An Adaptive Collocation Method and Mesh Refinement for Solving Non-smooth Trajectory Optimization Problems

2016 ◽  
Author(s):  
Wei Pang ◽  
Xiaofang Xie ◽  
Pengfei Fan ◽  
Jiaqi Liu
Keyword(s):  
Collocation Method ◽  
Trajectory Optimization ◽  
Optimization Problems ◽  
Mesh Refinement

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.

scholarly journals A trajectory design method for RLV via artificialmemory-principle optimization

2018 ◽  
Vol 189 ◽  
pp. 10019
Author(s):  
Hao Li ◽  
Changzhu Wei
Keyword(s):  
Trajectory Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Memory Cell ◽  
Optimization Method ◽  
Alternative Solution ◽  
Trajectory Design ◽  
Memory State ◽  
Artificial Memory

A trajectory optimization method for RLV based on artificial memory principles is proposed. Firstly the optimization problem is modelled in Euclidean space. Then in order to solve the complicated optimization problem of RLV in entry phase, Artificial-memory-principle optimization (AMPO) is introduced. AMPO is inspired by memory principles, in which a memory cell consists the whole information of an alternative solution. The information includes solution state and memory state. The former is an evolutional alternative solution, the latter indicates the state type of memory cell: temporary, short-and long-term. In the evolution of optimization, AMPO makes a various search (stimulus) to ensure adaptability, if the stimulus is good, memory state will turn temporary to short-term, even long-term, otherwise it not. Finally, simulation of different methods is carried out respectively. Results show that the method based on AMPO has better performance and high convergence speed when solving complicated optimization problems of RLV.

DirCol5i: Trajectory Optimization for Problems With High-Order Derivatives

2018 ◽  
Vol 141 (3) ◽  
Author(s):  
Matthew P. Kelly
Keyword(s):  
Nonlinear System ◽  
Trajectory Optimization ◽  
Optimization Problems ◽  
High Order ◽  
Robot Arm ◽  
Minimum Jerk ◽  
Higher Derivatives ◽  
A Chain ◽  
Fifth Order ◽  
Reference Trajectories

In this technical brief, we focus on solving trajectory optimization problems that have nonlinear system dynamics and that include high-order derivatives in the objective function. This type of problem comes up in robotics—for example, when computing minimum-snap reference trajectories for a quadrotor or computing minimum-jerk trajectories for a robot arm. DirCol5i is a transcription method that is specialized for solving this type of problem. It uses the fifth-order splines and analytic differentiation to compute higher-derivatives, rather than using a chain-integrator as would be required by traditional methods. We compare DirCol5i to traditional transcription methods. Although it is slower for some simple optimization problems, when solving problems with high-order derivatives DirCol5i is faster, more numerically robust, and does not require setting up a chain integrator.

Trajectory Optimization for Spacecraft Proximity Rendezvous Using Direct Collocation Method

2012 ◽  
Vol 433-440 ◽  
pp. 6652-6656 ◽  
Author(s):  
Tao Liu ◽  
Yu Shan Zhao ◽  
Peng Shi ◽  
Bao Jun Li
Keyword(s):  
Nonlinear Programming ◽  
Control Problem ◽  
Programming Problem ◽  
Collocation Method ◽  
Trajectory Optimization ◽  
Collocation Methods ◽  
Nonlinear Programming Problem ◽  
Reference Orbit ◽  
Direct Collocation ◽  
Direct Collocation Method

Trajectory optimization problem for spacecraft proximity rendezvous with path constraints was discussed using direct collocation method. Firstly, the model of spacecraft proximity rendezvous in elliptic orbit optimization control problem was presented, with the dynamic equations established in the target local orbital frame, and the performance index was minimizing the total fuel consumption. After that the optimal control problem was transcribed into a large scale problem of Nonlinear Programming Problem (NLP) by means of Hermite-Simpson discretization, which was one of the direct collocation methods. Then the nonlinear programming problem was solved using MATLAB software package SNOPT. Finally, to verify this method, the fuel-optimal trajectory for finite thrust was planned for proximity rendezvous with elliptic reference orbit. Numerical simulation results demonstrate that the proposed method was feasible, and was not sensitive to the initial condition, having good robustness.

scholarly journals Spacecraft Multiple-Impulse Trajectory Optimization Using Differential Evolution Algorithm with Combined Mutation Strategies and Boundary-Handling Schemes

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Yuehe Zhu ◽  
Hua Wang ◽  
Jin Zhang
Keyword(s):  
Differential Evolution ◽  
Trajectory Optimization ◽  
Optimization Problems ◽  
Differential Evolution Algorithm ◽  
Optimal Solution ◽  
Global Optimum ◽  
Local Optimum ◽  
Local Optima ◽  
Trial Vector ◽  
Mutation Strategies

Since most spacecraft multiple-impulse trajectory optimization problems are complex multimodal problems with boundary constraint, finding the global optimal solution based on the traditional differential evolution (DE) algorithms becomes so difficult due to the deception of many local optima and the probable existence of a bias towards suboptimal solution. In order to overcome this issue and enhance the global searching ability, an improved DE algorithm with combined mutation strategies and boundary-handling schemes is proposed. In the first stage, multiple mutation strategies are utilized, and each strategy creates a mutant vector. In the second stage, multiple boundary-handling schemes are used to simultaneously address the same infeasible trial vector. Two typical spacecraft multiple-impulse trajectory optimization problems are studied and optimized using the proposed DE method. The experimental results demonstrate that the proposed DE method efficiently overcomes the problem created by the convergence to a local optimum and obtains the global optimum with a higher reliability and convergence rate compared with some other popular evolutionary methods.

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