Numerical computation of singular control functions in trajectory optimization problems

1990 ◽  
Vol 13 (1) ◽  
pp. 153-159 ◽  
Author(s):  
Hans Joachim Oberle
Keyword(s):  
Numerical Computation ◽  
Trajectory Optimization ◽  
Optimization Problems ◽  
Singular Control ◽  
Control Functions

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.

scholarly journals P-Cyclic C-Contraction Result in Menger Spaces Using a Control Function

2016 ◽  
Vol 49 (2) ◽  
Author(s):  
B. S. Choudhury ◽  
S. K. Bhandari
Keyword(s):  
Contraction Mapping ◽  
Metric Spaces ◽  
Optimization Problems ◽  
Control Function ◽  
Probabilistic Metric Space ◽  
Probabilistic Metric Spaces ◽  
Control Functions ◽  
Menger Spaces ◽  
Cyclic Contractions ◽  
Probabilistic Metric

AbstractThe intrinsic flexibility of probabilistic metric spaces makes it possible to extend the idea of contraction mapping in several inequivalent ways, one of which being the C-contraction. Cyclic contractions are another type of contractions used extensively in global optimization problems. We introduced here p-cyclic contractions which are probabilistic C-contraction types. It involves p numbers of subsets of the spaces and involves two control functions for its definitions. We show that such contractions have fixed points in a complete probabilistic metric space. The main result is supported with an example and extends several existing results.

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.

scholarly journals METHOD FOR OPTIMIZING OF MOBILE ROBOT TRAJECTORY IN REPELLER SOURCES FIELD

2021 ◽  
Vol 20 (3) ◽  
pp. 690-726
Author(s):  
Mikhail Medvedev ◽  
Vladimir Kostjukov ◽  
Viacheslav Pshikhopov
Keyword(s):  
Trajectory Optimization ◽  
High Efficiency ◽  
Optimization Problems ◽  
Local Extremum ◽  
Adaptive Procedure ◽  
Local Maxima ◽  
Allowable Deviation ◽  
Input Variables ◽  
Field Decay ◽  
The One

The article discusses the procedure for correcting the trajectory of a robotic platform (RTP) on a plane in order to reduce the probability of its defeat/detection in the field of a finite number of repeller sources. Each of these sources is described by a mathematical model of some factor of counteraction to the RTP. This procedure is based, on the one hand, on the concept of a characteristic probability function of a system of repeller sources, which allows us to assess the degree of influence of these sources on the moving RTP. From this concept follows the probability of its successful completion used here as a criterion for optimizing the target trajectory. On the other hand, this procedure is based on solving local optimization problems that allow you to correct individual sections of the initial trajectory, taking into account the location of specific repeller sources with specified parameters in their vicinity. Each of these sources is characterized by the potential, frequency of impact, radius of action, and parameters of the field decay. The trajectory is adjusted iteratively and takes into account the target value of the probability of passing. The main restriction on the variation of the original trajectory is the maximum allowable deviation of the changed trajectory from the original one. If there is no such restriction, then the task may lose its meaning, because then you can select an area that covers all obstacles and sources, and bypass it around the perimeter. Therefore, we search for a local extremum that corresponds to an acceptable curve in the sense of the specified restriction. The iterative procedure proposed in this paper allows us to search for the corresponding local maxima of the probability of RTP passage in the field of several randomly located and oriented sources, in some neighborhood of the initial trajectory. First, the problem of trajectory optimization is set and solved under the condition of movement in the field of single source with the scope in the form of a circular sector, then the result is extended to the case of several similar sources. The main problem of the study is the choice of the General form of the functional at each point of the initial curve, as well as its adjustment coefficients. It is shown that the selection of these coefficients is an adaptive procedure, the input variables of which are characteristic geometric values describing the current trajectory in the source field. Standard median smoothing procedures are used to eliminate oscillations that occur as a result of the locality of the proposed procedure. The simulation results show the high efficiency of the proposed procedure for correcting the previously planned trajectory.

scholarly journals A full-space quasi-Lagrange-Newton-Krylov algorithm for trajectory optimization problems

2018 ◽  
Vol 49 ◽  
pp. 103-125
Author(s):  
Hsuan-Hao Wang ◽  
Yi-Su Lo ◽  
Feng-Tai Hwang ◽  
Feng-Nan Hwang
Keyword(s):  
Trajectory Optimization ◽  
Optimization Problems
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