• International Journal of Aeronautical and Space Sciences
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• 제10권1호
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• pp.112-121
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• 2009

This paper deals with supersonic air-breathing missile system. A supersonic air-breathing missile system has very complicated and incoherent thrust characteristics with respect to outer and inner environment during operation. For this reason, the missile system has many maneuver constraints and is allowed to operate within narrow flight envelope. In this paper, trajectory optimization of the missile is accomplished. The trajectory optimization problem is formulated as a discrete parameter optimization problem. For this formulation, Legendre Pseudo-Spectral method is introduced. This method is based on calculating the state and control variables on Legendre-Gauss-Lobatto (LGL) points. This approach helps to find approximated derivative and integration quantities simply. It is shown that, for this trajectory optimization, trend analysis is performed from thrust characteristics on various conditions so that the trajectory optimization is accomplished with fine initial guess with these results.

• International Journal of Aeronautical and Space Sciences
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• 제12권3호
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• pp.288-295
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• 2011

This paper addresses minimum-fuel, two-dimensional trajectory optimization for a soft lunar landing from a parking orbit to a desired landing site. The landing site is usually not considered when performing trajectory optimization so that the landing problem can be handled. However, for precise trajectories for landing at a desired site to be designed, the landing site has to be considered as the terminal constraint. To convert the trajectory optimization problem into a parameter optimization problem, a pseudospectral method was used, and C code for feasible sequential quadratic programming was used as a numerical solver. To check the reliability of the results obtained, a feasibility check was performed.

• 한국추진공학회:학술대회논문집
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• 한국추진공학회 2009년도 춘계학술대회 논문집
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• pp.411-413
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• 2009

본 논문은 초음속 추진을 이용한 미사일 시스템에 대한 궤적최적화에 대한 연구를 소개한다. 초음속 추진 시스템은 외부비행조건과 내부 연소 환경에 따른 복잡하고 비선형성이 강한 추력특성을 가진다. 이러한 이유로 초음속 비행체의 운용에 있어 많은 구속조건을 가지며 일반 비행체보다 좁은 비행영역안에서 운용되어야 한다. 본 논문에서는 이러한 특성을 가지는 초음속 비행체의 궤적최적화를 수행하고 보다 효율적인 운용에 대한 비전을 제시하고자 한다. 궤적최적화는 일반적인 초음속 추진에 관련한 구속조건들을 고려하며 수행되었고, 궤적최적화 결과를 통해 얻어진 효율적 연료공급 및 노즐 목 면적 제어에 대한 일반적인 운용 및 응용방안에 대해서 고찰하고자 한다.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2001년도 ICCAS
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• pp.156.2-156
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• 2001

Hypersonic civil airplanes are recently heated up again in USA and Japan, but there are several difficulties when we obtain its optimal trajectories. In this paper, we formulated the trajectory optimization problem as an optimal control problem and solved it by the direct shooting method with the Genetic Algorithm, GA. The result shows it is effective to use this method for the trajectory optimization of the hypersonic flight.

• Journal of Astronomy and Space Sciences
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• 제21권3호
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• pp.209-220
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• 2004

Some methods have been presented to get optimal formation trajectories in the step of configuration or reconfiguration, which subject to constraints of collision avoidance and final configuration. In this study, a method for optimal formation trajectory-planning is introduced in view of fuel/time minimization using parameter optimization technique which has not been applied to optimal trajectory-planning for satellite formation flying. New constraints of nonlinear equality are derived for final configuration and constraints of nonlinear inequality are used for collision avoidance. The final configuration constraints are that three or more satellites should be placed in an equilateral polygon of the circular horizontal plane orbit. Several examples are given to get optimal trajectories based on the parameter optimization problem which subjects to constraints of collision avoidance and final configuration. They show that the introduced method for trajectory-planning is well suited to trajectory design problems of formation flying missions.

• Advances in aircraft and spacecraft science
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• 제6권5호
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• pp.391-407
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• 2019

Flight trajectory optimization has become an important factor not only to reduce the operational costs (e.g.,, fuel and time related costs) of the airliners but also to reduce the environmental impact (e.g.,, emissions, contrails and noise etc.) caused by the airliners. So far, these factors have been dealt with in the context of 2D and 3D trajectory optimization, which are no longer efficient. Presently, the 4D trajectory optimization is required in order to cope with the current air traffic management (ATM). This study deals with a cubic spline approximation method for solving 4D trajectory optimization problem (TOP). The state vector, its time derivative and control vector are parameterized using cubic spline interpolation (CSI). Consequently, the objective function and constraints are expressed as functions of the value of state and control at the temporal nodes, this representation transforms the TOP into nonlinear programming problem (NLP). The proposed method is successfully applied to the generation of a minimum length optimal trajectories along 4D waypoints, where the method generated smooth 4D optimal trajectories with very accurate results.

• 전기학회논문지
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• 제68권1호
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• pp.159-166
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• 2019

Due to the various engagement situations, it is very difficult to generate the optimal trajectory with several constraints. This paper investigates the sequential convex programming for the impact angle control with the additional constraint of altitude limit. Recently, the SOCP(Second-Order Cone Programming), which is one area of the convex optimization, is widely used to solve variable optimal problems because it is robust to initial values, and resolves problems quickly and reliably. The trajectory optimization problem is reconstructed as convex optimization problem using appropriate linearization and discretization. Finally, simulation results are compared with analytic result and nonlinear optimization result for verification.

• Journal of Mechanical Science and Technology
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• 제20권10호
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• pp.1557-1566
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• 2006

We present a procedure for the application of global orthogonal polynomial into an atmospheric re-entry maneuvering problem. This trajectory optimization is imbedded in a family of canonically parameterized optimal control problem. The optimal control problem is transcribed to nonlinear programming via global orthogonal polynomial and is solved a sparse nonlinear optimization algorithm. We analyze the optimal trajectories with respect to the performance of re-entry maneuver.

• 한국항공우주학회지
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• 제37권1호
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• pp.42-54
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• 2009

비행체의 최적궤적문제에서는 최적화의 수렴성 및 효율성을 위해 3자유도 운동역학모델이 이용되며, 비선형 추종제어를 위해서는 6자유도 비선형 운동모델이 이용된다. 따라서, 3자유도 운동역학모델을 통해 획득한 최적궤적을 비선형 추종제어의 기준궤적으로 사용하는 경우에 두 모델간의 상이성으로 인한 문제가 발생하게 되며 성능이 보장하지 못한다. 본 논문에서는 이러한 두 모델간의 차이를 완화시키기 위한 새로운 최적궤적 생성 방법을 제안하였으며, 성층권비행선의 실제 구속조건과 성능조건 및 제트 스트림을 고려하여 최적궤적을 생성하고 기존 결과와 비교함으로써 제안한 방법의 장점을 검증하였다.

• 한국군사과학기술학회지
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• 제19권1호
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• pp.95-104
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• 2016

To make a firing table of artillery with trajectory simulation, a precise trajectory model which corresponds with real firing test is required. Recent 4-DOF modified point mass trajectory model is considered accurate as a theoretical model, but fitting coefficients are used in calculation to match with real firing test results. In this paper, modified point mass trajectory model is presented and method of setting ballistic coefficient is introduced by applying optimization algorithms. After comparing two different algorithms, Particle Swarm Optimization and Covariance Matrix Adaptation - Evolutionary Strategy, we found that using CMA-ES algorithm gives fine optimization result. This fitting coefficient setting method can be used to make trajectory simulation which is required for development of new projectiles in the future.