scholarly journals Trajectory Optimization Based on Multi-Interval Mesh Refinement Method

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Ningbo Li ◽  
Humin Lei ◽  
Lei Shao ◽  
Tao Liu ◽  
Bin Wang
Keyword(s):  
Convergence Rate ◽  
Optimization Model ◽  
Trajectory Optimization ◽  
Optimization Problems ◽  
Mesh Refinement ◽  
Pseudospectral Method ◽  
Collocation Points ◽  
Refinement Method ◽  
Simulation Results ◽  
Terminal Guidance

In order to improve the optimization accuracy and convergence rate for trajectory optimization of the air-to-air missile, a multi-interval mesh refinement Radau pseudospectral method was introduced. This method made the mesh endpoints converge to the practical nonsmooth points and decreased the overall collocation points to improve convergence rate and computational efficiency. The trajectory was divided into four phases according to the working time of engine and handover of midcourse and terminal guidance, and then the optimization model was built. The multi-interval mesh refinement Radau pseudospectral method with different collocation points in each mesh interval was used to solve the trajectory optimization model. Moreover, this method was compared with traditional h method. Simulation results show that this method can decrease the dimensionality of nonlinear programming (NLP) problem and therefore improve the efficiency of pseudospectral methods for solving trajectory optimization problems.

Trajectory Optimization Applied to Space Rendezvous

2013 ◽  
Vol 756-759 ◽  
pp. 3466-3470
Author(s):  
Xu Min Song ◽  
Qi Lin
Keyword(s):  
Simulated Annealing ◽  
Optimization Model ◽  
Trajectory Optimization ◽  
Optimization Problem ◽  
Optimization Method ◽  
Nonlinear Constraints ◽  
Design Variables ◽  
Adaptive Simulated Annealing ◽  
Simulation Results

The trajcetory plan problem of spece reandezvous mission was studied in this paper using nolinear optimization method. The optimization model was built based on the Hills equations. And by analysis property of the design variables, a transform was put forward , which eliminated the equation and nonlinear constraints as well as decreaseing the problem dimensions. The optimization problem was solved using Adaptive Simulated Annealing (ASA) method, and the rendezvous trajectory was designed.The method was validated by simulation results.

scholarly journals Trajectory optimization of UAV based on Hp-adaptive Radau pseudospectral method

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>

scholarly journals Dynamic Optimization Using Local Collocation Methods and Improved Multiresolution Technique

2018 ◽  
Vol 8 (9) ◽  
pp. 1680 ◽  
Author(s):  
Jisong Zhao ◽  
Teng Shang
Keyword(s):  
Process Control ◽  
Dynamic Optimization ◽  
Chemical Process ◽  
Optimization Problems ◽  
Mesh Refinement ◽  
Collocation Methods ◽  
Control Optimization ◽  
Refinement Method ◽  
Chemical Process Control ◽  
Refinement Algorithm

Dynamic optimization has wide applications in scientific and industrial researches. Multiresolution techniques provide an efficient way to solve dynamic optimization problems but have some disadvantages. An improved multiresolution technique is developed in this paper to overcome these disadvantages. The proposed technique consists of local collocation methods and a multiresolution-based mesh refinement method. New, generalized dyadic meshes are proposed to overcome the dyadic limitation, and the mesh refinement method is improved so that it can start with the coarsest generalized dyadic mesh. Additionally, the proposed technique involves a mesh refinement algorithm to remove the redundant mesh points in the constant control regions by analyzing the control slopes. The technique is applied to three chemical process control optimization problems and compared with other methods to demonstrate its effectiveness. Numerical results show that the proposed technique can solve chemical process control optimization problems accurately and efficiently and has advantages over other methods.

scholarly journals An Improved Adaptive hp Mesh Refinement Method in Solving Optimal Control Problems

2021 ◽  
Author(s):  
Changxin Luo ◽  
Jiong Li ◽  
Chijun Zhou ◽  
Humin Lei
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimal Control Problems ◽  
Computing Time ◽  
Mesh Refinement ◽  
Pseudospectral Method ◽  
Change Rate ◽  
Refinement Method ◽  
Effective Choice

Abstract The adaptive hp pseudospectral method is an effective choice in solving the optimal control problem. In order to improve the computing efficiency of the adaptive hp method, an improved adaptive hp mesh refinement method is proposed in this paper. There are two main cores in this method. The first is to refine the mesh in advance based on the change rate of the control, so that the algorithm can more efficiently deal with the optimal control problem with discontinuous control. And the second is to based on the accumulation of curvature values to ensure that those positions that need to be refined more can be quickly allocated to more mesh points. These two are combined with each other to improve the solving efficiency of the algorithm proposed in this paper, which shortens the required computing time. In addition, the convergence of the algorithm is proved in this paper. The simulation results show the effectiveness and superiority of the algorithm proposed in this paper.

A modified pseudospectral method for solving trajectory optimization problems with singular arc

2016 ◽  
Vol 40 (5) ◽  
pp. 1783-1793 ◽  
Author(s):  
Zahra Foroozandeh ◽  
Mostafa Shamsi ◽  
Vadim Azhmyakov ◽  
Masoud Shafiee
Keyword(s):  
Trajectory Optimization ◽  
Optimization Problems ◽  
Pseudospectral Method ◽  
Singular Arc

Reentry Trajectory Optimization of Airbreathing Hypersonic Vehicles Based on Gauss Pseudospectral Method

2011 ◽  
Vol 383-390 ◽  
pp. 7375-7380 ◽  
Author(s):  
Bo Yang ◽  
Shang Sun
Keyword(s):  
Trajectory Optimization ◽  
Optimization Problems ◽  
Kinetic Equations ◽  
Pseudospectral Method ◽  
Hypersonic Vehicles ◽  
Gauss Pseudospectral Method ◽  
Suboptimal Solution ◽  
Reentry Trajectory ◽  
Reentry Trajectory Optimization ◽  
And Control

According to the nonlinear, multivariable and multi-constraint features of the reentry trajectory optimization problem of airbreathing hypersonic vehicles, a suboptimal solution method is developed. The reentry trajectory generation is converted to a nonlinear programming (NLP) problem by using Gauss pseudospectral method (GPM). The state and control variables on Gauss nodes are chosen as parameters to be optimized and the minimum total heat absorption is chosen as the optimal performance index. Then the sequential quadratic programming (SQP) method is used to solve the NLP problem. The states of optimized trajectory are compared with the states obtained by the integral of kinetic equations. By simulating on an example of airbreathing hypersonic vehicles, it is demonstrated that the above method is not sensitive to the estimate of motion states and is easier to converge. And the method is effective to solve trajectory optimization problems.

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