scholarly journals The Earth-Mars Transfer Trajectory Optimization of Solar Sail Based on hp-Adaptive Pseudospectral Method

2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Yufei Guo ◽  
Dongzhu Feng ◽  
Xin Wang ◽  
Cong Li ◽  
Yunzhao Liu

Solar sails have many advantages over traditional chemical propulsion spacecraft, such as needlessness of fuel, high payload ratio, long service life, and great application potential in deep space exploration, interstellar voyage, and other aerospace application fields. However, the period of solar sail transfer from the initial orbit to the desired orbit is relatively long. Thus, it is necessary to optimize the transfer trajectory of solar sail according to specific tasks. The hp-adaptive pseudospectral method combines the global pseudospectral method with the finite element method, which adopts double layer optimization strategy to solve the optimal control problem and has higher computational efficiency and accuracy than the traditional global pseudospectral method. In this paper, the pressure of solar light acting on the solar sail is analyzed, and the kinematic equation of the solar sail is established in polar coordinate system first; then the basic principle of the hp-adaptive pseudospectral method is introduced, and the steps of solving the transfer trajectory optimization problem by hp-adaptive pseudospectral method are proposed; finally, the trajectory optimization of the solar sail from Earth orbit to Sun-centered Mars orbit is simulated as an example to demonstrate the effectiveness of hp-adaptive pseudospectral method in the orbit transfer optimization problem of solar sail. The simulation results show that the adopted method is not sensitive to the initial values and has more reasonable distribution and less computational cost than the Gauss pseudospectral method.

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Limin Zhang ◽  
Mingwei Sun ◽  
Zengqiang Chen ◽  
Zenghui Wang ◽  
Yongkun Wang

The trajectory optimization problem subject to terminal impact time and angle specifications can be reformulated as a nonlinear programming problem using the Gauss pseudospectral method. The cost function of the trajectory optimization problem is modified to reduce the terminal control energy. A receding horizon optimization strategy is implemented to reject the errors caused by the motion of a surface target. Several simulations were performed to validate the proposed method via the C programming language. The simulation results demonstrate the effectiveness of the proposed algorithm and that the real-time requirement can be easily achieved if the C programming language is used to realize it.


2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yi Cui ◽  
Xintong Fang ◽  
Gaoqi Liu ◽  
Bin Li

<p style='text-indent:20px;'>Unmanned Aerial Vehicles (UAVs) have been extensively studied to complete the missions in recent years. The UAV trajectory planning is an important area. Different from the commonly used methods based on path search, which are difficult to consider the UAV state and dynamics constraints, so that the planned trajectory cannot be tracked completely. The UAV trajectory planning problem is considered as an optimization problem for research, considering the dynamics constraints of the UAV and the terrain obstacle constraints during flight. An hp-adaptive Radau pseudospectral method based UAV trajectory planning scheme is proposed by taking the UAV dynamics into account. Numerical experiments are carried out to show the effectiveness and superior of the proposed method. Simulation results show that the proposed method outperform the well-known RRT* and A* algorithm in terms of tracking error.</p>


Author(s):  
Jinbo Wang ◽  
Naigang Cui ◽  
Changzhu Wei

Aiming at improving the autonomy of hypersonic entry vehicles, a rapid trajectory optimization algorithm, which has the potential to be implemented online and onboard, is proposed in this paper. The nonlinear and nonconvex hypersonic entry trajectory optimization problem is transformed into a series of convex subproblems through a proper combination of the pseudospectral method and an improved successive convexification method; thus, the high discretization accuracy of the pseudospectral method and the fast and deterministic convergence properties of the convex-optimization-based algorithm can be simultaneously exploited. The resulting subproblems can be solved efficiently by matured interior-point methods, and the solution converges rapidly by adopting a novel dynamic trust-region updating approach. The optimality of the solution is verified by the optimal control theory. The effectiveness of the algorithm is demonstrated by numerical experiments.


2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Zhengnan Li ◽  
Tao Yang ◽  
Zhiwei Feng

To solve the multiobjective optimization problem on hypersonic glider vehicle trajectory design subjected to complex constraints, this paper proposes a multiobjective trajectory optimization method that combines the boundary intersection method and pseudospectral method. The multiobjective trajectory optimization problem (MTOP) is established based on the analysis of the feature of hypersonic glider vehicle trajectory. The MTOP is translated into a set of general optimization subproblems by using the boundary intersection method and pseudospectral method. The subproblems are solved by nonlinear programming algorithm. In this method, the solution that has been solved is employed as the initial guess for the next subproblem so that the time consumption of the entire multiobjective trajectory optimization problem shortens. The maximal range and minimal peak heat problem is solved by the proposed method. The numerical results demonstrate that the proposed method can obtain the Pareto front of the optimal trajectory, which can provide the reference for the trajectory design of hypersonic glider vehicle.


2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Naiming Qi ◽  
Mingying Huo ◽  
Qiufan Yuan

Displaced orbits for spacecraft propelled by electric sails are investigated as an alternative to the use of solar sails. The orbital dynamics of electric sails based spacecraft are studied within a spherical coordinate system, which permits finding the solutions of displaced electric sail orbits and optimize transfer trajectory. Transfer trajectories from Earth's orbit to displaced orbit are also studied in an optimal framework, by using genetic algorithm and Gauss pseudospectral method. The initial guesses for the state and control histories used in the Gauss pseudospectral method are interpolated from the best solution of a genetic algorithm. Numerical simulations show that the electric sail is able to perform the transfer from Earth’s orbit to displaced orbit in acceptable time, and the hybrid optimization method has the capability to search the feasible and optimal solution without any initial value guess.


2014 ◽  
Vol 635-637 ◽  
pp. 1431-1437
Author(s):  
Wu Jun Huo ◽  
Xu Liu ◽  
Li Wang ◽  
Chao Song

Abstract:The application of Gauss pseudospectral method (GPM) to hypersonic aircraft reentry trajectory optimization problem with maximum cross range was introduced. The Gauss pseudospectral method was used to solve the reentry trajectory of the hypersonic vehicle with the maximum cross range. Firstly, the model of hypersonic aircraft reentry trajectory optimization control problem was established. Taking no account of course constraint, the maximum cross range was chosen as optimal performance index, and angle of attack and bank was chosen as control variable. Terminal state was constrained by position and velocity. Then GPM was applied to change trajectory optimization problem into nonlinear programming problem (NLP), and the state variables and control variables were selected as optimal parameters at all Gauss nodes. At last, optimal reentry trajectory was solved by solving the NLP with the help of SNOPT. The simulation results indicate that GPM does not need to estimate the initial cost variable, and it is not sensitive to the initial states and effective to solve trajectory optimization problem.


Energies ◽  
2018 ◽  
Vol 11 (12) ◽  
pp. 3302 ◽  
Author(s):  
Zhaoxiang Tan ◽  
Shaofeng Lu ◽  
Kai Bao ◽  
Shaoning Zhang ◽  
Chaoxian Wu ◽  
...  

Train speed trajectory optimization has been proposed as an efficient and feasible method for energy-efficient train operation without many further requirements to upgrade the current railway system. This paper focuses on an adaptive partial train speed trajectory optimization problem between two arbitrary speed points with a given traveling time and distance, in comparison with full speed trajectory with zero initial and end speeds between two stations. This optimization problem is of interest in dynamic applications where scenarios keep changing due to signaling and multi-train interactions. We present a detailed optimality analysis based on Pontryagin’s maximum principle (PMP) which is later used to design the optimization methods. We propose two optimization methods, one based on the PMP and another based on mixed-integer linear programming (MILP), to solve the problem. Both methods are designed using heuristics obtained from the developed optimality analysis based on the PMP. We develop an intuitive numerical algorithm to achieve the optimal speed trajectory in four typical case scenarios; meanwhile, we propose a new distance-based MILP approach to optimize the partial speed trajectory in the same scenarios with high modeling precision and computation efficiency. The MILP method is later used in a real engineering speed trajectory optimization to demonstrate its high computational efficiency, robustness, and adaptivity. This paper concludes with a comparison of both methods in addition to the widely applied pseudospectral method and propose the future work of this paper.


2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Chenxin Zhang ◽  
Yankun Zhang ◽  
Changzhu Wei

In this paper, a trajectory optimization strategy for the hypersonic morphing aircraft is proposed, and the AMPI method is used to generate the online trajectory with initial state errors. Firstly, the aerodynamic model and propulsion model of the hypersonic morphing aircraft were established considering the wingspan and the scramjet. Secondly, the optimization strategy was proposed via Gauss pseudospectral method considering the control variables including angle of attack (AOA) and wingspan. The optimized trajectory met the final constraints and path constraints with the objective to minimize the time of the ascent phase. Then, the AMPI method was used to generate online trajectory without solving OCP or NLP on the base of trajectory database calculated by the optimization strategy. The simulation results indicate high accuracy of AMPI method and the final errors corresponding to different initial errors were acceptable. The mean value of the CPU time of the method was about 0.1 second, which shows real-time capability.


2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Wan Zhang ◽  
Yao Zhang ◽  
Wenbo Li ◽  
Youyi Wang

A Gauss pseudospectral method is proposed in this study to solve the optimal trajectory-planning problem for satellite rapid large-angle maneuvers. In order to meet the requirement of rapid maneuver capability of agile small satellites, Single Gimbal Control Moment Gyros (SGCMGs) are adopted as the actuators for the attitude control systems (ACS). Because the singularity problem always exists for SGCMGs during the large-angle maneuvering of the satellites, a trajectory optimization method for the gimbal rates is developed based on the Gauss pseudospectral method. This method satisfies the control requirement of satellite rapid maneuvers and evades the singularity problem of SGCMGs. The method treats the large-angle maneuver problem as an optimization problem, which meets the boundary condition and a series of the physical constraints including the gimbal angle constraint, the gimbal rates constraint, the singularity index constraint, and some other performance criteria. This optimization problem is discretized as a nonlinear programming problem by the Gauss pseudospectral method. The optimal nonsingularity gimbal angle trajectory is obtained by the sequence of quadratic programming (SQP). This approach avoids the difficulties in solving the boundary value problem. The simulations reveal that the Gauss pseudospectral method effectively plans an optimal trajectory and satisfies all the constraints within a short time.


2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Zhifang Wei ◽  
Yang Cheng ◽  
Xiangxiang Guo ◽  
Senlin Liu

In this paper, an offline hybrid trajectory optimization approach is proposed for variable-sweep missiles to explore the superiority in the diving phase. Aiming at the maximal terminal velocity with the impact angle constraint, the trajectory optimization model is formulated under multiple constraints, and the aerodynamic analysis in different sweep angles is discussed. Unlike only the attack angle used for the optimization process traditionally, the two-variable optimization scheme on both the attack angle and sweep angle is investigated for variable-sweep missiles. Then, the trajectory optimization problem is transformed into the nonlinear programming problem via a hybrid optimization strategy combining the Gauss pseudospectral method and direct shooting method to obtain the high precision and fast convergence solution. Finally, to verify the feasibility of the optimal trajectory under uncertainties, the tracking guidance law is designed on basis of the gain scheduled linear quadratic regulator control. Numerical simulation results reveal not only of the proposed hybrid optimization strategy but also of the superiority of variable-sweep missiles compared with traditional missiles.


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