A novel algorithm for optimal design of impulsive orbit transfer using multi-phase Gauss pseudospectral method

2010 ◽  
Author(s):  
Hongxin Shen
Keyword(s):  
Optimal Design ◽  
Pseudospectral Method ◽  
Orbit Transfer ◽  
Gauss Pseudospectral Method ◽  
Multi Phase ◽  
Novel Algorithm

Trajectory Optimization of Hypersonic Vehicle Using Gauss Pseudospectral Method

2011 ◽  
Vol 110-116 ◽  
pp. 5232-5239 ◽  
Author(s):  
Rahman Tawfiqur ◽  
Hao Zhou ◽  
Yong Zhi Sheng ◽  
Ya Min Younis ◽  
Ke Nan Zhang
Keyword(s):  
Trajectory Optimization ◽  
Pseudospectral Method ◽  
High Accuracy ◽  
Hypersonic Vehicle ◽  
Computationally Efficient ◽  
Efficient Manner ◽  
Rocket Propulsion ◽  
Gauss Pseudospectral Method ◽  
Solid Rocket ◽  
Multi Phase

The paper presents a gauss pseudospectral solution for the trajectory optimization problem of a hypersonic vehicle. Determination of optimal trajectory of a hypersonic vehicle is of great interest due to the different path and boundary conditions that need to be met for high accuracy. Recent researches show that pseudospectral methods are capable of providing high accuracy in computationally efficient manner. The hypersonic vehicle optimized here is accelerated through solid rocket propulsion to mach 3.5 and after ejection of the rocket motor it is accelerated to mach 6 where it starts cruise for reaching target. The flight profile which is divided into boost, ascent, cruise and dive phase is optimized using multi-phase implementation programme of gauss pseudospectral method GPOPS. The optimization is carried out in 2D assuming non-rotating flat earth assumption and considering propulsion, dynamic and atmospheric constraints. The results are then analyzed for max range and max final velocity and hit angle. The results are found to be feasible.

scholarly journals Optimal Path-Following Guidance with Generalized Weighting Functions Based on Indirect Gauss Pseudospectral Method

2018 ◽  
Vol 2018 ◽  
pp. 1-17 ◽  
Author(s):  
Qi Chen ◽  
Xugang Wang ◽  
Jing Yang
Keyword(s):  
Degrees Of Freedom ◽  
Optimal Path ◽  
Pseudospectral Method ◽  
Path Following ◽  
Control Cost ◽  
Weighting Functions ◽  
Guidance Law ◽  
Computational Performance ◽  
Gauss Pseudospectral Method ◽  
Virtual Target

An indirect Gauss pseudospectral method based path-following guidance law is presented in this paper. A virtual target moving along the desired path with explicitly specified speed is introduced to formulate the guidance problem. By establishing a virtual target-fixed coordinate system, the path-following guidance is transformed into a terminal guidance with impact angle constraints, which is then solved by using indirect Gauss pseudospectral method. Meanwhile, the acceleration dynamics are modeled as the first-order lag to the command. Using the receding horizon technique a closed-loop guidance law, which considers generalized weighting functions (even discontinuous) of both the states and the control cost, is derived. The accuracy and effectiveness of the proposed guidance law are validated by numerical comparisons. A STM32 Nucleo board based on the ARM Cortex-M7 processor is used to evaluate the real-time computational performance of the proposed indirect Gauss pseudospectral method. Simulations for various types of desired paths are presented to show that the proposed guidance law has better performance when compared with the existing results for pure pursuit, a nonlinear guidance law, and trajectory shaping path-following guidance and provides more degrees of freedom in path-following guidance design applications.

Non-linear solution to the maximum height orbit transfer guidance problem

2012 ◽  
Vol 226 (6) ◽  
pp. 620-630 ◽  
Author(s):  
H H Afshari ◽  
E Taheri
Keyword(s):  
Linear Problem ◽  
Perturbation Technique ◽  
Variable Mass ◽  
Pseudospectral Method ◽  
Performance Measure ◽  
Maximum Height ◽  
Orbit Transfer ◽  
Linear Solution ◽  
Two Body Problem ◽  
Non Linear

An optimal control solution to the highly non-linear problem of orbit transfer mission is achieved by using a newly proposed analytical perturbation technique. The problem is classified as a two-point boundary value problem in order to optimize a performance measure in a given time. Assuming a constant thrust operating in a given length of time, it is sought to find the thrust direction history of a transfer from a given initial orbit to the largest possible orbit. The system dynamical model is stated by regarding a variable mass spacecraft moving in the variable gravitational field of the Earth, based on the two-body problem. To assess the perturbation solution fidelity, a numerical solution based on the Gauss pseudospectral method has been employed. The main novelty of this work is in applying a new analytical solution strategy that is a combination of perturbation technique and backward integration to a highly non-linear problem in the calculus of variations approach.

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