhibit high energy losses. By contrast, pump control systems offer a high efficiency. Nevertheless, their response ability is unsatisfactory. To fully utilize the advantages of pump and valve control systems, in this study, a new type of pump–valve compound drive system (PCDS) is designed, which can not only effectively reduce the energy loss, but can also ensure the response speed and response accuracy of the HDUs in robot joints to satisfy the performance requirements of robots. Herein, considering the force control requirements of energy conservation, high precision, and fast response of the robot joint HDU, a nonlinear mathematical model of the PCDS force control system is first introduced. In addition, pressure–flow nonlinearity, friction nonlinearity, load complexity and variability, and other factors affecting the system are considered, and a novel force control method based on quantitative feedback theory (QFT) and a disturbance torque observer (DTO) is designed, which is denoted as QFT–DTOC herein. This method improves the control accuracy and robustness of the force control system, reduces the effect of the disturbance torque on the control performance of the servo motor, and improves the overall force control performance of the system. Finally, experimental verification is performed using the PCDS performance test platform. The experimental results and quantitative data show that the QFT–DTOC proposed herein can significantly improve the force control performance of the PCDS. The relevant force control method can be used as a bottom-control method for the hydraulic servo system to provide a foundation for implementing the top-level trajectory planning of the robot.