scholarly journals Optimization for Far-distance Cooperative Rendezvous with Multiple Direction-fixed Thrusts

2021 ◽  
Vol 2068 (1) ◽  
pp. 012021
Author(s):  
Fei Ren
Keyword(s):  
Hybrid Algorithm ◽  
Optimization Method ◽  
Homotopy Method ◽  
Optimal Solutions ◽  
Low Thrust ◽  
Rendezvous Problem ◽  
Cooperative Rendezvous ◽  
Radial Thrust ◽  
Bang Bang Control ◽  
High Thrust

Abstract The continuous-thrust far-distance cooperative rendezvous problem between two spacecraft is investigated. The indirect optimization method, based on Pontryagin’s maximum principle (PMP), is applied to optimize fuel consumption. To overcome the difficulty in nonsmooth integration caused by the bang-bang control, the homotopy method is adopted to solve the fuel-optimal problem from a related energy-optimal problem. The quantum-behaved particle swarm optimization (QPSO) algorithm is used to obtain the energy-optimal solutions. The energy-optimal solutions are used as the initial values for the homotopic procedure to obtain the fuel-optimal solutions and optimal bang-bang control law. A hybrid algorithm combined homotopy method and sequential quadratic programming (SQP) algorithm is proposed. This hybrid algorithm can effectively obtain feasible optimal solutions even though the indirect optimization method exhibits a narrow convergence domain. Simulations of high-thrust and low-thrust rendezvous problems are provided and the proposed hybrid algorithm is verified. Moreover, the necessity of radial thrust is investigated.

A quadratic homotopy method for fuel-optimal low-thrust trajectory design

2018 ◽  
Vol 233 (5) ◽  
pp. 1741-1757 ◽  
Author(s):  
Binfeng Pan ◽  
Xun Pan ◽  
Yangyang Ma
Keyword(s):  
Trajectory Optimization ◽  
Transfer Problem ◽  
Quadratic Function ◽  
Homotopy Method ◽  
Linear Functions ◽  
Optimal Controls ◽  
Homotopy Methods ◽  
Low Thrust ◽  
Starting Point ◽  
Rendezvous Problem

Solving fuel-optimal low-thrust trajectory problems is a long-standing challenging topic, mainly due to the existence of discontinuous bang–bang controls and small convergence domain. Homotopy methods, the principle of which is to embed a given problem into a family of problems parameterized by a homotopic parameter, have been widely applied to address this difficulty. Linear homotopy methods, the homotopy functions of which are linear functions of the homotopic parameter, serve as useful tools to provide continuous optimal controls during the homotopic procedure with an energy-optimal low-thrust trajectory optimization problem as the starting point. However, solving energy-optimal problem is still not an easy task, particularly for the low-thrust orbital transfers with many revolutions or asteroids flyby, which is typically solved by other advanced numerical optimization algorithms or other homotopy methods. In this paper, a novel quadratic homotopy method, the homotopy function of which is a quadratic function of the homotopic parameter, is presented to circumvent this possible difficulty of solving the initial problem in the existing linear homotopy methods. A fixed-time full-thrust problem is constructed as the starting point of this proposed quadratic homotopy, the analytical solution of which can be easily obtained under a modified linear gravity approximation formulation. The criterion of energy-optimal problem is still involved in the homotopic procedure to provide continuous optimal controls until the original fuel-optimal problem is solved. Numerical demonstrations in an Earth to Venus rendezvous problem, a geostationary transfer orbit (GTO) to geosynchronous orbit (GEO) orbital transfer problem with many revolutions, and an Earth to Mars rendezvous problem with an asteroid flyby are presented to illustrate the applications of this proposed homotopy method.

Optimal control of rapid cooperative spacecraft rendezvous with multiple specific-direction thrusts

2020 ◽  
Vol 234 (16) ◽  
pp. 2296-2322
Author(s):  
Piaoyi Su ◽  
Weiming Feng ◽  
Yang Kun ◽  
Zhao Junfeng
Keyword(s):  
Optimal Control ◽  
Dynamic Theory ◽  
Quantum Particle ◽  
Optimization Method ◽  
Long Distance ◽  
Practical Strategy ◽  
Specific Direction ◽  
Rendezvous Problem ◽  
Cooperative Rendezvous ◽  
Convergent Solution

Focusing on the long-distance rapid cooperative rendezvous of two spacecraft under finite continuous thrust, this paper proposes a practical strategy for space operation using multiple specific-direction thrusts. Based on the orbital dynamic theory and Pontryagin’s maximum principle, the dynamic equations and optimal control equations for radial, circumferential, and normal thrust are determined. The optimization method is a hybrid algorithm. The initial costate variables for the fuel-optimal rapid cooperative rendezvous problem are obtained using quantum particle swarm optimization and subsequently set as the initial values in the sequence quadratic programming to search for the exact convergent solution. The elliptical and near-circular mission orbital rendezvous for spacecraft with multiple specific-direction thrusts are simulated and optimized. Numerical examples verifying the proposed method are provided. The results facilitate easier realization of rapid spacecraft maneuvering under continuous thrust conditions.

Planar High-Thrust and Low-Thrust Orbital Transfers from Earth to Europa

2004 ◽  
Vol 52 (4) ◽  
pp. 421-439
Author(s):  
Hans Seywald ◽  
Carlos M. Roithmayr ◽  
Daniel D. Mazanek ◽  
Frederic H. Stillwagen ◽  
Patrick A. Troutman ◽  
...  
Keyword(s):  
Low Thrust ◽  
Orbital Transfers ◽  
High Thrust

Multiobjective optimization of the flaxseed mucilage extraction process using normal-boundary intersection approach

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mariana Souza Rocha ◽  
Luiz Célio Souza Rocha ◽  
Marcia Barreto da Silva Feijó ◽  
Paula Luiza Limongi dos Santos Marotta ◽  
Samanta Cardozo Mourão
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Method ◽  
Extraction Process ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Fiber Concentration ◽  
Trade Off ◽  
Content Type ◽  
Normal Boundary

PurposeThe mucilage of the Linum usitatissimum L. seed (Linseed) is one of the natural mucilages that presents a great potential to provide a food hydrocolloid with potential applications in both food and pharmaceutical industries. To increase the yield and quality of linseed oil during its production process, it is necessary to previously extract its polysaccharides. Because of this, flax mucilage production can be made viable as a byproduct of oil extraction process, which is already a product of high commercial value consolidated in the market. Thus, the purpose of this work is to optimize the mucilage extraction process of L. usitatissimum L. using the normal-boundary intersection (NBI) multiobjective optimization method.Design/methodology/approachCurrently, the variables of the process of polysaccharide extraction from different sources are optimized using the response surface methodology. However, when the optimal points of the responses are conflicting it is necessary to study the best conditions to achieve a balance between these conflicting objectives (trade-offs) and to explore the available options it is necessary to formulate an optimization problem with multiple objectives. The multiobjective optimization method used in this work was the NBI developed to find uniformly distributed and continuous Pareto optimal solutions for a nonlinear multiobjective problem.FindingsThe optimum extraction point to obtain the maximum fiber concentration in the extracted material was pH 3.81, temperature of 46°C, time of 13.46 h. The maximum extraction yield of flaxseed was pH 6.45, temperature of 65°C, time of 14.41 h. This result confirms the trade-off relationship between the objectives. NBI approach was able to find uniformly distributed Pareto optimal solutions, which allows to analyze the behavior of the trade-off relationship. Thus, the decision-maker can set extraction conditions to achieve desired characteristics in mucilage.Originality/valueThe novelty of this paper is to confirm the existence of a trade-off relationship between the productivity parameter (yield) and the quality parameter (fiber concentration in the extracted material) during the flaxseed mucilage extraction process. The NBI approach was able to find uniformly distributed Pareto optimal solutions, which allows us to analyze the behavior of the trade-off relationship. This allows the decision-making to the extraction conditions according to the desired characteristics of the final product, thus being able to direct the extraction for the best applicability of the mucilage.

scholarly journals A Novel Hybrid Algorithm Based on Grey Wolf Optimizer and Fireworks Algorithm

Sensors ◽  
2020 ◽  
Vol 20 (7) ◽  
pp. 2147 ◽  
Author(s):  
Zhihang Yue ◽  
Sen Zhang ◽  
Wendong Xiao
Keyword(s):  
Hybrid Algorithm ◽  
Optimization Problems ◽  
Optimization Method ◽  
Grey Wolf Optimizer ◽  
Local Optimum ◽  
Grey Wolf ◽  
Optimal Search ◽  
Fireworks Algorithm ◽  
Wide Range ◽  
Search Capability

Grey wolf optimizer (GWO) is a meta-heuristic algorithm inspired by the hierarchy of grey wolves (Canis lupus). Fireworks algorithm (FWA) is a nature-inspired optimization method mimicking the explosion process of fireworks for optimization problems. Both of them have a strong optimal search capability. However, in some cases, GWO converges to the local optimum and FWA converges slowly. In this paper, a new hybrid algorithm (named as FWGWO) is proposed, which fuses the advantages of these two algorithms to achieve global optima effectively. The proposed algorithm combines the exploration ability of the fireworks algorithm with the exploitation ability of the grey wolf optimizer (GWO) by setting a balance coefficient. In order to test the competence of the proposed hybrid FWGWO, 16 well-known benchmark functions having a wide range of dimensions and varied complexities are used in this paper. The results of the proposed FWGWO are compared to nine other algorithms, including the standard FWA, the native GWO, enhanced grey wolf optimizer (EGWO), and augmented grey wolf optimizer (AGWO). The experimental results show that the FWGWO effectively improves the global optimal search capability and convergence speed of the GWO and FWA.

A Hybrid Algorithm for the Multi-Objective Time Dependent Vehicle Routing Problem

2014 ◽  
Vol 505-506 ◽  
pp. 1071-1075
Author(s):  
Yi Sun ◽  
Yue Chen ◽  
Chang Chun Pan ◽  
Gen Ke Yang
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Hybrid Algorithm ◽  
Time Windows ◽  
Time Dependent ◽  
Ant Colony System ◽  
Optimal Solutions ◽  
Test Results ◽  
Routing Problem ◽  
Traffic Conditions

This paper presents a real road network case based on the time dependent vehicle routing problem with time windows (TDVRPTW), which involves optimally routing a fleet of vehicles with fixed capacity when traffic conditions are time dependent and services at customers are only available in their own time tables. A hybrid algorithm based on the Genetic Algorithm (GA) and the Multi Ant Colony System (MACS) is introduced in order to find optimal solutions that minimize two hierarchical objectives: the number of tours and the total travel cost. The test results show that the integrated algorithm outperforms both of its traditional ones in terms of the convergence speed towards optimal solutions.

Sign in / Sign up

Export Citation Format

Share Document