Research on the Path Optimization of Satellite Formation Reconfiguration Based on Gauss Pseudospectral Method

2014 ◽  
Vol 926-930 ◽  
pp. 3688-3691
Author(s):  
Jian Wei Shi ◽  
Yuan Wen Cai ◽  
Xiao Chen Xing
Keyword(s):  
Optimization Problem ◽  
Pseudospectral Method ◽  
Path Optimization ◽  
Low Thrust ◽  
Satellite Formation ◽  
Formation Reconfiguration ◽  
Gauss Pseudospectral Method

Aim to the path programme problem of satellite formation reconfiguration under low thrust, optimization is simulated based on Gauss Pseudospectral Method (GPM). The simulation result demonstrates that the GPM can effectively solve the the path optimization problem.

Reentry Trajectory Optimization and Simulation of Hypersonic Vehicle with Maximum Cross Range Based on GPM

2014 ◽  
Vol 635-637 ◽  
pp. 1431-1437
Author(s):  
Wu Jun Huo ◽  
Xu Liu ◽  
Li Wang ◽  
Chao Song
Keyword(s):  
Trajectory Optimization ◽  
Optimization Problem ◽  
Control Variable ◽  
Pseudospectral Method ◽  
Hypersonic Vehicle ◽  
State Variables ◽  
Hypersonic Aircraft ◽  
Gauss Pseudospectral Method ◽  
Reentry Trajectory ◽  
Reentry Trajectory Optimization

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.

Fuel Optimal Maneuver of Passive and Periodic Circular-Like Satellite Formation: Legendre Pseudospectral Approach

2013 ◽  
Vol 389 ◽  
pp. 834-840
Author(s):  
Guang Yan Xu ◽  
Xiao Ying Wang
Keyword(s):  
Control Problem ◽  
Pseudospectral Method ◽  
Nonlinear Programming Problem ◽  
Low Thrust ◽  
Final Time ◽  
Satellite Formation ◽  
Thrust System ◽  
Legendre Pseudospectral Method ◽  
Nonlinear Optimal Control Problem

In this paper, an effective method was proposed to formulate and solve a fuel-optimal satellites maneuver control problem using a continuous low-thrust system. The design of the bounded desired final satellite formation is a passive and periodic circular-like formation at critical inclination underperturbation, which adjusts to long-term flying formation. The nonlinear optimal control problem is converted into a nonlinear programming problem by the application of the Legendre pseudospectral method. Due to the design includes the free final time and the precise final condition constraint, fuel-optimal maneuver is more reasonable, thereby it will achieve the minimum fuel consumption.

scholarly journals Receding Horizon Trajectory Optimization with Terminal Impact Specifications

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Limin Zhang ◽  
Mingwei Sun ◽  
Zengqiang Chen ◽  
Zenghui Wang ◽  
Yongkun Wang
Keyword(s):  
Programming Language ◽  
Trajectory Optimization ◽  
Optimization Problem ◽  
Pseudospectral Method ◽  
Optimization Strategy ◽  
Receding Horizon ◽  
C Programming Language ◽  
Gauss Pseudospectral Method ◽  
C Programming ◽  
The Cost

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.

scholarly journals Path Planning for Rapid Large-Angle Maneuver of Satellites Based on the Gauss Pseudospectral Method

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Wan Zhang ◽  
Yao Zhang ◽  
Wenbo Li ◽  
Youyi Wang
Keyword(s):  
Attitude Control ◽  
Trajectory Optimization ◽  
Optimal Trajectory ◽  
Optimization Problem ◽  
Large Angle ◽  
Pseudospectral Method ◽  
Performance Criteria ◽  
Planning Problem ◽  
Singularity Problem ◽  
Gauss Pseudospectral Method

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.

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