Path Planning for Rapid Large-Angle Maneuver of Satellites Based on the 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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Trajectory optimization of UAV based on Hp-adaptive Radau pseudospectral method

Journal of Industrial and Management Optimization ◽

10.3934/jimo.2021201 ◽

2021 ◽

Vol 0 (0) ◽

pp. 0

Author(s):

Yi Cui ◽

Xintong Fang ◽

Gaoqi Liu ◽

Bin Li

Keyword(s):

Trajectory Planning ◽

Trajectory Optimization ◽

Optimization Problem ◽

Tracking Error ◽

Pseudospectral Method ◽

Planning Problem ◽

A Algorithm ◽

Planning Scheme ◽

Path Search ◽

Simulation Results

<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>

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

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.635-637.1431 ◽

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.

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Receding Horizon Trajectory Optimization with Terminal Impact Specifications

Mathematical Problems in Engineering ◽

10.1155/2014/604705 ◽

2014 ◽

Vol 2014 ◽

pp. 1-8 ◽

Cited By ~ 3

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.

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