In order to address the issue of sensor configuration redundancy in intelligent driving,this paper constructs a multi-objective optimization model that considers cost,coverage ability,and perception performance.And th...In order to address the issue of sensor configuration redundancy in intelligent driving,this paper constructs a multi-objective optimization model that considers cost,coverage ability,and perception performance.And then,combining a specific set of parameters,the NSGA-II algorithm is used to solve the multi-objective model established in this paper,and a Pareto front containing 24 typical configuration schemes is extracted after considering empirical constraints.Finally,using the decision preference method proposed in this paper that combines subjective and objective factors,decision scores are calculated and ranked for various configuration schemes from both cost and performance preferences.The research results indicate that the multi-objective optimization model established in this paper can screen and optimize various configuration schemes from the optimal principle of the vehicle,and the optimized configuration schemes can be quantitatively ranked to obtain the decision results for the vehicle under different preference tendencies.展开更多
To be close to the practical flight process and increase the precision of optimal trajectory, a six-degree-offreedom(6-DOF) trajectory is optimized for the reusable launch vehicle(RLV) using the Gauss pseudospectr...To be close to the practical flight process and increase the precision of optimal trajectory, a six-degree-offreedom(6-DOF) trajectory is optimized for the reusable launch vehicle(RLV) using the Gauss pseudospectral method(GPM). Different from the traditional trajectory optimization problem which generally considers the RLV as a point mass, the coupling between translational dynamics and rotational dynamics is taken into account. An optimization problem is formulated to minimize a performance index subject to 6-DOF equations of motion, including translational and rotational dynamics. A two-step optimal strategy is then introduced to reduce the large calculations caused by multiple variables and convergence confinement in 6-DOF trajectory optimization. The simulation results demonstrate that the 6-DOF trajectory optimal strategy for RLV is feasible.展开更多
The control problem of trajectory based path following for passenger vehicles is studied. Comprehensive nonlinear vehicle model is utilized for simulation vehicle response during various maneuvers in MATLAB/Simulink. ...The control problem of trajectory based path following for passenger vehicles is studied. Comprehensive nonlinear vehicle model is utilized for simulation vehicle response during various maneuvers in MATLAB/Simulink. In order to follow desired path, a driver model is developed to enhance closed loop driver/vehicle model. Then, linear quadratic regulator(LQR) controller is developed which regulates direct yaw moment and corrective steering angle on wheels. Particle swam optimization(PSO) method is utilized to optimize the LQR controller for various dynamic conditions. Simulation results indicate that, over various maneuvers, side slip angle and lateral acceleration can be reduced by 10% and 15%, respectively, which sustain the vehicle stable. Also, anti-lock brake system is designed for longitudinal dynamics of vehicle to achieve desired slip during braking and accelerating. Proposed comprehensive controller demonstrates that vehicle steerability can increase by about 15% during severe braking by preventing wheel from locking and reducing stopping distance.展开更多
Both the seat and cab system of truck play a vital role in ride comfort.The damping matching methods of the two systems are studied separately at present.However,the driver,seat,and cab system are one inseparable whol...Both the seat and cab system of truck play a vital role in ride comfort.The damping matching methods of the two systems are studied separately at present.However,the driver,seat,and cab system are one inseparable whole.In order to further improve ride comfort,the seat suspension is regarded as the fifth suspension of the cab,a new idea of "Five-suspensions" is proposed.Based on this idea,a 4 degree-of-freedom driver-seat-cab coupled system model is presented.Using the tested cab suspensions excitations as inputs and seat acceleration response as compared output,the simulation model is built.Taking optimal ride comfort as target,a new method of damping collaborative optimization for Five-suspensions is proposed.With a practical example of seat and cab system,the damping parameters are optimized and validated by simulation and bench test.The results show the seat vertical frequency-weighted RMS acceleration values tested for the un-optimized and optimized Five-suspensions are 0.50 m/s~2 and 0.39 m/s~2,respectively,with a decrease by 22.0%,which proves the model and method proposed are correct and reliable.The idea of "Five-suspensions" and the method proposed provide a reference for achieving global optimal damping matching of seat suspension and cab suspensions.展开更多
The 7-DOF model of a full vehicle with an active suspension is developed in this paper.The model is written into the state equation style.Actuator forces are treated as inputs in the state equations.Based on the basic...The 7-DOF model of a full vehicle with an active suspension is developed in this paper.The model is written into the state equation style.Actuator forces are treated as inputs in the state equations.Based on the basic optimal control theory,the optimal gains for the control system are figured out.So an optimal controller is developed and implemented using Matlab/Simulink,where the Riccati equation with coupling terms is deduced using the Hamilton equation.The all state feedback is chosen for the controller.The gains for all vehicle variables are traded off so that majority of indexes were up to optimal.The active suspension with optimal control is simulated in frequency domain and time domain separately,and compared with a passive suspension.Throughout all the simulation results,the optimal controller developed in this paper works well in the majority of instances.In all,the comfort and ride performance of the vehicle are improved under the active suspension with optimal control.展开更多
To realize the stabilization and the tracking of flight control for an air-breathing hypersonic cruise vehicle, the linearization of the longitudinal model under trimmed cruise condition is processed firstly. Furtherm...To realize the stabilization and the tracking of flight control for an air-breathing hypersonic cruise vehicle, the linearization of the longitudinal model under trimmed cruise condition is processed firstly. Furthermore, the flight control problem is formulated as a robust model tracking control problem. And then, based on the robust parametric approach, eigenstructure assignment and reference model tracking theory, a parametric optimization method for robust controller design is presented. The simulation results show the effectiveness of the proposed approach.展开更多
The reentry trajectory optimization for hypersonic vehicle(HV)is a current problem of great interest.Some complex constraints,such as waypoints for reconnaissance and no-fly zones for threat avoidance,are inevitably...The reentry trajectory optimization for hypersonic vehicle(HV)is a current problem of great interest.Some complex constraints,such as waypoints for reconnaissance and no-fly zones for threat avoidance,are inevitably involved in a global strike mission.Of the many direct methods,Gauss pseudospectral method(GPM)has been demonstrated as an effective tool to solve the trajectory optimization problem with typical constraints.However,a series of diffculties arises for complex constraints,such as the uncertainty of passage time for waypoints and the inaccuracy of approximate trajectory near no-fly zones.The research herein proposes a multi-phase technique based on the GPM to generate an optimal reentry trajectory for HV satisfying waypoint and nofly zone constraints.Three kinds of specifc breaks are introduced to divide the full trajectory into multiple phases.The continuity conditions are presented to ensure a smooth connection between each pair of phases.Numerical examples for reentry trajectory optimization in free-space flight and with complex constraints are used to demonstrate the proposed technique.Simulation results show the feasible application of multi-phase technique in reentry trajectory optimization with waypoint and no-fly zone constraints.展开更多
A novel method to calculate fuel-electric conversion factor for full hybrid electric vehicle(HEV)equipped with continuously variable transmission(CVT)is proposed.Based on consideration of the efficiency of pivotal...A novel method to calculate fuel-electric conversion factor for full hybrid electric vehicle(HEV)equipped with continuously variable transmission(CVT)is proposed.Based on consideration of the efficiency of pivotal components,electric motor,system efficiency optimization models are developed.According to the target of instantaneous optimization of system efficiency,operating ranges of each mode of power-train are determined,and the corresponding energy management strategies are established.The simulation results demonstrate that the energy management strategy proposed can substantially improve the vehicle fuel economy,and keep battery state of charge(SOC)change in a reasonable variation range.展开更多
The accurate prediction of vehicle speed plays an important role in vehicle's real-time energy management and online optimization control. However, the current forecast methods are mostly based on traffic conditio...The accurate prediction of vehicle speed plays an important role in vehicle's real-time energy management and online optimization control. However, the current forecast methods are mostly based on traffic conditions to predict the speed, while ignoring the impact of the driver-vehicle-road system on the actual speed profile. In this paper, the correlation of velocity and its effect factors under various driving conditions were firstly analyzed based on driver-vehicle-road-traffic data records for a more accurate prediction model. With the modeling time and prediction time considered separately, the effectiveness and accuracy of several typical artificial-intelligence speed prediction algorithms were analyzed. The results show that the combination of niche immunegenetic algorithm-support vector machine(NIGA-SVM) prediction algorithm on the city roads with genetic algorithmsupport vector machine(GA-SVM) prediction algorithm on the suburb roads and on the freeway can sharply improve the accuracy and timeliness of vehicle speed forecasting. Afterwards, the optimized GA-SVM vehicle speed prediction model was established in accordance with the optimized GA-SVM prediction algorithm at different times. And the test results verified its validity and rationality of the prediction algorithm.展开更多
This paper presents a simple and useful modeling method to acquire a dynamics model of an aerial vehicle containing unknown parameters using mechanism modeling,and then to design different identifcation experiments to...This paper presents a simple and useful modeling method to acquire a dynamics model of an aerial vehicle containing unknown parameters using mechanism modeling,and then to design different identifcation experiments to identify the parameters based on the sources and features of its unknown parameters.Based on the mathematical model of the aerial vehicle acquired by modeling and identifcation,a design for the structural parameters of the attitude control system is carried out,and the results of the attitude control flaps are verifed by simulation experiments and flight tests of the aerial vehicle.Results of the mathematical simulation and flight tests show that the mathematical model acquired using parameter identifcation is comparatively accurate and of clear mechanics,and can be used as the reference and basis for the structural design.展开更多
This paper investigates the problem of fuel-efficient and safe control of autonomous vehicle platoons. We present a two-part hierarchical control method that can guarantee platoon stability with minimal fuel consumpti...This paper investigates the problem of fuel-efficient and safe control of autonomous vehicle platoons. We present a two-part hierarchical control method that can guarantee platoon stability with minimal fuel consumption. The first part vehicle controller is derived in the context of receding horizon optimal control by constructing and solving an optimization problem of overall fuel consumption. The Second part platoon controller is a complementation of the first part, which is given on the basis of platoon stability analysis. The effectiveness of the presented platoon control method is demonstrated by both numerical simulations and experiments with laboratory-scale Arduino cars.展开更多
Besides grid-to-vehicle(G2 V) and vehicle-to-grid(V2 G) functions, the battery of an electric vehicle(EV) also has the specific feature of mobility. This means that EVs not only have the potential to utilize the stora...Besides grid-to-vehicle(G2 V) and vehicle-to-grid(V2 G) functions, the battery of an electric vehicle(EV) also has the specific feature of mobility. This means that EVs not only have the potential to utilize the storage of cheap electricity for use in high energy price periods, but can also transfer energy from one place to another place. Based on these special features of an EV battery, a new EV energy scheduling method has been developed and is described in this article. The approach is aimed at optimizing the utilization EV energy for EVs that are regularly used in multiple places. The objective is to minimize electricity costs from multiple meter points. This work applies real data in order to analyze the effectiveness of the method. The results show that by applying the control strategy presented in this paper at locations where the EVs are parked, the electricity cost can be reduced without shifting the demand and lowering customer's satisfaction. The effects of PV size and number of EVs on our model are also analyzed in this paper. This model has the potential to be used by energy system designers as a new perspective to determine optimal sizes of generators or storage devices in energy systems.展开更多
Delays of both pedestrians,who are classified according to whether complying with traffic law,and vehicles at a signalized crosswalk are analyzed in this paper.The truncated Adams' model is applied to generate the...Delays of both pedestrians,who are classified according to whether complying with traffic law,and vehicles at a signalized crosswalk are analyzed in this paper.The truncated Adams' model is applied to generate the probability and mean of delay of pedestrians non-complying with traffic law.Using the section-based traffic queuing-theory and the stochastic decomposition property of M/G/1vacation system with exhaustive service,the mean delay of vehicles is formulated.A multi-objective optimization model simultaneously minimizing the delays of pedestrians and vehicles during a signal period is proposed.The effects,which several model parameters have on the delays and the optimal solution of the model,are illustrated by numerical examples.展开更多
In this paper, on-road trajectory planning is solved by introducing intelligent computing budget allocation(ICBA) into a candidate-curve-based planning algorithm, namely, ordinal-optimization-based differential evolut...In this paper, on-road trajectory planning is solved by introducing intelligent computing budget allocation(ICBA) into a candidate-curve-based planning algorithm, namely, ordinal-optimization-based differential evolution(OODE). The proposed algorithm is named IOODE with ‘I' representing ICBA. OODE plans the trajectory in two parts: trajectory curve and acceleration profile. The best trajectory curve is picked from a set of candidate curves, where each curve is evaluated by solving a subproblem with the differential evolution(DE) algorithm. The more iterations DE performs, the more accurate the evaluation will become. Thus, we intelligently allocate the iterations to individual curves so as to reduce the total number of iterations performed. Meanwhile, the selected best curve is ensured to be one of the truly top curves with a high enough probability. Simulation results show that IOODE is 20% faster than OODE while maintaining the same performance in terms of solution quality. The computing budget allocation framework presented in this paper can also be used to enhance the efficiency of other candidate-curve-based planning methods.展开更多
文摘In order to address the issue of sensor configuration redundancy in intelligent driving,this paper constructs a multi-objective optimization model that considers cost,coverage ability,and perception performance.And then,combining a specific set of parameters,the NSGA-II algorithm is used to solve the multi-objective model established in this paper,and a Pareto front containing 24 typical configuration schemes is extracted after considering empirical constraints.Finally,using the decision preference method proposed in this paper that combines subjective and objective factors,decision scores are calculated and ranked for various configuration schemes from both cost and performance preferences.The research results indicate that the multi-objective optimization model established in this paper can screen and optimize various configuration schemes from the optimal principle of the vehicle,and the optimized configuration schemes can be quantitatively ranked to obtain the decision results for the vehicle under different preference tendencies.
基金supported by the National Basic Research Program of China(973 Program)(2012CB720003)the National Natural Science Foundation of China(10772011)
文摘To be close to the practical flight process and increase the precision of optimal trajectory, a six-degree-offreedom(6-DOF) trajectory is optimized for the reusable launch vehicle(RLV) using the Gauss pseudospectral method(GPM). Different from the traditional trajectory optimization problem which generally considers the RLV as a point mass, the coupling between translational dynamics and rotational dynamics is taken into account. An optimization problem is formulated to minimize a performance index subject to 6-DOF equations of motion, including translational and rotational dynamics. A two-step optimal strategy is then introduced to reduce the large calculations caused by multiple variables and convergence confinement in 6-DOF trajectory optimization. The simulation results demonstrate that the 6-DOF trajectory optimal strategy for RLV is feasible.
文摘The control problem of trajectory based path following for passenger vehicles is studied. Comprehensive nonlinear vehicle model is utilized for simulation vehicle response during various maneuvers in MATLAB/Simulink. In order to follow desired path, a driver model is developed to enhance closed loop driver/vehicle model. Then, linear quadratic regulator(LQR) controller is developed which regulates direct yaw moment and corrective steering angle on wheels. Particle swam optimization(PSO) method is utilized to optimize the LQR controller for various dynamic conditions. Simulation results indicate that, over various maneuvers, side slip angle and lateral acceleration can be reduced by 10% and 15%, respectively, which sustain the vehicle stable. Also, anti-lock brake system is designed for longitudinal dynamics of vehicle to achieve desired slip during braking and accelerating. Proposed comprehensive controller demonstrates that vehicle steerability can increase by about 15% during severe braking by preventing wheel from locking and reducing stopping distance.
基金Supported by National Natural Science Foundation of China(Grant No.51575325)Shandong Provincial Natural Science Foundation of China(Grant No.ZR2013EEM007)
文摘Both the seat and cab system of truck play a vital role in ride comfort.The damping matching methods of the two systems are studied separately at present.However,the driver,seat,and cab system are one inseparable whole.In order to further improve ride comfort,the seat suspension is regarded as the fifth suspension of the cab,a new idea of "Five-suspensions" is proposed.Based on this idea,a 4 degree-of-freedom driver-seat-cab coupled system model is presented.Using the tested cab suspensions excitations as inputs and seat acceleration response as compared output,the simulation model is built.Taking optimal ride comfort as target,a new method of damping collaborative optimization for Five-suspensions is proposed.With a practical example of seat and cab system,the damping parameters are optimized and validated by simulation and bench test.The results show the seat vertical frequency-weighted RMS acceleration values tested for the un-optimized and optimized Five-suspensions are 0.50 m/s~2 and 0.39 m/s~2,respectively,with a decrease by 22.0%,which proves the model and method proposed are correct and reliable.The idea of "Five-suspensions" and the method proposed provide a reference for achieving global optimal damping matching of seat suspension and cab suspensions.
文摘The 7-DOF model of a full vehicle with an active suspension is developed in this paper.The model is written into the state equation style.Actuator forces are treated as inputs in the state equations.Based on the basic optimal control theory,the optimal gains for the control system are figured out.So an optimal controller is developed and implemented using Matlab/Simulink,where the Riccati equation with coupling terms is deduced using the Hamilton equation.The all state feedback is chosen for the controller.The gains for all vehicle variables are traded off so that majority of indexes were up to optimal.The active suspension with optimal control is simulated in frequency domain and time domain separately,and compared with a passive suspension.Throughout all the simulation results,the optimal controller developed in this paper works well in the majority of instances.In all,the comfort and ride performance of the vehicle are improved under the active suspension with optimal control.
基金Sponsored by the Major Program of National Natural Science Foundation of China (Grant No.60710002)the Program for Changjiang Scholars and Innovative Research Team in University
文摘To realize the stabilization and the tracking of flight control for an air-breathing hypersonic cruise vehicle, the linearization of the longitudinal model under trimmed cruise condition is processed firstly. Furthermore, the flight control problem is formulated as a robust model tracking control problem. And then, based on the robust parametric approach, eigenstructure assignment and reference model tracking theory, a parametric optimization method for robust controller design is presented. The simulation results show the effectiveness of the proposed approach.
基金supported by Aviation Science Foundation of China(No.2011ZC13001 and 2013ZA18001)National Natural Science Foundation of China(Nos:60975073,61273349,61175109 and 61203223)Innovation Foundation of BUAA for PhD Graduates
文摘The reentry trajectory optimization for hypersonic vehicle(HV)is a current problem of great interest.Some complex constraints,such as waypoints for reconnaissance and no-fly zones for threat avoidance,are inevitably involved in a global strike mission.Of the many direct methods,Gauss pseudospectral method(GPM)has been demonstrated as an effective tool to solve the trajectory optimization problem with typical constraints.However,a series of diffculties arises for complex constraints,such as the uncertainty of passage time for waypoints and the inaccuracy of approximate trajectory near no-fly zones.The research herein proposes a multi-phase technique based on the GPM to generate an optimal reentry trajectory for HV satisfying waypoint and nofly zone constraints.Three kinds of specifc breaks are introduced to divide the full trajectory into multiple phases.The continuity conditions are presented to ensure a smooth connection between each pair of phases.Numerical examples for reentry trajectory optimization in free-space flight and with complex constraints are used to demonstrate the proposed technique.Simulation results show the feasible application of multi-phase technique in reentry trajectory optimization with waypoint and no-fly zone constraints.
基金Supported by the National Science and Technology Support Program(2013BAG12B01)Foundational and Advanced Research Program General Project of Chongqing City(cstc2013jcyjjq60002)
文摘A novel method to calculate fuel-electric conversion factor for full hybrid electric vehicle(HEV)equipped with continuously variable transmission(CVT)is proposed.Based on consideration of the efficiency of pivotal components,electric motor,system efficiency optimization models are developed.According to the target of instantaneous optimization of system efficiency,operating ranges of each mode of power-train are determined,and the corresponding energy management strategies are established.The simulation results demonstrate that the energy management strategy proposed can substantially improve the vehicle fuel economy,and keep battery state of charge(SOC)change in a reasonable variation range.
基金supported by the Nanjing University of Aeronautics and Astronautics Research Funding(Grant No.NS2015028)
文摘The accurate prediction of vehicle speed plays an important role in vehicle's real-time energy management and online optimization control. However, the current forecast methods are mostly based on traffic conditions to predict the speed, while ignoring the impact of the driver-vehicle-road system on the actual speed profile. In this paper, the correlation of velocity and its effect factors under various driving conditions were firstly analyzed based on driver-vehicle-road-traffic data records for a more accurate prediction model. With the modeling time and prediction time considered separately, the effectiveness and accuracy of several typical artificial-intelligence speed prediction algorithms were analyzed. The results show that the combination of niche immunegenetic algorithm-support vector machine(NIGA-SVM) prediction algorithm on the city roads with genetic algorithmsupport vector machine(GA-SVM) prediction algorithm on the suburb roads and on the freeway can sharply improve the accuracy and timeliness of vehicle speed forecasting. Afterwards, the optimized GA-SVM vehicle speed prediction model was established in accordance with the optimized GA-SVM prediction algorithm at different times. And the test results verified its validity and rationality of the prediction algorithm.
基金supported by the National Natural Science Foundation of China(No.11102019)
文摘This paper presents a simple and useful modeling method to acquire a dynamics model of an aerial vehicle containing unknown parameters using mechanism modeling,and then to design different identifcation experiments to identify the parameters based on the sources and features of its unknown parameters.Based on the mathematical model of the aerial vehicle acquired by modeling and identifcation,a design for the structural parameters of the attitude control system is carried out,and the results of the attitude control flaps are verifed by simulation experiments and flight tests of the aerial vehicle.Results of the mathematical simulation and flight tests show that the mathematical model acquired using parameter identifcation is comparatively accurate and of clear mechanics,and can be used as the reference and basis for the structural design.
基金supported by the National Natural Science Foundation of China(Grant Nos.61273107 and 61573077)Dalian Leading Talent(Grant No.841252)
文摘This paper investigates the problem of fuel-efficient and safe control of autonomous vehicle platoons. We present a two-part hierarchical control method that can guarantee platoon stability with minimal fuel consumption. The first part vehicle controller is derived in the context of receding horizon optimal control by constructing and solving an optimization problem of overall fuel consumption. The Second part platoon controller is a complementation of the first part, which is given on the basis of platoon stability analysis. The effectiveness of the presented platoon control method is demonstrated by both numerical simulations and experiments with laboratory-scale Arduino cars.
基金supported by the China Scholarship Council and Donghua University Graduate Student Degree Thesis Innovation Fund Project (Grant No. CUSF-DH-D-2013059)
文摘Besides grid-to-vehicle(G2 V) and vehicle-to-grid(V2 G) functions, the battery of an electric vehicle(EV) also has the specific feature of mobility. This means that EVs not only have the potential to utilize the storage of cheap electricity for use in high energy price periods, but can also transfer energy from one place to another place. Based on these special features of an EV battery, a new EV energy scheduling method has been developed and is described in this article. The approach is aimed at optimizing the utilization EV energy for EVs that are regularly used in multiple places. The objective is to minimize electricity costs from multiple meter points. This work applies real data in order to analyze the effectiveness of the method. The results show that by applying the control strategy presented in this paper at locations where the EVs are parked, the electricity cost can be reduced without shifting the demand and lowering customer's satisfaction. The effects of PV size and number of EVs on our model are also analyzed in this paper. This model has the potential to be used by energy system designers as a new perspective to determine optimal sizes of generators or storage devices in energy systems.
基金supported by the National Natural Science Foundation of China under Grant Nos.71261016and 71401050the Program for New Century Excellent Talents in University under Grant No.NCET-12-1016+1 种基金the Natural Science Foundation of Inner Mongolia of China under Grant No.2014JQ03the Fundamental Research Funds for the Central Universities under Grant No.2013HGBZ0174
文摘Delays of both pedestrians,who are classified according to whether complying with traffic law,and vehicles at a signalized crosswalk are analyzed in this paper.The truncated Adams' model is applied to generate the probability and mean of delay of pedestrians non-complying with traffic law.Using the section-based traffic queuing-theory and the stochastic decomposition property of M/G/1vacation system with exhaustive service,the mean delay of vehicles is formulated.A multi-objective optimization model simultaneously minimizing the delays of pedestrians and vehicles during a signal period is proposed.The effects,which several model parameters have on the delays and the optimal solution of the model,are illustrated by numerical examples.
基金supported by the National Natural Science Foundation of China(No.61273039)
文摘In this paper, on-road trajectory planning is solved by introducing intelligent computing budget allocation(ICBA) into a candidate-curve-based planning algorithm, namely, ordinal-optimization-based differential evolution(OODE). The proposed algorithm is named IOODE with ‘I' representing ICBA. OODE plans the trajectory in two parts: trajectory curve and acceleration profile. The best trajectory curve is picked from a set of candidate curves, where each curve is evaluated by solving a subproblem with the differential evolution(DE) algorithm. The more iterations DE performs, the more accurate the evaluation will become. Thus, we intelligently allocate the iterations to individual curves so as to reduce the total number of iterations performed. Meanwhile, the selected best curve is ensured to be one of the truly top curves with a high enough probability. Simulation results show that IOODE is 20% faster than OODE while maintaining the same performance in terms of solution quality. The computing budget allocation framework presented in this paper can also be used to enhance the efficiency of other candidate-curve-based planning methods.