Accelerated Particle Swarm Optimization Research Articles

LOAD FREQUENCY CONTROL STRATEGY FOR MICROGRID SYSTEMS USING COMPUTATIONAL INTELLIGENCE OPTIMIZED PID CONTROLLER

This paper presents Load Frequency Control (LFC) strategy for Microgrid (MG) systems, proposing a strategy based on a PID optimized controller using computational intelligence (CI) technique. The MG system, relying solely on Renewable Energy Sources(RES) is modeled in SIMULINK. A novel multi-objective function comprising of Weighted Integral Square Error, WISE and Weighted Integral Absolute Square Error WIASE (WISE+WIASE) is proposed to enhance system performance. Using Particle Swarm Optimization (PSO) and Accelerated Particle Swarm Optimization (APSO), the Proportional, Integral and Derivative controller parameters are tuned. Simulation results revealed the superiority of the PSO-PID with the least steady state error of 4.1560e-07 and overshoot 0.0611 respectively over the APSO-PID with steady state error value of 4.8144e-07 and overshoot of 0.1334 respectively. PSO-PID also outperformed APSO-PID across other indices (ITAE, IAE, ITSE and ISE) making the PSO-PID to excel over the APSO-PID in terms of steady state error and overshoot. The controllers proved to be robust in various conditions with the PSO-PID controller exhibiting more robustness and stability than the APSO-PID controller. Comparing PSO and APSO algorithms, PSO outperformed APSO in terms of robustness because for five number of runs in both algorithms, the PSO algorithm presents a more quality and consistent results and also display a better convergence than the APSO algorithm . Conversely, APSO surpasses PSO in fast computational time and convergence speed. These findings underscore the effectiveness of the proposed LFC strategy for RES based Microgrid systems, providing valuable insights into comparative performance of PSO and APSO algorithms.

Comparative assessment of differently randomized accelerated particle swarm optimization and squirrel search algorithms for selective harmonics elimination problem

A random initialization of the search particles is a strong argument in favor of the deployment of nature-inspired metaheuristic algorithms when the knowledge of a good initial guess is lacked. This article analyses the impact of the type of randomization on the working of algorithms and the acquired solutions. In this study, five different types of randomizations are applied to the Accelerated Particle Swarm Optimization (APSO) and Squirrel Search Algorithm (SSA) during the initializations and proceedings of the search particles for selective harmonics elimination (SHE). The types of randomizations include exponential, normal, Rayleigh, uniform, and Weibull characteristics. The statistical analysis shows that the type of randomization does impact the working of optimization algorithms and the fittest value of the objective function.

The Parameter Identification of Structure with TMD considering Seismic Soil-Structure Interaction

Parameter identification is of great significance for the postearthquake performance evaluation of structure equipped with tuned mass damper (TMD). However, the soil-structure interaction (SSI) effects have not been considered in the parameter identification of structure with TMD yet, which influence the dynamic characteristics and seismic responses of structures. This paper aims at proposing a framework for identifying the physical parameters of soil-structure-TMD system. Firstly, the accelerated particle swarm optimization (APSO) algorithm is combined with the search space reduction (SSR) method. Then, the frequency response function and transmissibility function are adopted for output-input and input-only cases, respectively, and a simplified mechanical model for soil-structure-TMD system is employed. Next, the measured responses are used to identify the physical parameters of structure with TMD considering SSI effects. Finally, the effectiveness of the proposed identification method is investigated, and the influences of frequency band and noise pollution on the identification performance are discussed. The results show that the proposed strategy can identify the system physical parameters accurately and quickly. It is worth noting that high frequency bands and noise pollution may lead to estimation error, especially for output-only case.

Sizing of Degradation Based Battery Storage Systems for Operating Cost Minimization in Microgrids

Abstract: A microgrid is a low voltage distribution network designed to provide power for small scale and isolated communities consisting of distributed generation and Energy Storage Systems .One of the major issues in the isolated microgrids with intermittent nature of distributed generation is the balance of energy demand. This can be achieved by appending renewable energy sources with suitable Battery Energy Storage Systems, to provide the reserve support in meeting the load demand. Battery degradation effect plays a major role in analysing the performance of BESS Life Time. This depends on average kWh and average MWh throughput discharge from BESS. Therefore, microgrid system with BESS considering degradation effect should be optimized in such a way as to obtain minimum operating cost while ensuring minimum electricity cost to customers. This paper presents an optimization algorithm for microgrid operating cost and customer electricity cost minimization for 24hrs time horizon while considering BESS degradation effect by determining kWh and MWh throughput. Particle Swarm Optimization (PSO), Accelerated particle swarm optimization (APSO), Jaya optimization (JAYA) technique and Linear programming interior point algorithm (LP-IP) have been applied to determine the optimal operating cost and electricity cost by simulating BESS degradation parameters

Minimize Total Cost and Maximize Total Profit for Power Systems with Pumped Storage Hydro and Renewable Power Plants Using Improved Self-Organizing Migration Algorithm

This study presents the application of an improved self-organizing migration algorithm (ISOMA) for minimizing the total electricity production expenditure (TEPE) and maximizing the total electricity sale profit (TPRF) for hydrothermal power systems (HTPS) without and with renewable energies. Two power system configurations were employed to test the real efficiency of ISOMA while dealing with two objective functions. In the first configuration, there was one thermal power plant and one hydropower plant, while in the second configuration, wind and solar energy were both connected to the first system. The results achieved in the first configuration with the first objective function indicated that ISOMA not only outperformed SOMA according to all comparison criteria but was also superior to other methods such as evolutionary programming (EP), acceleration factor-based particle swarm optimization (AFPSO), and accelerated particle swarm optimization (APSO). The evaluation of the results achieved by ISOMA in the second configuration with the objective function of maximizing the TPRF revealed that ISOMA could reach better profits than SOMA in terms of maximum, mean and minimum TPRF values over fifty trial runs. As a result, it was concluded that pumped storage hydropower plants are very useful in integrating with renewable power plants to cut total cost for thermal power plants and in reaching the highest profit for the whole system. Also, ISOMA is a suitable algorithm for the considered problem.

Hybrid Simulated Annealing‐Evaporation Rate‐Based Water Cycle Algorithm Application for Medical Image Enhancement

Visualizing medical images is difficult due to artifacts, poor local contrast, low soft tissue contrast, excessive noise levels, and a wide dynamic range. This has created a serious problem for physicians, resulting in unapproachable and inaccurate disease diagnoses. To circumvent this problem, this research proposes a medical image enhancement (MIE) approach based on the hybrid simulated annealing‐evaporation rate‐based water cycle algorithm (SA‐ERWCA). The ERWCA enhances distorted medical images by finding the best optimal solution for the transformation parameters according to the fitness function. The fitness function consists of three objective measurements, namely, entropy, number of edges, and sum of edge intensities. Due to its high potential for finding a globally optimal solution, SA is applied solely to determine the optimized initial population of the ERWCA, thereby enhancing its convergence characteristics. To simply put, the main objective of SA is to avoid premature convergence of the ERWCA. Thus, blending SA and ERWCA produces better‐quality medical images. The performance of the proposed algorithm was compared to histogram equalization (HE), low contrast stretching (LCS), contrast‐limited adaptive histogram equalization (CLAHE), particle swarm optimization (PSO), accelerated PSO (APSO), and the water cycle algorithm (WCA). Along with the objective function fitness, seven full reference (FR) image quality assessment (IQA) metrics were implemented to evaluate image quality and compare performance. The findings of the present study showed that the proposed strategy outperforms all of the compared methods in terms of objective function fitness and perceptual visual IQA metrics such as the Harr wavelet‐based perceptual similarity index (HaarPSI), visual signal‐to‐noise ratio (VSNR), and information content weighted structural similarity index measure (IW‐SSIM). The suggested technique also exhibited better stability and faster convergence time to the optimum solution. Furthermore, the proposed approach outperformed others by avoiding premature convergence to the best solution and providing excellent optimization results with acceptable computational efficiency.

Accelerated Particle Swarm Optimization Algorithm for Efficient Cluster Head Selection in WSN

Accelerated Particle Swarm Optimization Algorithm for Efficient Cluster Head Selection in WSN

Optimal Model-Free Finite-Time Control Based on Terminal Sliding Mode for a Coaxial Rotor

This study focuses on addressing the tracking control problem for a coaxial unmanned aerial vehicle (UAV) without any prior knowledge of its dynamic model. To overcome the limitations of model-based control, a model-free approach based on terminal sliding mode control is proposed for achieving precise position and rotation tracking. The terminal sliding mode technique is utilized to approximate the unknown nonlinear model of the system, while the global stability with finite-time convergence of the overall system is guaranteed using the Lyapunov theory. Additionally, the selection of control parameters is addressed by incorporating the accelerated particle swarm optimization (APSO) algorithm. Finally, numerical simulation tests are provided to demonstrate the effectiveness and feasibility of the proposed design approach, which demonstrates the capability of the model-free control approach to achieve accurate tracking control even without prior knowledge of the system’s dynamic model.

Time series-based hybrid ensemble learning model with multivariate multidimensional feature coding for DNA methylation prediction

BackgroundDNA methylation is a form of epigenetic modification that impacts gene expression without modifying the DNA sequence, thereby exerting control over gene function and cellular development. The prediction of DNA methylation is vital for understanding and exploring gene regulatory mechanisms. Currently, machine learning algorithms are primarily used for model construction. However, several challenges remain to be addressed, including limited prediction accuracy, constrained generalization capability, and insufficient learning capacity.ResultsIn response to the aforementioned challenges, this paper leverages the similarities between DNA sequences and time series to introduce a time series-based hybrid ensemble learning model, called Multi2-Con-CAPSO-LSTM. The model utilizes multivariate and multidimensional encoding approach, combining three types of time series encodings with three kinds of genetic feature encodings, resulting in a total of nine types of feature encoding matrices. Convolutional Neural Networks are utilized to extract features from DNA sequences, including temporal, positional, physicochemical, and genetic information, thereby creating a comprehensive feature matrix. The Long Short-Term Memory model is then optimized using the Chaotic Accelerated Particle Swarm Optimization algorithm for predicting DNA methylation.ConclusionsThrough cross-validation experiments conducted on 17 species involving three types of DNA methylation (6 mA, 5hmC, and 4mC), the results demonstrate the robust predictive capabilities of the Multi2-Con-CAPSO-LSTM model in DNA methylation prediction across various types and species. Compared with other benchmark models, the Multi2-Con-CAPSO-LSTM model demonstrates significant advantages in sensitivity, specificity, accuracy, and correlation. The model proposed in this paper provides valuable insights and inspiration across various disciplines, including sequence alignment, genetic evolution, time series analysis, and structure–activity relationships.

A new cockroach-like compliant mechanism with SLA-3D printing for micromanipulation and micropolishing of biomaterials

The traditional compliant mechanisms often employ displacement amplification mechanisms to magnitude the workspace but their displacements are still smaller than 1 mm. Unlike previous studies, the present paper proposes a new conceptual design of compliant mechanism which is inspired from biomechanics of cockroach animal. The developed compliant mechanism for two specific functions, such as microgripper and micropositioner which can handle biomaterials. It can permit a large stroke over 1 mm. Modeling of the performances of the proposed mechanism are built by a couple of adaptive neuro fuzzy inference system (ANIFS) and particle swarm optimization (PSO) where PSO is to optimize the ANFIS. To enhance the performances of the mechanism, accelerated particle swarm optimization (APSO) is utilized to search the optimal design parameters. Lastly, the optimized mechanism is printed by Stereolithography (SLA) 3D technique, and the experimental verifications are performed. The results indicated that circumstance #1, the stroke is about 1.5279 mm, the frequency is 49.02103 Hz, the crosstalk error is 0.01108 mm, and the stress is 8.50514 MPa. In circumstance #2, the stroke is 1.44544 mm, the frequency is 54.51361 Hz, the crosstalk error is 0.0248 mm, and the stress is 8.35604 MPa. In last circumstance, the optimized results are achieved the stroke of 1.62369 mm, frequency of 51.62278 Hz, crosstalk of 0.028141 mm, and stress of 7.71713 MPa. The results indicated that the safety factor of three cases are over 2.5 to ensure a safe operation. The tested results are well satisfied with the simulated results.

Optimal Sizing of Battery Energy Storage Systems Considering Degradation Effect for Operating and Electricity Cost Minimization in Microgrids

A microgrid is a low‐voltage distribution network designed to provide power for small‐scale and isolated communities consisting of distributed generation and energy storage systems. In order to achieve reliable power and proper energy utilization, energy storage systems plays a vital role in microgrids by storing energy during off peak hours and discharges energy during peak hours. One of the major issues in the isolated microgrids with intermittent nature of distributed generations is the balance of energy demand. This can be achieved by appending renewable energy sources with suitable battery energy storage systems (BESS), to provide the reserve support in meeting the load demand. Battery degradation effect plays a major role in analyzing the performance of BESS lifetime. Battery degradation effect relates the capacity reduction of energy of BESS that is to be delivered to meet the load demand. Therefore, microgrid systems with BESS considering degradation effect should be optimized in such a way as to obtain minimum operating cost while ensuring minimum electricity cost to customers. Simulations of hourly battery discharges rates and simulation of actual discharge rates with obtained simulated rates need to be calculated to determine the degradation effect. The battery degradation cost and lifetime can be calculated correspondingly to minimize the objectives. Correspondingly, herein, an optimization algorithm for microgrid operating cost and customer electricity cost minimization for 24 h time horizon while considering BESS degradation effect by determining kWh and MWh throughput is presented. Particle swarm optimization (PSO), accelerated particle swarm optimization (APSO), Jaya optimization (JAYA) technique, and linear programming interior point algorithm (LP‐IP) are applied to determine the optimal operating cost and electricity cost by simulating BESS degradation parameters. Results obtained using PSO, APSO, JAYA are compared with LP‐IP solver‐based algorithm for BESS lifetime, BESS degradation cost, microgrid operating cost, and customer electricity cost for 24 h.

Heuristic algorithms based optimal tuning of FOLQI controller for quadruple tank process under disturbance conditions

Design of centralised disturbance rejection controllers for an highly interacting MIMO quadruple tank process is tedious. Recently, centralised disturbance rejection Fractional Order LQI (FOLQI) controller is designed for such system to meet the desired specifications with better performance than various disturbance rejection controllers that are available in the literature. In this paper, an optimisation problem is formulated to obtain the optimal parameters of FOLQI controller providing minimum control effort by applying various widely used heuristic methods like Cuckoo Search (CS), Accelerated Particle Swarm Optimisation (APSO) and FireFly (FF) algorithms. A detailed simulation study is carried out to compare the performance of the FOLQI and Integer Order LQI (IOLQI) controllers obtained by these heuristic algorithms under disturbance and parameter uncertainty conditions. From the simulation study it is inferred that (i) FOLQI controller provides better time domain specifications % Mp, ts and J in comparison to IOLQI controllers and (ii) FF tuned FOLQI and IOLQI controllers provide better robustness characteristics compared to CS and APSO tuned controllers.

Allocation of synchronized phasor measurement units for power grid observability using advanced binary accelerated particle swarm optimization approach

Large-scale power grid observability is still a challenge because of deteriorating infrastructure and the incorporation of renewable energy sources. A smart grid that makes use of cutting-edge technology, such as a phasor measurement unit (PMU), is an excellent option for monitoring and bringing networks up to speed with the latest information. Latterly, the considerable investment required for the deployment locations has slowed down the adoption of PMU. Therefore, because PMUs are expensive, it is necessary to deploy them in the best possible places on large-scale power grids. The most significant share of optimal PMU placement problems (OPPP) is defined as 0–1 knapsack problems. Considering this, the development of an effective optimization technique that can handle difficulties has emerged as an appealing topic in recent years. In this paper, a meta-heuristic algorithm based on the binary particle swarm algorithm (BPSO), a binary accelerated particle swarm optimization (BAPSO), is offered for solving OPPP. Since earlier research has shown that BPSO is likely to stick to local optima, the majority of them evaluated their suggested technique using small-scale test systems. The technique that has been suggested searches for the optimal solution by employing two topologies—one global and one local—that are analogous to BPSO. This work determines the optimal PMU position for a large network in a reasonable amount of time by fine-tuning the acceleration factor. Additionally, in order to employ fewer PMUs, an integration strategy was put into place for the radial buses. The OPPP solutions are provided by the suggested method within a reasonable period with prior solutions published in reliable publications, according to computational findings.

Particle-Based Optimization Algorithms for Longitudinal Control of Autonomous Vehicle: A Comparative Study

In order to improve the stability and performance of an autonomous vehicle, optimization needs to be explicitly performed in the controllers, which has an essential part in the tracking system. This work proposes a novel longitudinal control optimization scheme and a novel longitudinal controller consisting of a feed-forward and feedback term. The feed-forward term is inspired by the vehicle’s steady-state response, whereas the feedback term is a proportional-integral-derivative (PID) controller. Also, a model representing the longitudinal vehicle dynamics is designed based on physical phenomena affecting the vehicle. Besides, some nature-inspired optimization algorithms are used to determine the optimal model parameters and optimize the controller parameters, i.e., Particle Swarm Optimization (PSO), Accelerated PSO (APSO), Flower Pollination Algorithm (FPA), and Modified FPA (MFPA). The algorithms are compared in optimizing the longitudinal vehicle model and controller using the CARLA simulator, and stability tests are also done for each algorithm. In addition, the characteristics of several cost functions in controller optimization are inspected. The results show that the MFPA is the most stable algorithm, the proposed model represents the system satisfactorily, and optimizing the controller using a regularized cost function leads to better overall performance. Our code is available in https://github.com/fadamsyah/Particle-Based-Optimization-for-Longitudinal-Control.

Analysis of Electrical Characteristics of Composite Insulators with the Presence of Optimum Layer of ZnO Microvaristors

The electric field distribution of insulator surface is nonuniform, and the maximum electric field is visible around two terminals of the insulator. Using a microvaristor layer is one of the methods of field control that can reduce the electric field stresses to prevent an extension of discharges on the insulator surface and a complete flashover caused by the subsequent development of arcing. This study targets the effect of zinc oxide (ZnO) microvaristors on the electric field distribution along the contaminated and clean composite insulators that have been investigated. In addition, the impact of the insertion of microvaristor layers on the critical flashover voltage (CFO) of the insulators through a mathematical formula has been presented for the first time. The estimation of electric field distribution is conducted through finite element method (FEM) on a 400 kV insulator using COMSOL Multiphysics, in which the optimal dimensions of the microvaristor layer were obtained using the accelerated particle swarm optimization (APSO) algorithm. Then, for the first time, the analysis of the influence of the ZnO insertion on the transient performance of the insulator, i.e., the outage rate of the network, is performed in EMTP software for the insulator with the optimized insertion of the microvaristor layer. Modelling techniques were used to simulate the components of a transmission network according to the valid models. Finally, by setting different values for CFO, Monte Carlo simulation, and linking EMTP and MATLAB software, the lightning flashover rate (LFOR) and the failure risk (F.R.) of the different insulator models are calculated. It is shown that the proposed method reduces the maximum electric field of the inside and outside of the insulator, which in turn leads to a reduction in the outage rate of the power network and the insulation risk of the insulator, and an increase in CFO of the insulator.

Least Mean Mixed Norm Square/Fourth Adaptive Algorithm With Optimized FOPID Gains for Voltage Power Quality Mitigation

The conventional adaptive Least Mean Square (LMS) algorithm employs Mean Square Error (MSE) as a cost function based on second-order power error. This limits the extraction of fundamental signals from the noise and suffers from performance degradation in certain dynamic scenarios. The proposed approach addresses this problem with a mixed norm-based step size adaptive algorithm which is devised from the second and fourth-order error optimization. The proposed Mixed-Norm Constraint-based Improved Proportionate Normalized Least Mean Square Fourth (MNC-IPNLMS/F) control strategy extracts the fundamental weight quantity from the polluted grid voltage and generates the reference load voltage. This method exploits the enhancement of Dynamic Voltage Restorer (DVR) performance in terms of convergence and stability. The DC and AC-link voltage is regulated by Fractional Order Proportional Integral Derivative (FOPID) controller. The coefficients of FOPID are self-tuned by several optimizations namely, JAYA algorithm, Accelerated Particle Swarm Optimization (APSO), and Biogeography Based Optimization (BBO). This reduces manual tuning and computational complexity. The major improvements of the proposed approach are less overshoot (6.6%), undershoot (3.3%), and fast settling time (0.14s). The comparative study reveals that the FOPID control based on JAYA Optimization (JO) outperforms the others. The efficacy of the MNC-IPNLMS/F is investigated through the performance results.

Contribution to a Techno-economic Optimization for the Optimal Sizing and Management of a Secured Residential PV/Battery System

The present paper introduced a collaboration of techno-economic optimization of a PV-Battery system based on a hybrid iterative evolutionary algorithm. The major aim was to conceive the most effective design of the PV-battery system components based on an on-line Power Management Strategy (PMS) and considering the desired required energy reliability $$\left({LPSP}_{d}\right)$$ with the lowest installation cost. The PMS control algorithm enables the proposed management control to highlight the optimal sizing methodology. In fact, the data base collected from the PMS strategy affects the convergence of the proposed sizing optimization design by considering them, for each day of the month, as a new physical constraint to the next economic optimization process. Indeed, the deployed optimization approach is considered as dynamic taking into account at each step, the previous states of optimization and management algorithms. To this end, an original modeling tool dedicated to techno-economic co-optimization approach was investigated and implemented to characterize the PV/Battery system performance. To highlight the effectiveness of the proposed economic optimization approach, a comparative study between Particle Swarm Optimization (PSO) algorithm and the Accelerated Particle Swarm Optimization (APSO) algorithm was performed. The obtained simulation results showed the robustness of the APSO algorithm in terms of speed of convergence and optimum system configuration.

A Brain Storm and Chaotic Accelerated Particle Swarm Optimization Hybridization

Brain storm optimization (BSO) and particle swarm optimization (PSO) are two popular nature-inspired optimization algorithms, with BSO being the more recently developed one. It has been observed that BSO has an advantage over PSO regarding exploration with a random initialization, while PSO is more capable at local exploitation if given a predetermined initialization. The two algorithms have also been examined as a hybrid. In this work, the BSO algorithm was hybridized with the chaotic accelerated particle swarm optimization (CAPSO) algorithm in order to investigate how such an approach could serve as an improvement to the stand-alone algorithms. CAPSO is an advantageous variant of APSO, an accelerated, exploitative and minimalistic PSO algorithm. We initialized CAPSO with BSO in order to study the potential benefits from BSO’s initial exploration as well as CAPSO’s exploitation and speed. Seven benchmarking functions were used to compare the algorithms’ behavior. The chosen functions included both unimodal and multimodal benchmarking functions of various complexities and sizes of search areas. The functions were tested for different numbers of dimensions. The results showed that a properly tuned BSO–CAPSO hybrid could be significantly more beneficial over stand-alone BSO, especially with respect to computational time, while it heavily outperformed stand-alone CAPSO in the vast majority of cases.

Accelerated Particle Swarm Optimization Algorithms Coupled with Analysis of Variance for Intelligent Charging of Plug-in Hybrid Electric Vehicles

Plug-in hybrid electric vehicles (PHEVs) and plug-in electric vehicles (PEVs) have gained enormous attention for their ability to reduce fuel consumption in transportation and are, thus, helpful in the reduction of the greenhouse effect and pollution. However, they bring up some technical problems that should be resolved. Due to the ever-increasing demand for these PHEVs, the simultaneous connection of large PEVs and PHEVs to the electric grid can cause overloading, which results in disturbance to overall power system stability and quality and can cause a blackout. Such situations can be avoided by adequately manipulating power available from the grid and vehicle power demand. State of charge (SoC) is the leading performance parameter that should be optimized using computational techniques to charge vehicles efficiently. In this research, an efficient metaheuristic algorithm, accelerated particle swarm optimization (APSO), and its five variants were applied to allocate power to vehicles connected to the grid intelligently. For this, the maximization of average SoC is considered a fitness function, and each PHEV can be connected to the grid once a day so that the maximum number of cars can be charged daily. To statistically compare the performance of these six algorithms, one-way ANOVA was used. Simulation and statistical results obtained by maximizing this highly non-linear objective function show that accelerated particle swarm optimization with Variant 5 achieved some improvements in terms of computational time and best fitness value. The APSO-5 solution has a considerable percentage increase compared with the solution of other variants of APSO for the four PHEV datasets considered. Moreover, after 30 trials, APSO 5 gives the highest possible fitness value among all the algorithms.

Modeling and Analysis of a Novel 3R Parallel Compliant Mechanism

This paper presents and investigates a new three-rotation (3R) parallel compliant mechanism that uses compliant rods to achieve three rotations. The mechanism is designed for use in pointing devices or as a spatial parallel manipulator. The mobility analysis is based on the Cosserat rod model and Lagrangian dynamics equations. The dynamics equations are then effectively solved using the back-propagation neural network and chaos-enhanced accelerated particle swarm optimization. After studying the mobility of the moving platform, a simplified model is proposed and used for kinematic analysis. The analysis of motion includes discussions on forward kinematics, inverse kinematics, singularities, and the workspace. Furthermore, experiments with a prototype are conducted to verify the accuracy and stability of the mobility analysis and the simplified model.