The problems associated with vibrations of viaducts and low-frequency structural noise radiation caused by train excitation continue to increase in importance.A new floating-slab track vibration isolator-non-obstructi...The problems associated with vibrations of viaducts and low-frequency structural noise radiation caused by train excitation continue to increase in importance.A new floating-slab track vibration isolator-non-obstructive particle damping-phononic crystal vibration isolator is proposed herein,which uses the particle damping vibration absorption technology and bandgap vibration control theory.The vibration reduction performance of the NOPD-PCVI was analyzed from the perspective of vibration control.The paper explores the structure-borne noise reduction performance of the NOPD-PCVIs installed on different bridge structures under varying service conditions encountered in practical engineering applications.The load transferred to the bridge is obtained from a coupled train-FST-bridge analytical model considering the different structural parameters of bridges.The vibration responses are obtained using the finite element method,while the structural noise radiation is simulated using the frequency-domain boundary element method.Using the particle swarm optimization algorithm,the parameters of the NOPD-PCVI are optimized so that its frequency bandgap matches the dominant bridge structural noise frequency range.The noise reduction performance of the NOPD-PCVIs is compared to the steel-spring isolation under different service conditions.展开更多
In order to improve the efficiency of traffic signal control for an over-saturated intersection group, a nondominated sorting genetic algorithm Ⅱ(NSGA-Ⅱ) based traffic signal control optimization algorithm is prop...In order to improve the efficiency of traffic signal control for an over-saturated intersection group, a nondominated sorting genetic algorithm Ⅱ(NSGA-Ⅱ) based traffic signal control optimization algorithm is proposed. The throughput maximum and average queue ratio minimum for the critical route of the intersection group are selected as the optimization objectives of the traffic signal control for the over-saturated condition. The consequences of the efficiency between traffic signal timing plans generated by the proposed algorithm and a commonly utilized signal timing optimization software Synchro are compared in a VISSIM signal control application programming interfaces (SCAPI) simulation environment by using real filed observed traffic data. The simulation results indicate that the signal timing plan generated by the proposed algorithm is more efficient in managing oversaturated flows at intersection groups, and, thus, it has the capability of optimizing signal timing under the over-saturated conditions.展开更多
In order to incorporate the decision maker's preference into multiobjective optimization a preference-based multiobjective artificial bee colony algorithm PMABCA is proposed.In the proposed algorithm a novel referenc...In order to incorporate the decision maker's preference into multiobjective optimization a preference-based multiobjective artificial bee colony algorithm PMABCA is proposed.In the proposed algorithm a novel reference point based preference expression method is addressed.The fitness assignment function is defined based on the nondominated rank and the newly defined preference distance.An archive set is introduced for saving the nondominated solutions and an improved crowding-distance operator is addressed to remove the extra solutions in the archive.The experimental results of two benchmark test functions show that a preferred set of solutions and some other non-preference solutions are achieved simultaneously.The simulation results of the proportional-integral-derivative PID parameter optimization for superheated steam temperature verify that the PMABCA is efficient in aiding to making a reasonable decision.展开更多
This study presents analysis, control and comparison of three hybrid approaches for the direct torque control (DTC) of the dual star induction motor (DSIM) drive. Its objective consists of combining three different he...This study presents analysis, control and comparison of three hybrid approaches for the direct torque control (DTC) of the dual star induction motor (DSIM) drive. Its objective consists of combining three different heuristic optimization techniques including PID-PSO, Fuzzy-PSO and GA-PSO to improve the DSIM speed controlled loop behavior. The GA and PSO algorithms are developed and implemented into MATLAB. As a result, fuzzy-PSO is the most appropriate scheme. The main performance of fuzzy-PSO is reducing high torque ripples, improving rise time and avoiding disturbances that affect the drive performance.展开更多
Coverage challenge for small considered to be a optlmlzation is a main cell clusters which are promising solution to provide seamless cellular coverage for large indoor or outdoor areas. This paper focuses on small ce...Coverage challenge for small considered to be a optlmlzation is a main cell clusters which are promising solution to provide seamless cellular coverage for large indoor or outdoor areas. This paper focuses on small cell cluster coverage problems and proposes both centralized and distributed self-optimization methods. Modified Particle swarm optimization (MPSO) is introduced to centralized optimization which employs particle swarm optimization (PSO) and introduces a heuristic power control scheme to accelerate the algorithm to search tbr the global optimum solution. Distributed coverage optimization is modeled as a non-cooperative game, with a utility function considering both throughput and interference. An iterative power control algorithm is then proposed using game theory (DGT) which converges to Nash Equilibrium (NE). Simulation results show that both MPSO and DGT have excellent performance in coverage optimization and outperform optimization using simulated annealing algorithm (SA), reaching higher coverage ratio and throughput while with less iterations.展开更多
Proton Exchange Membrane Fuel Cells (PEMFCs) are the main focus of their current development as power sources because they are capable of higher power density and faster start-up than other fuel cells. The humidificat...Proton Exchange Membrane Fuel Cells (PEMFCs) are the main focus of their current development as power sources because they are capable of higher power density and faster start-up than other fuel cells. The humidification system and output performance of PEMFC stack are briefly analyzed. Predictive control of PEMFC based on Support Vector Regression Machine (SVRM) is presented and the SVRM is constructed. The processing plant is modelled on SVRM and the predictive control law is obtained by using Particle Swarm Optimization (PSO). The simulation and the results showed that the SVRM and the PSO re-ceding optimization applied to the PEMFC predictive control yielded good performance.展开更多
A new intelligent anti-swing control scheme,which combined fuzzy neural network(FNN) and sliding mode control(SMC) with particle swarm optimization(PSO),was presented for bridge crane.The outputs of three fuzzy neural...A new intelligent anti-swing control scheme,which combined fuzzy neural network(FNN) and sliding mode control(SMC) with particle swarm optimization(PSO),was presented for bridge crane.The outputs of three fuzzy neural networks were used to approach the uncertainties of the positioning subsystem,lifting-rope subsystem and anti-swing subsystem.Then,the parameters of the controller were optimized with PSO to enable the system to have good dynamic performances.During the process of high-speed load hoisting and dropping,this method can not only realize the accurate position of the trolley and eliminate the sway of the load in spite of existing uncertainties,and the maximum swing angle is only ±0.1 rad,but also completely eliminate the chattering of conventional sliding mode control and improve the robustness of system.The simulation results show the correctness and validity of this method.展开更多
Polarization mode dispersion(PMD) is considered to be the ultimate limitation in high-speed optical fiber communication systems. Establishing an effective control algorithm for adaptive PMD compensation is a challengi...Polarization mode dispersion(PMD) is considered to be the ultimate limitation in high-speed optical fiber communication systems. Establishing an effective control algorithm for adaptive PMD compensation is a challenging task, because PMD possesses the time-varying and statistical properties. The particle swarm optimization(PSO) algorithm is introduced into self-adaptive PMD compensation as feedback control algorithm. The experiment results show that PSO-based control algorithm has some unique features of rapid convergence to the global optimum without being trapped in local sub-optima and good robustness to noise in the optical fiber transmission line that has never been achieved in PMD compensation before.展开更多
S surface controllers have been proven to provide effective motion control for an autonomous underwater vehicle (AUV).However, it is difficult to adjust their control parameters manually.Choosing the optimum parameter...S surface controllers have been proven to provide effective motion control for an autonomous underwater vehicle (AUV).However, it is difficult to adjust their control parameters manually.Choosing the optimum parameters for the controller of a particular AUV is a significant challenge.To automate the process, a modified particle swarm optimization (MPSO) algorithm was proposed.It was based on immune theory, and used a nonlinear regression strategy for inertia weight to optimize AUV control parameters.A semi-physical simulation system for the AUV was developed as a platform to verify the proposed control method, and its structure was considered.The simulation results indicated that the semi-physical simulation platform was helpful, the optimization algorithm has good local and global searching abilities, and the method can be reliably used for an AUV.展开更多
Most conventional robust design methods assume design solutions are fixed values. Using these methods, designers set each control factor to a fixed value to maximize the robustness of objective characteristics. Howeve...Most conventional robust design methods assume design solutions are fixed values. Using these methods, designers set each control factor to a fixed value to maximize the robustness of objective characteristics. However, fluctuations in the objective characteristic often exceed the allowable range in a design problem. Consequently, it is difficult to obtain sufficient robustness using conventional methods. This research defines adjustable control factors whose values can be adjusted within a given range to increase robustness and proposes a method to calculate robustness, including factors to adjust the objective characteristic and derive optimum ranges of the factors. The robustness index, which indicates the feasibility that the objective characteristic values are within the tolerance by the adjustment, is calculated by the Monte Carlo method, while the range of adjustable control factors is optimized using the Vector evaluated particle swarm optimization. Finally, an engineering example is presented to demonstrate the applicability of the proposed method.展开更多
Aiming at the diversity and nonlinearity of the elevator system control target, an effective group method based on a hybrid algorithm of genetic algorithm and neural network is presented in this paper. The genetic alg...Aiming at the diversity and nonlinearity of the elevator system control target, an effective group method based on a hybrid algorithm of genetic algorithm and neural network is presented in this paper. The genetic algorithm is used to search the weight of the neural network. At the same time, the multi-objective-based evaluation function is adopted, in which there are three main indicators including the passenger waiting time, car passengers number and the number of stops. Different weights are given to meet the actual needs. The optimal values of the evaluation function are obtained, and the optimal dispatch control of the elevator group control system based on neural network is realized. By analyzing the running of the elevator group control system, all the processes and steps are presented. The validity of the hybrid algorithm is verified by the dynamic imitation performance.展开更多
A new chaotic particle swarm algorithm is proposed in order to avoid the premature convergence of the particle swarm optimization and the shortcomings of the chaotic optimization, such as slow searching speed and low ...A new chaotic particle swarm algorithm is proposed in order to avoid the premature convergence of the particle swarm optimization and the shortcomings of the chaotic optimization, such as slow searching speed and low accuracy when used in the multivariable systems or in large search space. The new algorithm combines the particle swarm algorithm and the chaotic optimization, using randomness and ergodicity of chaos to overcome the premature convergence of the particle swarm optimization. At the same time, a new neural network feedback linearization control system is built to control the single-machine infinite-bus system. The network parameters are trained by the chaos particle swarm algorithm, which makes the control achieve optimization and the control law of prime mover output torque obtained. Finally, numerical simulation and practical application validate the effectiveness of the method.展开更多
This paper addresses the enhancement of power system stability by simultaneous tuning of synergetic excitation damping controller and SVC (static var compensator)-based damping controllers. Each machine or generator...This paper addresses the enhancement of power system stability by simultaneous tuning of synergetic excitation damping controller and SVC (static var compensator)-based damping controllers. Each machine or generator is considered as a subsystem and its interaction with the remaining part of the system, the SVC inclusive, is modeled as a quadratic function of the active power delivered by the generator. Stable manifold is constructed for each excitation controller and based on that, an effective damping controller is derived. A lead-lag compensator is employed as a supplementary controller for the SVC. PSO (particle swarm optimization) algorithm is effectively utilized to simultaneously tune the parameters for the excitation damping controller(s) and the SVC supplementary controller. The coordination of the controllers effectively dampens the power angle oscillation and regulates the generator terminal voltage when a fault occurs. Simulation results are obtained by using the PAT (power analysis toolbox) for a SMIB (single machine infinite bus) system and a two area power system.展开更多
RES (renewable energy sources), such as wind and photovoltaic power plants, suffer from their stochastic nature that is why their behavior on market is very delicate. In order to diversify risk, a concept of VPP (v...RES (renewable energy sources), such as wind and photovoltaic power plants, suffer from their stochastic nature that is why their behavior on market is very delicate. In order to diversify risk, a concept of VPP (virtual power plant) has been developed. The VPP is composed of several RES, from which at least one of them is fully controllable. Because the production of noncontrollable RES can not be forecasted perfectly, therefore an optimal dispatch schedule within VPP is needed. To address this problem, an APSO (accelerated particle swarm optimization) is used to solve the constrained optimal dispatch problem within VPP. The experimental results show that the proposed optimization method provides high quality solutions while meeting constraints.展开更多
An optimal motion planning of a free-falling cat based on the spline approximation is investigated.Nonholonomicity arises in a free-falling cat subjected to nonintegrable velocity constraints or nonintegrable conserva...An optimal motion planning of a free-falling cat based on the spline approximation is investigated.Nonholonomicity arises in a free-falling cat subjected to nonintegrable velocity constraints or nonintegrable conservation laws.The equation of dynamics of a free-falling cat is obtained by using the model of two symmetric rigid bodies.The control of the system can be converted to the motion planning problem for a driftless system.A cost function is used to incorporate the final errors and control energy.The motion planning is to determine control inputs to minimize the cost function and is formulated as an infinite dimensional optimal control problem.By using the control parameterization,the infinite dimensional optimal control problem can be transformed to a finite dimensional one.The particle swarm optimization(PSO) algorithm with the cubic spline approximation is proposed to solve the finite dimension optimal control problem.The cubic spline approximation is introduced to realize the control parameterization.The resulting controls are smooth and the initial and terminal values of the control inputs are zeros,so they can be easily generated by experiment.Simulations are also performed for the nonholonomic motion planning of a free-falling cat.Simulated experimental results show that the proposed algorithm is more effective than the Newtoian algorithm.展开更多
基金Project(51978585)supported by the National Natural Science Foundation,ChinaProject(2022YFB2603404)supported by the National Key Research and Development Program,China+1 种基金Project(U1734207)supported by the High-speed Rail Joint Fund Key Projects of Basic Research,ChinaProject(2023NSFSC1975)supported by the Sichuan Nature and Science Foundation Innovation Research Group Project,China。
文摘The problems associated with vibrations of viaducts and low-frequency structural noise radiation caused by train excitation continue to increase in importance.A new floating-slab track vibration isolator-non-obstructive particle damping-phononic crystal vibration isolator is proposed herein,which uses the particle damping vibration absorption technology and bandgap vibration control theory.The vibration reduction performance of the NOPD-PCVI was analyzed from the perspective of vibration control.The paper explores the structure-borne noise reduction performance of the NOPD-PCVIs installed on different bridge structures under varying service conditions encountered in practical engineering applications.The load transferred to the bridge is obtained from a coupled train-FST-bridge analytical model considering the different structural parameters of bridges.The vibration responses are obtained using the finite element method,while the structural noise radiation is simulated using the frequency-domain boundary element method.Using the particle swarm optimization algorithm,the parameters of the NOPD-PCVI are optimized so that its frequency bandgap matches the dominant bridge structural noise frequency range.The noise reduction performance of the NOPD-PCVIs is compared to the steel-spring isolation under different service conditions.
基金The National Natural Science Foundation of China(No.51208054)
文摘In order to improve the efficiency of traffic signal control for an over-saturated intersection group, a nondominated sorting genetic algorithm Ⅱ(NSGA-Ⅱ) based traffic signal control optimization algorithm is proposed. The throughput maximum and average queue ratio minimum for the critical route of the intersection group are selected as the optimization objectives of the traffic signal control for the over-saturated condition. The consequences of the efficiency between traffic signal timing plans generated by the proposed algorithm and a commonly utilized signal timing optimization software Synchro are compared in a VISSIM signal control application programming interfaces (SCAPI) simulation environment by using real filed observed traffic data. The simulation results indicate that the signal timing plan generated by the proposed algorithm is more efficient in managing oversaturated flows at intersection groups, and, thus, it has the capability of optimizing signal timing under the over-saturated conditions.
基金The National Natural Science Foundation of China(No.51306082,51476027)
文摘In order to incorporate the decision maker's preference into multiobjective optimization a preference-based multiobjective artificial bee colony algorithm PMABCA is proposed.In the proposed algorithm a novel reference point based preference expression method is addressed.The fitness assignment function is defined based on the nondominated rank and the newly defined preference distance.An archive set is introduced for saving the nondominated solutions and an improved crowding-distance operator is addressed to remove the extra solutions in the archive.The experimental results of two benchmark test functions show that a preferred set of solutions and some other non-preference solutions are achieved simultaneously.The simulation results of the proportional-integral-derivative PID parameter optimization for superheated steam temperature verify that the PMABCA is efficient in aiding to making a reasonable decision.
基金Project supported by Faculty of Technology,Department of Electrical Engineering,University of Batna,Algeria
文摘This study presents analysis, control and comparison of three hybrid approaches for the direct torque control (DTC) of the dual star induction motor (DSIM) drive. Its objective consists of combining three different heuristic optimization techniques including PID-PSO, Fuzzy-PSO and GA-PSO to improve the DSIM speed controlled loop behavior. The GA and PSO algorithms are developed and implemented into MATLAB. As a result, fuzzy-PSO is the most appropriate scheme. The main performance of fuzzy-PSO is reducing high torque ripples, improving rise time and avoiding disturbances that affect the drive performance.
基金supported by the National High-Tech Development 863 Program of China (Grant DOS. 2012AA012801)National Natural Science Foundation of China(No.61331009)
文摘Coverage challenge for small considered to be a optlmlzation is a main cell clusters which are promising solution to provide seamless cellular coverage for large indoor or outdoor areas. This paper focuses on small cell cluster coverage problems and proposes both centralized and distributed self-optimization methods. Modified Particle swarm optimization (MPSO) is introduced to centralized optimization which employs particle swarm optimization (PSO) and introduces a heuristic power control scheme to accelerate the algorithm to search tbr the global optimum solution. Distributed coverage optimization is modeled as a non-cooperative game, with a utility function considering both throughput and interference. An iterative power control algorithm is then proposed using game theory (DGT) which converges to Nash Equilibrium (NE). Simulation results show that both MPSO and DGT have excellent performance in coverage optimization and outperform optimization using simulated annealing algorithm (SA), reaching higher coverage ratio and throughput while with less iterations.
基金Project (No. 2003AA517020) supported by the Hi-Tech Researchand Development Program (863) of China
文摘Proton Exchange Membrane Fuel Cells (PEMFCs) are the main focus of their current development as power sources because they are capable of higher power density and faster start-up than other fuel cells. The humidification system and output performance of PEMFC stack are briefly analyzed. Predictive control of PEMFC based on Support Vector Regression Machine (SVRM) is presented and the SVRM is constructed. The processing plant is modelled on SVRM and the predictive control law is obtained by using Particle Swarm Optimization (PSO). The simulation and the results showed that the SVRM and the PSO re-ceding optimization applied to the PEMFC predictive control yielded good performance.
基金Project(51075289) supported by the National Natural Science Foundation of ChinaProject(20122014) supported by the Doctor Foundation of Taiyuan University of Science and Technology,China
文摘A new intelligent anti-swing control scheme,which combined fuzzy neural network(FNN) and sliding mode control(SMC) with particle swarm optimization(PSO),was presented for bridge crane.The outputs of three fuzzy neural networks were used to approach the uncertainties of the positioning subsystem,lifting-rope subsystem and anti-swing subsystem.Then,the parameters of the controller were optimized with PSO to enable the system to have good dynamic performances.During the process of high-speed load hoisting and dropping,this method can not only realize the accurate position of the trolley and eliminate the sway of the load in spite of existing uncertainties,and the maximum swing angle is only ±0.1 rad,but also completely eliminate the chattering of conventional sliding mode control and improve the robustness of system.The simulation results show the correctness and validity of this method.
基金National Natural Science Foundation of China(60577046) Cooperation Building Project of Beijing EducationCommittee(XK100130437)
文摘Polarization mode dispersion(PMD) is considered to be the ultimate limitation in high-speed optical fiber communication systems. Establishing an effective control algorithm for adaptive PMD compensation is a challenging task, because PMD possesses the time-varying and statistical properties. The particle swarm optimization(PSO) algorithm is introduced into self-adaptive PMD compensation as feedback control algorithm. The experiment results show that PSO-based control algorithm has some unique features of rapid convergence to the global optimum without being trapped in local sub-optima and good robustness to noise in the optical fiber transmission line that has never been achieved in PMD compensation before.
基金Supported by the 863 Project under Grant No.2008AA092301the Fundamental Research Foundation of Harbin Engineering University under Grant No.2007001
文摘S surface controllers have been proven to provide effective motion control for an autonomous underwater vehicle (AUV).However, it is difficult to adjust their control parameters manually.Choosing the optimum parameters for the controller of a particular AUV is a significant challenge.To automate the process, a modified particle swarm optimization (MPSO) algorithm was proposed.It was based on immune theory, and used a nonlinear regression strategy for inertia weight to optimize AUV control parameters.A semi-physical simulation system for the AUV was developed as a platform to verify the proposed control method, and its structure was considered.The simulation results indicated that the semi-physical simulation platform was helpful, the optimization algorithm has good local and global searching abilities, and the method can be reliably used for an AUV.
文摘Most conventional robust design methods assume design solutions are fixed values. Using these methods, designers set each control factor to a fixed value to maximize the robustness of objective characteristics. However, fluctuations in the objective characteristic often exceed the allowable range in a design problem. Consequently, it is difficult to obtain sufficient robustness using conventional methods. This research defines adjustable control factors whose values can be adjusted within a given range to increase robustness and proposes a method to calculate robustness, including factors to adjust the objective characteristic and derive optimum ranges of the factors. The robustness index, which indicates the feasibility that the objective characteristic values are within the tolerance by the adjustment, is calculated by the Monte Carlo method, while the range of adjustable control factors is optimized using the Vector evaluated particle swarm optimization. Finally, an engineering example is presented to demonstrate the applicability of the proposed method.
基金Supported by National Natural Science Foundation of China (No60874077) Specialized Research Funds for Doctoral Program of Higher Education of China (No20060056054) Research Funds for Scientific Financing Projects of Quality Control Public Welfare Profession (No2007GYB172)
文摘Aiming at the diversity and nonlinearity of the elevator system control target, an effective group method based on a hybrid algorithm of genetic algorithm and neural network is presented in this paper. The genetic algorithm is used to search the weight of the neural network. At the same time, the multi-objective-based evaluation function is adopted, in which there are three main indicators including the passenger waiting time, car passengers number and the number of stops. Different weights are given to meet the actual needs. The optimal values of the evaluation function are obtained, and the optimal dispatch control of the elevator group control system based on neural network is realized. By analyzing the running of the elevator group control system, all the processes and steps are presented. The validity of the hybrid algorithm is verified by the dynamic imitation performance.
基金This work is supported by National Natural Science Foundation of China (50776005).
文摘A new chaotic particle swarm algorithm is proposed in order to avoid the premature convergence of the particle swarm optimization and the shortcomings of the chaotic optimization, such as slow searching speed and low accuracy when used in the multivariable systems or in large search space. The new algorithm combines the particle swarm algorithm and the chaotic optimization, using randomness and ergodicity of chaos to overcome the premature convergence of the particle swarm optimization. At the same time, a new neural network feedback linearization control system is built to control the single-machine infinite-bus system. The network parameters are trained by the chaos particle swarm algorithm, which makes the control achieve optimization and the control law of prime mover output torque obtained. Finally, numerical simulation and practical application validate the effectiveness of the method.
文摘This paper addresses the enhancement of power system stability by simultaneous tuning of synergetic excitation damping controller and SVC (static var compensator)-based damping controllers. Each machine or generator is considered as a subsystem and its interaction with the remaining part of the system, the SVC inclusive, is modeled as a quadratic function of the active power delivered by the generator. Stable manifold is constructed for each excitation controller and based on that, an effective damping controller is derived. A lead-lag compensator is employed as a supplementary controller for the SVC. PSO (particle swarm optimization) algorithm is effectively utilized to simultaneously tune the parameters for the excitation damping controller(s) and the SVC supplementary controller. The coordination of the controllers effectively dampens the power angle oscillation and regulates the generator terminal voltage when a fault occurs. Simulation results are obtained by using the PAT (power analysis toolbox) for a SMIB (single machine infinite bus) system and a two area power system.
文摘RES (renewable energy sources), such as wind and photovoltaic power plants, suffer from their stochastic nature that is why their behavior on market is very delicate. In order to diversify risk, a concept of VPP (virtual power plant) has been developed. The VPP is composed of several RES, from which at least one of them is fully controllable. Because the production of noncontrollable RES can not be forecasted perfectly, therefore an optimal dispatch schedule within VPP is needed. To address this problem, an APSO (accelerated particle swarm optimization) is used to solve the constrained optimal dispatch problem within VPP. The experimental results show that the proposed optimization method provides high quality solutions while meeting constraints.
基金supported by the National Natural Science Foundation of China (Grant No. 11072038)the Municipal Key Programs of Natural Science Foundation of Beijing,China (Grant No. KZ201110772039)
文摘An optimal motion planning of a free-falling cat based on the spline approximation is investigated.Nonholonomicity arises in a free-falling cat subjected to nonintegrable velocity constraints or nonintegrable conservation laws.The equation of dynamics of a free-falling cat is obtained by using the model of two symmetric rigid bodies.The control of the system can be converted to the motion planning problem for a driftless system.A cost function is used to incorporate the final errors and control energy.The motion planning is to determine control inputs to minimize the cost function and is formulated as an infinite dimensional optimal control problem.By using the control parameterization,the infinite dimensional optimal control problem can be transformed to a finite dimensional one.The particle swarm optimization(PSO) algorithm with the cubic spline approximation is proposed to solve the finite dimension optimal control problem.The cubic spline approximation is introduced to realize the control parameterization.The resulting controls are smooth and the initial and terminal values of the control inputs are zeros,so they can be easily generated by experiment.Simulations are also performed for the nonholonomic motion planning of a free-falling cat.Simulated experimental results show that the proposed algorithm is more effective than the Newtoian algorithm.