In this paper,we investigate the application of the Unmanned Aerial Vehicle(UAV)-enabled relaying system in emergency communications,where one UAV is applied as a relay to help transmit information from ground users t...In this paper,we investigate the application of the Unmanned Aerial Vehicle(UAV)-enabled relaying system in emergency communications,where one UAV is applied as a relay to help transmit information from ground users to a Base Station(BS).We maximize the total transmitted data from the users to the BS,by optimizing the user communication scheduling and association along with the power allocation and the trajectory of the UAV.To solve this non-convex optimization problem,we propose the traditional Convex Optimization(CO)and the Reinforcement Learning(RL)-based approaches.Specifically,we apply the block coordinate descent and successive convex approximation techniques in the CO approach,while applying the soft actor-critic algorithm in the RL approach.The simulation results show that both approaches can solve the proposed optimization problem and obtain good results.Moreover,the RL approach establishes emergency communications more rapidly than the CO approach once the training process has been completed.展开更多
The welding of medium and thick plates has a wide range of applications in the engineering field.Industrial welding robots are gradually replacing traditional welding operations due to their significant advantages,suc...The welding of medium and thick plates has a wide range of applications in the engineering field.Industrial welding robots are gradually replacing traditional welding operations due to their significant advantages,such as high welding quality,high work efficiency,and effective reduction of labor intensity.Ensuring the accuracy of the welding trajectory for the welding robot is crucial for guaranteeing welding quality.In this paper,the author uses the chaos sparrow search algorithm to optimize the trajectory of a multi-layer and multi-pass welding robot for medium and thick plates.Firstly,the Sparrow Search Algorithm(SSA)is improved by introducing tent chaotic mapping and Gaussian mutation of the inertia weight factor.Secondly,in order to prevent the welding robot arm from colliding with obstacles in the welding environment during the welding process,maintain the stability of the welding robot,and ensure the continuous stability of the changes in each joint angle,joint angular velocity,and angular velocity of the joint angle,a welding robot model is established by improving the Denavit-Hartenberg parameter method.A multi-objective optimization fitness function is used to optimize the trajectory of the welding robot,minimizing time and energy consumption.Thirdly,the optimization and convergence performance of SSA and Chaos Sparrow Search Algorithm(CSSA)are compared through 10 benchmark test functions.Based on the six sets of test functions,the CSSA algorithm consistently maintains superior optimization performance and has excellent stability,with a faster decline in the convergence curve compared to the SSA algorithm.Finally,the accuracy of welding is tested through V-shaped multi-layer and multi-pass welding experiments.The experimental results show that the CSSA algorithm has a strong superiority in trajectory optimization of multi-layer and multi-pass welding for medium and thick plates,with an accuracy rate of 99.5%.It is an effective optimization method that can meet the actual needs of production.展开更多
The dynamic motion capability of humanoid robots is a key indicator for evaluating their performance.Jumping,as a typical dynamic motion,is of great significance for enhancing the robot’s flexibility and terrain adap...The dynamic motion capability of humanoid robots is a key indicator for evaluating their performance.Jumping,as a typical dynamic motion,is of great significance for enhancing the robot’s flexibility and terrain adaptability in unstructured environments.However,achieving high-dynamic jumping control of humanoid robots has become a challenge due to the high degree of freedom and strongly coupled dynamic characteristics.The idea for this paper originated from the human response process to jumping commands,aiming to achieve online trajectory optimization and jumping motion control of humanoid robots.Firstly,we employ nonlinear optimization in combination with the Single Rigid Body Model(SRBM)to generate a robot’s Center of Mass(CoM)trajectory that complies with physical constraints and minimizes the angular momentum of the CoM.Then,a Model Predictive Controller(MPC)is designed to track and control the CoM trajectory,obtaining the required contact forces at the robot’s feet.Finally,a Whole-Body Controller(WBC)is used to generate full-body joint motion trajectories and driving torques,based on the prioritized sequence of tasks designed for the jumping process.The control framework proposed in this paper considers the dynamic characteristics of the robot’s jumping process,with a focus on improving the real-time performance of trajectory optimization and the robustness of controller.Simulation and experimental results demonstrate that our robot successfully executed high jump motions,long jump motions and continuous jump motions under complex working conditions.展开更多
A hierarchic optimization strategy based on the offline path planning process and online trajectory planning process is presented to solve the trajectory optimization problem of multiple quad-rotor unmanned aerial veh...A hierarchic optimization strategy based on the offline path planning process and online trajectory planning process is presented to solve the trajectory optimization problem of multiple quad-rotor unmanned aerial vehicles in the collaborative assembling task. Firstly, the path planning process is solved by a novel parallel intelligent optimization algorithm, the central force optimization-genetic algorithm （CFO-GA）, which combines the central force optimization （CFO） algorithm with the genetic algorithm （GA）. Because of the immaturity of the CFO, the convergence analysis of the CFO is completed by the stability theory of the linear time-variant discrete-time sys- tems. The results show that the parallel CFO-GA algorithm converges faster than the parallel CFO and the central force optimization-sequential quadratic programming （CFO-SQP） algorithm. Then, the trajectory planning problem is established based on the path planning results. In order to limit the range of the attitude angle and guarantee the fight stability, the optimized object is changed from the ordinary six-degree-of-freedom rigid-body dynamic model to the dynamic model with an inner-loop attitude controller. The results show that the trajectory planning process can be solved by the mature SQP algorithm easily. Finally, the discussion and analysis of the real-time per- formance of the hierarchic optimization strategy are presented around the group number of the wav^oints and the eoual interval time.展开更多
Current successes in artificial intelligence domain have revitalized interest in neural networks and demonstrated their potential in solving spacecraft trajectory optimization problems. This paper presents a data-free...Current successes in artificial intelligence domain have revitalized interest in neural networks and demonstrated their potential in solving spacecraft trajectory optimization problems. This paper presents a data-free deep neural network(DNN) based trajectory optimization method for intercepting noncooperative maneuvering spacecraft, in a continuous low-thrust scenario. Firstly, the problem is formulated as a standard constrained optimization problem through differential game theory and minimax principle. Secondly, a new DNN is designed to integrate interception dynamic model into the network and involve it in the process of gradient descent, which makes the network endowed with the knowledge of physical constraints and reduces the learning burden of the network. Thus, a DNN based method is proposed, which completely eliminates the demand of training datasets and improves the generalization capacity. Finally, numerical results demonstrate the feasibility and efficiency of our proposed method.展开更多
Aiming at increasing the calculation efficiency of the pseudospectral methods, a multiple- interval Radau pseudospectral method （RPM） is presented to generate a reusable launch vehicle （RLV） ＇s optimal re-entry t...Aiming at increasing the calculation efficiency of the pseudospectral methods, a multiple- interval Radau pseudospectral method （RPM） is presented to generate a reusable launch vehicle （RLV） ＇s optimal re-entry trajectory. After dividing the optimal control problem into many intervals, the state and control variables are approximated using many fixed- and low-degree Lagrange polyno- mials in each interval. Convergence of the numerical discretization is then achieved by increasing the number of intervals. With the application of the proposed method, the normal nonlinear program- ming （NLP） problem transcribed from the optimal control problem can avoid being dense because of the low-degree approximation polynomials in each interval. Thus, the NLP solver can easily compute a solution. Finally, simulation results show that the optimized re-entry trajectories satisfy the path constraints and the boundary constraints successfully. Compared with the single interval RPM, the multiple-interval RPM is significantly faster and has higher calculation efficiency. The results indicate that the multiple-interval RPM can be applied for real-time trajectory generation due to its high effi- ciency and high precision.展开更多
This study aims to provide the pilot with optimal control time histories for stabilization of a helicopter after releasing the slung load in aerial delivery missions. A model with 21 degrees of freedom(21-DOF) has bee...This study aims to provide the pilot with optimal control time histories for stabilization of a helicopter after releasing the slung load in aerial delivery missions. A model with 21 degrees of freedom(21-DOF) has been developed and validated for a helicopter slung load system. The control history is generated with detailed procedure based on trajectory optimization. Effects of the objective function formulation on the results are discussed and rules are obtained to assist in the objective function determination. We conclude that the pilot should first decrease and then increase the collective control and adjust the longitudinal control to stabilize the helicopter after the in-hover slung load release. The obtained control history is reasonable and helpful for safety and efficiency improvement. Effects of path constraints and the Flight Control System(FCS) are studied. More stringent path constraints will lead to longer time spent and more controls. Stronger stiffness and weaker damping from the FCS will cause milder control histories but sharper on-axis state histories.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
Unmanned aerial vehicles(UAVs)are en-visioned as a promising means of providing wireless services for various complex terrains and emergency situations.In this paper,we consider a wireless UAV-enabled cognitive commun...Unmanned aerial vehicles(UAVs)are en-visioned as a promising means of providing wireless services for various complex terrains and emergency situations.In this paper,we consider a wireless UAV-enabled cognitive communication network,where a rotary-wing UAV transmits confidential information to a ground cognitive user over the spectrum assigned to primary users(PUs),while eavesdroppers attempt to wiretap the legitimate transmission.In order to en-hance the secrecy performance of wireless communi-cations,the secrecy rate(SR)of the UAV-enabled cog-nitive communication system is maximized through optimizing UAV three-dimensional(3D)flying trajec-tory while satisfying the requirements of UAV’s initial and final locations and guaranteeing the constraint of maximum speed of UAV and the interference thresh-old of each PU.However,the formulated SR maxi-mization(SRM)problem is non-convex.For the pur-pose of dealing with this intractable problem,we em-ploy the difference of two-convex functions approxi-mation approach to convert the non-convex optimiza-tion problem into a convex one,which is then solved through applying standard convex optimization tech-niques.Moreover,an iterative 3D trajectory opti-mization algorithm for SRM scheme is proposed to achieve the near-optimal 3D trajectory.Simulation re-sults show that our proposed 3D trajectory optimiza-tion based SRM algorithm has good convergence,and the proposed SRM scheme outperforms the bench-mark approach in terms of the SR performance.展开更多
The optimal yawing angle of sun-tracking solar aircraft is tightly related to the solar azimuth angle,which results in a large arc flight path to dynamically track the sun position.However,the limited detection range ...The optimal yawing angle of sun-tracking solar aircraft is tightly related to the solar azimuth angle,which results in a large arc flight path to dynamically track the sun position.However,the limited detection range of payload usually requires solar aircraft to loiter over areas of interest for persistent surveillance missions.The large arc sun-tracking flight may cause the target area on the ground to be outside the maximum coverage area of payload.The present study therefore develops an optimal flight control approach for planning the flight path of sun-tracking solar aircraft within a mission region.The proposed method enables sun-tracking solar aircraft to maintain the optimal yawing angle most of the time during daylight flight,except when the aircraft reverses its direction by turning flight.For a circular region with a mission radius of 50km,the optimal flight trajectory and controls of an example K-shaped sun-tracking solar aircraft are investigated theoretically.Results demonstrate the effectiveness of the proposed approach to optimize the flight path of the sun-tracking aircraft under the given circular region while maximizing the battery input power.Furthermore,the effects of varying the mission radius on energy performance are explored numerically.It has been proved that both net energy and energy balance remain nearly constant as the radius constraint varies,which enables the solar aircraft to achieve perpetual flight at almost the same latitude as the large arc flight.The method and results presented in this paper can provide reference for the persistent operation of sun-tracking solar aircraft within specific mission areas.展开更多
This paper proposes new methods and strategies for Multi-UAVs cooperative attacks with safety and time constraints in a complex environment.Delaunay triangle is designed to construct a map of the complex flight enviro...This paper proposes new methods and strategies for Multi-UAVs cooperative attacks with safety and time constraints in a complex environment.Delaunay triangle is designed to construct a map of the complex flight environment for aerial vehicles.Delaunay-Map,Safe Flight Corridor(SFC),and Relative Safe Flight Corridor(RSFC)are applied to ensure each UAV flight trajectory's safety.By using such techniques,it is possible to avoid the collision with obstacles and collision between UAVs.Bezier-curve is further developed to ensure that multi-UAVs can simultaneously reach the target at the specified time,and the trajectory is within the flight corridor.The trajectory tracking controller is also designed based on model predictive control to track the planned trajectory accurately.The simulation and experiment results are presented to verifying developed strategies of Multi-UAV cooperative attacks.展开更多
The optimization of the Earth-moon trajectory using solar electric propulsion is presented. A feasible method is proposed to optimize the transfer trajectory starting from a low Earth circular orbit （500 km altitude...The optimization of the Earth-moon trajectory using solar electric propulsion is presented. A feasible method is proposed to optimize the transfer trajectory starting from a low Earth circular orbit （500 km altitude） to a low lunar circular orbit （200 km altitude）. Due to the use of low-thrust solar electric propulsion, the entire transfer trajectory consists of hundreds or even thousands of orbital revolutions around the Earth and the moon. The Earth-orbit ascending （from low Earth orbit to high Earth orbit） and lunar descending （from high lunar orbit to low lunar orbit） trajectories in the presence of J2 perturbations and shadowing effect are computed by an analytic orbital averaging technique. A direct/indirect method is used to optimize the control steering for the trans-lunar trajectory segment, a segment from a high Earth orbit to a high lunar orbit, with a fixed thrust-coast-thrust engine sequence. For the trans-lunar trajectory segment, the equations of motion are expressed in the inertial coordinates about the Earth and the moon using a set of nonsingular equinoctial elements inclusive of the gravitational forces of the sun, the Earth, and the moon. By way of the analytic orbital averaging technique and the direct/indirect method, the Earth-moon transfer problem is converted to a parameter optimization problem, and the entire transfer trajectory is formulated and optimized in the form of a single nonlinear optimization problem with a small number of variables and constraints. Finally, an example of an Earth-moon transfer trajectory using solar electric propulsion is demonstrated.展开更多
This paper proposes a unified trajectory optimization approach that simultaneously optimizes the trajectory of the center of mass and footholds for legged locomotion.Based on a generic point-mass model,the approach is...This paper proposes a unified trajectory optimization approach that simultaneously optimizes the trajectory of the center of mass and footholds for legged locomotion.Based on a generic point-mass model,the approach is formulated as a nonlinear optimization problem,incorporating constraints such as robot kinematics,dynamics,ground reaction forces,obstacles,and target location.The unified optimization approach can be applied to both long-term motion planning and the reactive online planning through the use of model predictive control,and it incorporates vector field guidance to converge to the long-term planned motion.The effectiveness of the approach is demonstrated through simulations and physical experiments,showing its ability to generate a variety of walking and jumping gaits,as well as transitions between them,and to perform reactive walking in obstructed environments.展开更多
The advantage of using a spline function to evaluate the trajectory parameters optimization is discussed. A new method that using adaptive varied terminal-node spline interpolation for solving trajectory optimization ...The advantage of using a spline function to evaluate the trajectory parameters optimization is discussed. A new method that using adaptive varied terminal-node spline interpolation for solving trajectory optimization is proposed. And it is validated in optimizing the trajectory of guided bombs and extended range guided munitions （ERGM）. The solutions are approximate to the real optimization results. The advantage of this arithmetic is that it can be used to solve the trajectory optimization with complex models. Thus, it is helpful for solving the practical engineering optimization problem.展开更多
The trajectory optimization of an unpowered reentry vehicle via artificial emotion memory optimization(AEMO)is discussed.Firstly,reentry dynamics are established based on multiple constraints and parameterized control...The trajectory optimization of an unpowered reentry vehicle via artificial emotion memory optimization(AEMO)is discussed.Firstly,reentry dynamics are established based on multiple constraints and parameterized control variables with finite dimensions are designed.If the constraint is not satisfied,a distance measure and an adaptive penalty function are used to address this scenario.Secondly,AEMO is introduced to solve the trajectory optimization problem.Based on the theories of biology and cognition,the trial solutions based on emotional memory are established.Three search strategies are designed for realizing the random search of trial solutions and for avoiding becoming trapped in a local minimum.The states of the trial solutions are determined according to the rules of memory enhancement and forgetting.As the iterations proceed,the trial solutions with poor quality will gradually be forgotten.Therefore,the number of trial solutions is decreased,and the convergence of the algorithm is accelerated.Finally,a numerical simulation is conducted,and the results demonstrate that the path and terminal constraints are satisfied and the method can realize satisfactory performance.展开更多
With the objective of reducing the flight cost and the amount of polluting emissions released in the atmosphere, a new optimization algorithm considering the climb, cruise and descent phases is presented for the refer...With the objective of reducing the flight cost and the amount of polluting emissions released in the atmosphere, a new optimization algorithm considering the climb, cruise and descent phases is presented for the reference vertical flight trajectory. The selection of the reference vertical navigation speeds and altitudes was solved as a discrete combinatory problem by means of a graphtree passing through nodes using the beam search optimization technique. To achieve a compromise between the execution time and the algorithm＇s ability to find the global optimal solution, a heuristic methodology introducing a parameter called ‘‘optimism coefficient was used in order to estimate the trajectory＇s flight cost at every node. The optimal trajectory cost obtained with the developed algorithm was compared with the cost of the optimal trajectory provided by a commercial flight management system（FMS）. The global optimal solution was validated against an exhaustive search algorithm（ESA）, other than the proposed algorithm. The developed algorithm takes into account weather effects, step climbs during cruise and air traffic management constraints such as constant altitude segments, constant cruise Mach, and a pre-defined reference lateral navigation route. The aircraft fuel burn was computed using a numerical performance model which was created and validated using flight test experimental data.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
This paper proposes a new direct method for an efficient trajectory optimization using the point that the dynamics of a deterministic system are uniquely determined by initial states and controls imposed over the time...This paper proposes a new direct method for an efficient trajectory optimization using the point that the dynamics of a deterministic system are uniquely determined by initial states and controls imposed over the time horizon of interest.To effectively implement this concept,the Hermite spline is adopted to interpolate the continuous controls and the system dynamics are integrated with corresponding control parameters in prior.As a result,the optimal control problem can be transcribed into a nonlinear programming problem which has no dynamic equality constraints and no intermediate states in its design variables.In addition,the paper proposes an efficient recursive Jacobian estimation technique and introduces a Jacobian transformation matrix to straightforwardly handle the general state constraints.Important properties of the present method are thoroughly investigated through its applications to the trajectory optimization for a soft lunar landing from a parking orbit,including the detailed analyses for the de-orbiting phase.The computed results are compared with those using the pseudo-spectral method to demonstrate an extreme outperformance of the proposed method in the aerospace applications over the traditional direct method.展开更多
This work presents a novel approach combining radial basis function(RBF)interpolation with Galerkin projection to efficiently solve general optimal control problems.The goal is to develop a highly flexible solution to...This work presents a novel approach combining radial basis function(RBF)interpolation with Galerkin projection to efficiently solve general optimal control problems.The goal is to develop a highly flexible solution to optimal control problems,especially nonsmooth problems involving discontinuities,while accounting for trajectory accuracy and computational efficiency simultaneously.The proposed solution,called the RBF-Galerkin method,offers a highly flexible framework for direct transcription by using any interpolant functions from the broad class of global RBFs and any arbitrary discretization points that do not necessarily need to be on a mesh of points.The RBF-Galerkin costate mapping theorem is developed that describes an exact equivalency between the Karush-Kuhn-Tucker(KKT)conditions of the nonlinear programming problem resulted from the RBF-Galerkin method and the discretized form of the first-order necessary conditions of the optimal control problem,if a set of discrete conditions holds.The efficacy of the proposed method along with the accuracy of the RBF-Galerkin costate mapping theorem is confirmed against an analytical solution for a bang-bang optimal control problem.In addition,the proposed approach is compared against both local and global polynomial methods for a robot motion planning problem to verify its accuracy and computational efficiency.展开更多
Constrained reentry trajectory optimization for hypersonic vehicles is a challenging job. In particular, this problem becomes more difficult when several objectives with preemptive priorities are expected for differen...Constrained reentry trajectory optimization for hypersonic vehicles is a challenging job. In particular, this problem becomes more difficult when several objectives with preemptive priorities are expected for different purposes. In this paper, a fuzzy satisfactory goal programming method is proposed to solve the multi-objective reentry trajectory optimization problem. Firstly, direct collocation approach is used to discretize the reentry trajectory optimal-control problem with nonlinear constraints into nonlinear multiobjective programming problem with preemptive priorities, where attack angles and bank angles at nodes and collocation nodes are selected as control variables. Secondly, the preemptive priorities are transformed into the relaxed order of satisfactory degrees according to the principle that the objective with higher priority has higher satisfactory degree. Then the fuzzy satisfactory goal programming model is proposed. The balance between optimization and priorities is realized by regulating parameter λ, such that the satisfactory reentry trajectory can be acquired. The simulation demonstrates that the proposed method is effective for the multi-objective reentry trajectory optimization of hypersonic vehicles.展开更多
基金supported in part by the Shenzhen Basic Research Project under Grant JCYJ20220531103008018 and Grant 20200812112423002in part by the Guangdong Basic Research Program under Grant 2019A1515110358,2021A1515012097in part by the open research fund of National Mobile Communications Research Laboratory,Southeast University (No.2021D16)。
文摘In this paper,we investigate the application of the Unmanned Aerial Vehicle(UAV)-enabled relaying system in emergency communications,where one UAV is applied as a relay to help transmit information from ground users to a Base Station(BS).We maximize the total transmitted data from the users to the BS,by optimizing the user communication scheduling and association along with the power allocation and the trajectory of the UAV.To solve this non-convex optimization problem,we propose the traditional Convex Optimization(CO)and the Reinforcement Learning(RL)-based approaches.Specifically,we apply the block coordinate descent and successive convex approximation techniques in the CO approach,while applying the soft actor-critic algorithm in the RL approach.The simulation results show that both approaches can solve the proposed optimization problem and obtain good results.Moreover,the RL approach establishes emergency communications more rapidly than the CO approach once the training process has been completed.
基金support by Ningxia Key R&D projects“Integration and demonstration application of intelligent finishing system for large casting riser robot”(No.2021BEE03002)Ningxia Natural Science Foundation Project“Research on detection and location of large casting welding seam based on depth learning”(No.2020AAC03201).
文摘The welding of medium and thick plates has a wide range of applications in the engineering field.Industrial welding robots are gradually replacing traditional welding operations due to their significant advantages,such as high welding quality,high work efficiency,and effective reduction of labor intensity.Ensuring the accuracy of the welding trajectory for the welding robot is crucial for guaranteeing welding quality.In this paper,the author uses the chaos sparrow search algorithm to optimize the trajectory of a multi-layer and multi-pass welding robot for medium and thick plates.Firstly,the Sparrow Search Algorithm(SSA)is improved by introducing tent chaotic mapping and Gaussian mutation of the inertia weight factor.Secondly,in order to prevent the welding robot arm from colliding with obstacles in the welding environment during the welding process,maintain the stability of the welding robot,and ensure the continuous stability of the changes in each joint angle,joint angular velocity,and angular velocity of the joint angle,a welding robot model is established by improving the Denavit-Hartenberg parameter method.A multi-objective optimization fitness function is used to optimize the trajectory of the welding robot,minimizing time and energy consumption.Thirdly,the optimization and convergence performance of SSA and Chaos Sparrow Search Algorithm(CSSA)are compared through 10 benchmark test functions.Based on the six sets of test functions,the CSSA algorithm consistently maintains superior optimization performance and has excellent stability,with a faster decline in the convergence curve compared to the SSA algorithm.Finally,the accuracy of welding is tested through V-shaped multi-layer and multi-pass welding experiments.The experimental results show that the CSSA algorithm has a strong superiority in trajectory optimization of multi-layer and multi-pass welding for medium and thick plates,with an accuracy rate of 99.5%.It is an effective optimization method that can meet the actual needs of production.
基金supported in part by the National Key Research and Development Program of China(2020YFB13134)Major Project of National Natural Science Foundation of China(U2013602)+2 种基金The National Nature Science Foundation of China(52075115)HIT Major Campus Cultivation Project(2023FRFK01001)National independent project(SKLRS202301A12).
文摘The dynamic motion capability of humanoid robots is a key indicator for evaluating their performance.Jumping,as a typical dynamic motion,is of great significance for enhancing the robot’s flexibility and terrain adaptability in unstructured environments.However,achieving high-dynamic jumping control of humanoid robots has become a challenge due to the high degree of freedom and strongly coupled dynamic characteristics.The idea for this paper originated from the human response process to jumping commands,aiming to achieve online trajectory optimization and jumping motion control of humanoid robots.Firstly,we employ nonlinear optimization in combination with the Single Rigid Body Model(SRBM)to generate a robot’s Center of Mass(CoM)trajectory that complies with physical constraints and minimizes the angular momentum of the CoM.Then,a Model Predictive Controller(MPC)is designed to track and control the CoM trajectory,obtaining the required contact forces at the robot’s feet.Finally,a Whole-Body Controller(WBC)is used to generate full-body joint motion trajectories and driving torques,based on the prioritized sequence of tasks designed for the jumping process.The control framework proposed in this paper considers the dynamic characteristics of the robot’s jumping process,with a focus on improving the real-time performance of trajectory optimization and the robustness of controller.Simulation and experimental results demonstrate that our robot successfully executed high jump motions,long jump motions and continuous jump motions under complex working conditions.
文摘A hierarchic optimization strategy based on the offline path planning process and online trajectory planning process is presented to solve the trajectory optimization problem of multiple quad-rotor unmanned aerial vehicles in the collaborative assembling task. Firstly, the path planning process is solved by a novel parallel intelligent optimization algorithm, the central force optimization-genetic algorithm （CFO-GA）, which combines the central force optimization （CFO） algorithm with the genetic algorithm （GA）. Because of the immaturity of the CFO, the convergence analysis of the CFO is completed by the stability theory of the linear time-variant discrete-time sys- tems. The results show that the parallel CFO-GA algorithm converges faster than the parallel CFO and the central force optimization-sequential quadratic programming （CFO-SQP） algorithm. Then, the trajectory planning problem is established based on the path planning results. In order to limit the range of the attitude angle and guarantee the fight stability, the optimized object is changed from the ordinary six-degree-of-freedom rigid-body dynamic model to the dynamic model with an inner-loop attitude controller. The results show that the trajectory planning process can be solved by the mature SQP algorithm easily. Finally, the discussion and analysis of the real-time per- formance of the hierarchic optimization strategy are presented around the group number of the wav^oints and the eoual interval time.
基金supported by the National Defense Science and Technology Innovation (18-163-15-Lz-001-004-13)。
文摘Current successes in artificial intelligence domain have revitalized interest in neural networks and demonstrated their potential in solving spacecraft trajectory optimization problems. This paper presents a data-free deep neural network(DNN) based trajectory optimization method for intercepting noncooperative maneuvering spacecraft, in a continuous low-thrust scenario. Firstly, the problem is formulated as a standard constrained optimization problem through differential game theory and minimax principle. Secondly, a new DNN is designed to integrate interception dynamic model into the network and involve it in the process of gradient descent, which makes the network endowed with the knowledge of physical constraints and reduces the learning burden of the network. Thus, a DNN based method is proposed, which completely eliminates the demand of training datasets and improves the generalization capacity. Finally, numerical results demonstrate the feasibility and efficiency of our proposed method.
文摘Aiming at increasing the calculation efficiency of the pseudospectral methods, a multiple- interval Radau pseudospectral method （RPM） is presented to generate a reusable launch vehicle （RLV） ＇s optimal re-entry trajectory. After dividing the optimal control problem into many intervals, the state and control variables are approximated using many fixed- and low-degree Lagrange polyno- mials in each interval. Convergence of the numerical discretization is then achieved by increasing the number of intervals. With the application of the proposed method, the normal nonlinear program- ming （NLP） problem transcribed from the optimal control problem can avoid being dense because of the low-degree approximation polynomials in each interval. Thus, the NLP solver can easily compute a solution. Finally, simulation results show that the optimized re-entry trajectories satisfy the path constraints and the boundary constraints successfully. Compared with the single interval RPM, the multiple-interval RPM is significantly faster and has higher calculation efficiency. The results indicate that the multiple-interval RPM can be applied for real-time trajectory generation due to its high effi- ciency and high precision.
基金supported by the National Natural Science Foundation of China (Nos. 11672128)A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions。
文摘This study aims to provide the pilot with optimal control time histories for stabilization of a helicopter after releasing the slung load in aerial delivery missions. A model with 21 degrees of freedom(21-DOF) has been developed and validated for a helicopter slung load system. The control history is generated with detailed procedure based on trajectory optimization. Effects of the objective function formulation on the results are discussed and rules are obtained to assist in the objective function determination. We conclude that the pilot should first decrease and then increase the collective control and adjust the longitudinal control to stabilize the helicopter after the in-hover slung load release. The obtained control history is reasonable and helpful for safety and efficiency improvement. Effects of path constraints and the Flight Control System(FCS) are studied. More stringent path constraints will lead to longer time spent and more controls. Stronger stiffness and weaker damping from the FCS will cause milder control histories but sharper on-axis state histories.
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National Natural Sci-ence Foundation of China(Nos.61631020,61671253,62071253 and 91738201)the Key Project of Nat-ural Science Research of Higher Education Institu-tions of Jiangsu Province(Grant No.18KJB510031).
文摘Unmanned aerial vehicles(UAVs)are en-visioned as a promising means of providing wireless services for various complex terrains and emergency situations.In this paper,we consider a wireless UAV-enabled cognitive communication network,where a rotary-wing UAV transmits confidential information to a ground cognitive user over the spectrum assigned to primary users(PUs),while eavesdroppers attempt to wiretap the legitimate transmission.In order to en-hance the secrecy performance of wireless communi-cations,the secrecy rate(SR)of the UAV-enabled cog-nitive communication system is maximized through optimizing UAV three-dimensional(3D)flying trajec-tory while satisfying the requirements of UAV’s initial and final locations and guaranteeing the constraint of maximum speed of UAV and the interference thresh-old of each PU.However,the formulated SR maxi-mization(SRM)problem is non-convex.For the pur-pose of dealing with this intractable problem,we em-ploy the difference of two-convex functions approxi-mation approach to convert the non-convex optimiza-tion problem into a convex one,which is then solved through applying standard convex optimization tech-niques.Moreover,an iterative 3D trajectory opti-mization algorithm for SRM scheme is proposed to achieve the near-optimal 3D trajectory.Simulation re-sults show that our proposed 3D trajectory optimiza-tion based SRM algorithm has good convergence,and the proposed SRM scheme outperforms the bench-mark approach in terms of the SR performance.
基金the support of the National Natural Science Foundation of China(Nos.11902156 and 11672133)supported by the Fundamental Research Funds for the Central Universities,China(No.309201A8802)。
文摘The optimal yawing angle of sun-tracking solar aircraft is tightly related to the solar azimuth angle,which results in a large arc flight path to dynamically track the sun position.However,the limited detection range of payload usually requires solar aircraft to loiter over areas of interest for persistent surveillance missions.The large arc sun-tracking flight may cause the target area on the ground to be outside the maximum coverage area of payload.The present study therefore develops an optimal flight control approach for planning the flight path of sun-tracking solar aircraft within a mission region.The proposed method enables sun-tracking solar aircraft to maintain the optimal yawing angle most of the time during daylight flight,except when the aircraft reverses its direction by turning flight.For a circular region with a mission radius of 50km,the optimal flight trajectory and controls of an example K-shaped sun-tracking solar aircraft are investigated theoretically.Results demonstrate the effectiveness of the proposed approach to optimize the flight path of the sun-tracking aircraft under the given circular region while maximizing the battery input power.Furthermore,the effects of varying the mission radius on energy performance are explored numerically.It has been proved that both net energy and energy balance remain nearly constant as the radius constraint varies,which enables the solar aircraft to achieve perpetual flight at almost the same latitude as the large arc flight.The method and results presented in this paper can provide reference for the persistent operation of sun-tracking solar aircraft within specific mission areas.
基金National Natural Science Foundation of China(No.61903350)Beijing Institute of Technology Research Fund Program for Young Scholars。
文摘This paper proposes new methods and strategies for Multi-UAVs cooperative attacks with safety and time constraints in a complex environment.Delaunay triangle is designed to construct a map of the complex flight environment for aerial vehicles.Delaunay-Map,Safe Flight Corridor(SFC),and Relative Safe Flight Corridor(RSFC)are applied to ensure each UAV flight trajectory's safety.By using such techniques,it is possible to avoid the collision with obstacles and collision between UAVs.Bezier-curve is further developed to ensure that multi-UAVs can simultaneously reach the target at the specified time,and the trajectory is within the flight corridor.The trajectory tracking controller is also designed based on model predictive control to track the planned trajectory accurately.The simulation and experiment results are presented to verifying developed strategies of Multi-UAV cooperative attacks.
基金National Natural Science Foundation of China (10603005)
文摘The optimization of the Earth-moon trajectory using solar electric propulsion is presented. A feasible method is proposed to optimize the transfer trajectory starting from a low Earth circular orbit （500 km altitude） to a low lunar circular orbit （200 km altitude）. Due to the use of low-thrust solar electric propulsion, the entire transfer trajectory consists of hundreds or even thousands of orbital revolutions around the Earth and the moon. The Earth-orbit ascending （from low Earth orbit to high Earth orbit） and lunar descending （from high lunar orbit to low lunar orbit） trajectories in the presence of J2 perturbations and shadowing effect are computed by an analytic orbital averaging technique. A direct/indirect method is used to optimize the control steering for the trans-lunar trajectory segment, a segment from a high Earth orbit to a high lunar orbit, with a fixed thrust-coast-thrust engine sequence. For the trans-lunar trajectory segment, the equations of motion are expressed in the inertial coordinates about the Earth and the moon using a set of nonsingular equinoctial elements inclusive of the gravitational forces of the sun, the Earth, and the moon. By way of the analytic orbital averaging technique and the direct/indirect method, the Earth-moon transfer problem is converted to a parameter optimization problem, and the entire transfer trajectory is formulated and optimized in the form of a single nonlinear optimization problem with a small number of variables and constraints. Finally, an example of an Earth-moon transfer trajectory using solar electric propulsion is demonstrated.
基金supported by the Natural Science Foundation of Hebei Province of China(no.E2022203095)Cultivation Project for Basic Research and Innovation of Yanshan University(no.2021LGQN004)National Natural Science Foundation of China(no.51905465 and No.52122503).
文摘This paper proposes a unified trajectory optimization approach that simultaneously optimizes the trajectory of the center of mass and footholds for legged locomotion.Based on a generic point-mass model,the approach is formulated as a nonlinear optimization problem,incorporating constraints such as robot kinematics,dynamics,ground reaction forces,obstacles,and target location.The unified optimization approach can be applied to both long-term motion planning and the reactive online planning through the use of model predictive control,and it incorporates vector field guidance to converge to the long-term planned motion.The effectiveness of the approach is demonstrated through simulations and physical experiments,showing its ability to generate a variety of walking and jumping gaits,as well as transitions between them,and to perform reactive walking in obstructed environments.
文摘The advantage of using a spline function to evaluate the trajectory parameters optimization is discussed. A new method that using adaptive varied terminal-node spline interpolation for solving trajectory optimization is proposed. And it is validated in optimizing the trajectory of guided bombs and extended range guided munitions （ERGM）. The solutions are approximate to the real optimization results. The advantage of this arithmetic is that it can be used to solve the trajectory optimization with complex models. Thus, it is helpful for solving the practical engineering optimization problem.
基金supported by the Defense Science and Technology Key Laboratory Fund of Luoyang Electro-optical Equipment Institute,Aviation Industry Corporation of China(6142504200108).
文摘The trajectory optimization of an unpowered reentry vehicle via artificial emotion memory optimization(AEMO)is discussed.Firstly,reentry dynamics are established based on multiple constraints and parameterized control variables with finite dimensions are designed.If the constraint is not satisfied,a distance measure and an adaptive penalty function are used to address this scenario.Secondly,AEMO is introduced to solve the trajectory optimization problem.Based on the theories of biology and cognition,the trial solutions based on emotional memory are established.Three search strategies are designed for realizing the random search of trial solutions and for avoiding becoming trapped in a local minimum.The states of the trial solutions are determined according to the rules of memory enhancement and forgetting.As the iterations proceed,the trial solutions with poor quality will gradually be forgotten.Therefore,the number of trial solutions is decreased,and the convergence of the algorithm is accelerated.Finally,a numerical simulation is conducted,and the results demonstrate that the path and terminal constraints are satisfied and the method can realize satisfactory performance.
基金the team of the Business-led Network of Centers of Excellence Green Aviation Research & Development Network (GARDN)in particular Mr. Sylvan Cofsky, for the funds received for this project (GARDNⅡ–Project: CMC-21)conducted at The Research Laboratory in Active Controls, Avionics and Aeroservoelasticity (LARCASE) in the framework of the global project ‘‘Optimized Descent and Cruise”
文摘With the objective of reducing the flight cost and the amount of polluting emissions released in the atmosphere, a new optimization algorithm considering the climb, cruise and descent phases is presented for the reference vertical flight trajectory. The selection of the reference vertical navigation speeds and altitudes was solved as a discrete combinatory problem by means of a graphtree passing through nodes using the beam search optimization technique. To achieve a compromise between the execution time and the algorithm＇s ability to find the global optimal solution, a heuristic methodology introducing a parameter called ‘‘optimism coefficient was used in order to estimate the trajectory＇s flight cost at every node. The optimal trajectory cost obtained with the developed algorithm was compared with the cost of the optimal trajectory provided by a commercial flight management system（FMS）. The global optimal solution was validated against an exhaustive search algorithm（ESA）, other than the proposed algorithm. The developed algorithm takes into account weather effects, step climbs during cruise and air traffic management constraints such as constant altitude segments, constant cruise Mach, and a pre-defined reference lateral navigation route. The aircraft fuel burn was computed using a numerical performance model which was created and validated using flight test experimental data.
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.
基金supported by the National Research Foundation of Korea(NRF)grant funded by the Korea government(MSIT)(No.NRF-2020R1A2C2011955)supported by Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(No.2020R1A6A1A03046811)。
文摘This paper proposes a new direct method for an efficient trajectory optimization using the point that the dynamics of a deterministic system are uniquely determined by initial states and controls imposed over the time horizon of interest.To effectively implement this concept,the Hermite spline is adopted to interpolate the continuous controls and the system dynamics are integrated with corresponding control parameters in prior.As a result,the optimal control problem can be transcribed into a nonlinear programming problem which has no dynamic equality constraints and no intermediate states in its design variables.In addition,the paper proposes an efficient recursive Jacobian estimation technique and introduces a Jacobian transformation matrix to straightforwardly handle the general state constraints.Important properties of the present method are thoroughly investigated through its applications to the trajectory optimization for a soft lunar landing from a parking orbit,including the detailed analyses for the de-orbiting phase.The computed results are compared with those using the pseudo-spectral method to demonstrate an extreme outperformance of the proposed method in the aerospace applications over the traditional direct method.
文摘This work presents a novel approach combining radial basis function(RBF)interpolation with Galerkin projection to efficiently solve general optimal control problems.The goal is to develop a highly flexible solution to optimal control problems,especially nonsmooth problems involving discontinuities,while accounting for trajectory accuracy and computational efficiency simultaneously.The proposed solution,called the RBF-Galerkin method,offers a highly flexible framework for direct transcription by using any interpolant functions from the broad class of global RBFs and any arbitrary discretization points that do not necessarily need to be on a mesh of points.The RBF-Galerkin costate mapping theorem is developed that describes an exact equivalency between the Karush-Kuhn-Tucker(KKT)conditions of the nonlinear programming problem resulted from the RBF-Galerkin method and the discretized form of the first-order necessary conditions of the optimal control problem,if a set of discrete conditions holds.The efficacy of the proposed method along with the accuracy of the RBF-Galerkin costate mapping theorem is confirmed against an analytical solution for a bang-bang optimal control problem.In addition,the proposed approach is compared against both local and global polynomial methods for a robot motion planning problem to verify its accuracy and computational efficiency.
基金supported by National Natural Science Foundation of China(No.61074064)Natural Science Foundation of Tianjin(No.12JCZDJC30300)
文摘Constrained reentry trajectory optimization for hypersonic vehicles is a challenging job. In particular, this problem becomes more difficult when several objectives with preemptive priorities are expected for different purposes. In this paper, a fuzzy satisfactory goal programming method is proposed to solve the multi-objective reentry trajectory optimization problem. Firstly, direct collocation approach is used to discretize the reentry trajectory optimal-control problem with nonlinear constraints into nonlinear multiobjective programming problem with preemptive priorities, where attack angles and bank angles at nodes and collocation nodes are selected as control variables. Secondly, the preemptive priorities are transformed into the relaxed order of satisfactory degrees according to the principle that the objective with higher priority has higher satisfactory degree. Then the fuzzy satisfactory goal programming model is proposed. The balance between optimization and priorities is realized by regulating parameter λ, such that the satisfactory reentry trajectory can be acquired. The simulation demonstrates that the proposed method is effective for the multi-objective reentry trajectory optimization of hypersonic vehicles.
