Generating dynamically feasible trajectory for fixed-wing Unmanned Aerial Vehicles(UAVs)in dense obstacle environments remains computationally intractable.This paper proposes a Safe Flight Corridor constrained Sequent...Generating dynamically feasible trajectory for fixed-wing Unmanned Aerial Vehicles(UAVs)in dense obstacle environments remains computationally intractable.This paper proposes a Safe Flight Corridor constrained Sequential Convex Programming(SFC-SCP)to improve the computation efficiency and reliability of trajectory generation.SFC-SCP combines the front-end convex polyhedron SFC construction and back-end SCP-based trajectory optimization.A Sparse A^(*)Search(SAS)driven SFC construction method is designed to efficiently generate polyhedron SFC according to the geometric relation among obstacles and collision-free waypoints.Via transforming the nonconvex obstacle-avoidance constraints to linear inequality constraints,SFC can mitigate infeasibility of trajectory planning and reduce computation complexity.Then,SCP casts the nonlinear trajectory optimization subject to SFC into convex programming subproblems to decrease the problem complexity.In addition,a convex optimizer based on interior point method is customized,where the search direction is calculated via successive elimination to further improve efficiency.Simulation experiments on dense obstacle scenarios show that SFC-SCP can generate dynamically feasible safe trajectory rapidly.Comparative studies with state-of-the-art SCP-based methods demonstrate the efficiency and reliability merits of SFC-SCP.Besides,the customized convex optimizer outperforms off-the-shelf optimizers in terms of computation time.展开更多
With the rapid changes of the flight environment and situation,there will be various unexpected situations while multiple missiles are performing the missions.To fast cope with the various situations in mission execut...With the rapid changes of the flight environment and situation,there will be various unexpected situations while multiple missiles are performing the missions.To fast cope with the various situations in mission executions,the conventional sequential convex programming algorithm and the parallel-based sequential convex programming algorithm for multiple missiles fast trajectory replanning are proposed in this paper.The originally non-convex trajectory optimization problem is reformulated into a series of convex optimization subproblems based on the sequential convex programming method.The conventional sequential convex programming algorithm is developed through linearization,successive convexification,and relaxation techniques to solve the convex optimization subproblems iteratively.However,multiple missiles are related through various cooperative constraints.When the trajectory optimization of multiple missiles is formulated as an optimal control problem to solve,the complexity of the problem will increase dramatically as the number of missiles increases.To alleviate the coupled effect caused by multiple aerodynamically controlled missiles,the parallel-based sequential convex programming algorithm is proposed to solve the trajectory optimization problem for multiple missiles in parallel,reducing the complexity of the trajectory optimization problem and significantly shortening the computation time.Numerical simulations are provided to verify the convergence and effectiveness of the conventional sequential convex programming algorithm and the parallel-based sequential convex programming algorithm to cope with the trajectory optimization problem with various constraints.Furthermore,the optimality and the real-time performance of the proposed algorithms are discussed in comparative simulation examples.展开更多
In this paper, we describe a method to solve large-scale structural optimization problems by sequential convex programming （SCP）. A predictor-corrector interior point method is applied to solve the strictly convex s...In this paper, we describe a method to solve large-scale structural optimization problems by sequential convex programming （SCP）. A predictor-corrector interior point method is applied to solve the strictly convex subproblems. The SCP algorithm and the topology optimization approach are introduced. Especially, different strategies to solve certain linear systems of equations are analyzed. Numerical results are presented to show the efficiency of the proposed method for solving topology optimization problems and to compare different variants.展开更多
An optimal preventive-corrective control model for static voltage stability under multiple N-1 contingencies considering the wind power uncertainty is established in this paper.The objective is to minimize the control...An optimal preventive-corrective control model for static voltage stability under multiple N-1 contingencies considering the wind power uncertainty is established in this paper.The objective is to minimize the control variable adjustment cost including the load shedding cost of each contingency.The chance constraints of the static voltage stability margins(SvSMs)in the normal operation state and after each N-1 contingency are included.The approximate functions between the probability density functions(PDFs)of SVSMs and load shedding quantity with respect to preventive control variables are obtained to transform the expectation of load shedding quantity and the SvSM chance constraints into deterministic expressions.An approximate sequential convex quadratically constrained quadratic programming iteration method is proposed to solve the optimal control model.In each iteration,the approximate expressions and range are determined by the generated data samples.Moreover,a fast approximation calculation method of second-order matrices is proposed.By the naive Bayes classifier,the most severe N-1 contingencies are selected to replace all the contingencies to be added to the optimization model to improve the computational efficiency.Case studies on the IEEE-39 bus system and an actual provincial power grid demonstrate the effectiveness and efficiency of the proposed method.展开更多
In this paper,an efficient approach is developed to plan jerk-constrained smooth trajectories passing through desired way-points with allowable accuracy for an autonomous quadrotor.First,based on the B-spline model,we...In this paper,an efficient approach is developed to plan jerk-constrained smooth trajectories passing through desired way-points with allowable accuracy for an autonomous quadrotor.First,based on the B-spline model,we introduce the sequential convex programming(SCP)into the flexible path planning method to satisfy the way-points constraints.By approximating the quadrotor and obstacles as spheres and directed planes,the length-optimal and collision-free path planning problem is formulated as a nonconvex optimization problem and solved by SCP.The initial C^(3) continuous path curve for optimization is constructed efficiently based on a proposed strategy of generating new way-points near the obstacles without the need to calculate the embedding distance between the curve and the obstacles.On this basis,the time-optimal speed planning problem is addressed in two steps.In the first step,the forward-backward approach is introduced to solve the problem under the chord error,velocity,and acceleration constraints by changing the variables and deforming the constraints.Then by relaxing the constraints appropriately,the problem under jerk constraints is formulated into a linear programming(LP)problem.The feasibility of the proposed approach is verified through simulations and an indoor navigation experiment.The proposed approach can generate a C^(3) continuous collision-free trajectory that passes through the sparse desired way-points with allowable accuracy while guaranteeing the chord error,velocity,acceleration,and jerk constraints.When the number of sample points is 3000,the proposed speed planning method reduces the calculation time by 40%compared to an existing method.展开更多
This paper develops a sequential convex programming(SCP)-based method to solve the minimum-fuel variable-specific-impulse low-thrust transfer problem considering shutdown constraint,with emphasize on improving the com...This paper develops a sequential convex programming(SCP)-based method to solve the minimum-fuel variable-specific-impulse low-thrust transfer problem considering shutdown constraint,with emphasize on improving the computational efficiency.The variable parameter engine is more applicable for many low-thrust scenarios,therefore,both a continuously variable model and a ladder variable model are adopted.First,the original problem is convexified by processing the constraint feasible domain,which is composed of the nonlinear dynamic equations and second-order equality constraint,into convex sets.Then,the approximation is generated to close the optimal solution of the low-thrust problem by iteratively solving the convexified subproblem.Moreover,the switching self-detection and adaptive node refinement methods are presented,which can improve the accuracy of the solution and accelerate the convergence during the approximation process and is especially necessary and effective in the scenarios with shutdown constraint.In numerical simulations,the comparison with the homotopic approach shows that the proposed method only needs 4%computational time as that of the homotopic approach,and two variable-specificimpulse examples further demonstrate the effectiveness and efficiency of the proposed method.展开更多
基金supported by the National Natural Science Foundation of China(No.62203256)。
文摘Generating dynamically feasible trajectory for fixed-wing Unmanned Aerial Vehicles(UAVs)in dense obstacle environments remains computationally intractable.This paper proposes a Safe Flight Corridor constrained Sequential Convex Programming(SFC-SCP)to improve the computation efficiency and reliability of trajectory generation.SFC-SCP combines the front-end convex polyhedron SFC construction and back-end SCP-based trajectory optimization.A Sparse A^(*)Search(SAS)driven SFC construction method is designed to efficiently generate polyhedron SFC according to the geometric relation among obstacles and collision-free waypoints.Via transforming the nonconvex obstacle-avoidance constraints to linear inequality constraints,SFC can mitigate infeasibility of trajectory planning and reduce computation complexity.Then,SCP casts the nonlinear trajectory optimization subject to SFC into convex programming subproblems to decrease the problem complexity.In addition,a convex optimizer based on interior point method is customized,where the search direction is calculated via successive elimination to further improve efficiency.Simulation experiments on dense obstacle scenarios show that SFC-SCP can generate dynamically feasible safe trajectory rapidly.Comparative studies with state-of-the-art SCP-based methods demonstrate the efficiency and reliability merits of SFC-SCP.Besides,the customized convex optimizer outperforms off-the-shelf optimizers in terms of computation time.
基金supported by the National Natural Science Foundation of China(Grant No.12372044).
文摘With the rapid changes of the flight environment and situation,there will be various unexpected situations while multiple missiles are performing the missions.To fast cope with the various situations in mission executions,the conventional sequential convex programming algorithm and the parallel-based sequential convex programming algorithm for multiple missiles fast trajectory replanning are proposed in this paper.The originally non-convex trajectory optimization problem is reformulated into a series of convex optimization subproblems based on the sequential convex programming method.The conventional sequential convex programming algorithm is developed through linearization,successive convexification,and relaxation techniques to solve the convex optimization subproblems iteratively.However,multiple missiles are related through various cooperative constraints.When the trajectory optimization of multiple missiles is formulated as an optimal control problem to solve,the complexity of the problem will increase dramatically as the number of missiles increases.To alleviate the coupled effect caused by multiple aerodynamically controlled missiles,the parallel-based sequential convex programming algorithm is proposed to solve the trajectory optimization problem for multiple missiles in parallel,reducing the complexity of the trajectory optimization problem and significantly shortening the computation time.Numerical simulations are provided to verify the convergence and effectiveness of the conventional sequential convex programming algorithm and the parallel-based sequential convex programming algorithm to cope with the trajectory optimization problem with various constraints.Furthermore,the optimality and the real-time performance of the proposed algorithms are discussed in comparative simulation examples.
基金This work was mainly done while the first author was visiting the University of Bayreuth, and was supported by the Chinese Scholarship Council, German Academic Exchange Service （DAAD） and the National Natural Science Foundation of China.
文摘In this paper, we describe a method to solve large-scale structural optimization problems by sequential convex programming （SCP）. A predictor-corrector interior point method is applied to solve the strictly convex subproblems. The SCP algorithm and the topology optimization approach are introduced. Especially, different strategies to solve certain linear systems of equations are analyzed. Numerical results are presented to show the efficiency of the proposed method for solving topology optimization problems and to compare different variants.
基金supported by the National Natural Science Foundation of China under Grant 51977080the Natural Science Foundation of Guangdong Province(2023A1515240075).
文摘An optimal preventive-corrective control model for static voltage stability under multiple N-1 contingencies considering the wind power uncertainty is established in this paper.The objective is to minimize the control variable adjustment cost including the load shedding cost of each contingency.The chance constraints of the static voltage stability margins(SvSMs)in the normal operation state and after each N-1 contingency are included.The approximate functions between the probability density functions(PDFs)of SVSMs and load shedding quantity with respect to preventive control variables are obtained to transform the expectation of load shedding quantity and the SvSM chance constraints into deterministic expressions.An approximate sequential convex quadratically constrained quadratic programming iteration method is proposed to solve the optimal control model.In each iteration,the approximate expressions and range are determined by the generated data samples.Moreover,a fast approximation calculation method of second-order matrices is proposed.By the naive Bayes classifier,the most severe N-1 contingencies are selected to replace all the contingencies to be added to the optimization model to improve the computational efficiency.Case studies on the IEEE-39 bus system and an actual provincial power grid demonstrate the effectiveness and efficiency of the proposed method.
基金This work was partially supported by the National Natural Science Foundation of China(Grant Nos.51822506 and 51975348).
文摘In this paper,an efficient approach is developed to plan jerk-constrained smooth trajectories passing through desired way-points with allowable accuracy for an autonomous quadrotor.First,based on the B-spline model,we introduce the sequential convex programming(SCP)into the flexible path planning method to satisfy the way-points constraints.By approximating the quadrotor and obstacles as spheres and directed planes,the length-optimal and collision-free path planning problem is formulated as a nonconvex optimization problem and solved by SCP.The initial C^(3) continuous path curve for optimization is constructed efficiently based on a proposed strategy of generating new way-points near the obstacles without the need to calculate the embedding distance between the curve and the obstacles.On this basis,the time-optimal speed planning problem is addressed in two steps.In the first step,the forward-backward approach is introduced to solve the problem under the chord error,velocity,and acceleration constraints by changing the variables and deforming the constraints.Then by relaxing the constraints appropriately,the problem under jerk constraints is formulated into a linear programming(LP)problem.The feasibility of the proposed approach is verified through simulations and an indoor navigation experiment.The proposed approach can generate a C^(3) continuous collision-free trajectory that passes through the sparse desired way-points with allowable accuracy while guaranteeing the chord error,velocity,acceleration,and jerk constraints.When the number of sample points is 3000,the proposed speed planning method reduces the calculation time by 40%compared to an existing method.
基金supported by the National Key R&D Program of China(Grant No.2020YFC2201200)the National Natural Science Foundation of China(Grant No.U20B2001)。
文摘This paper develops a sequential convex programming(SCP)-based method to solve the minimum-fuel variable-specific-impulse low-thrust transfer problem considering shutdown constraint,with emphasize on improving the computational efficiency.The variable parameter engine is more applicable for many low-thrust scenarios,therefore,both a continuously variable model and a ladder variable model are adopted.First,the original problem is convexified by processing the constraint feasible domain,which is composed of the nonlinear dynamic equations and second-order equality constraint,into convex sets.Then,the approximation is generated to close the optimal solution of the low-thrust problem by iteratively solving the convexified subproblem.Moreover,the switching self-detection and adaptive node refinement methods are presented,which can improve the accuracy of the solution and accelerate the convergence during the approximation process and is especially necessary and effective in the scenarios with shutdown constraint.In numerical simulations,the comparison with the homotopic approach shows that the proposed method only needs 4%computational time as that of the homotopic approach,and two variable-specificimpulse examples further demonstrate the effectiveness and efficiency of the proposed method.
