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정유연,방효충 한국항공우주학회 2015 한국항공우주학회 학술발표회 논문집 Vol.2015 No.4
화성의 대기권 통과 시 발생하는 항법오차가 존재하는 조건에서도 목표지점에 정밀하게 착륙할 수 있는 기술이 필요하다. 본 논문에서는 매 시간스텝마다 새로운 측정치를 이용한 최적화를 수행하는 모델예측제어이론에 기반하여 화성정밀착륙 유도법칙을 제안하였다. 전역 최적 해를 보장할 수 없는 모델예측제어이론의 단점을 화성착륙 운동방정식의 볼록 최적화를 통하여 해결하였으며 Laguerre 함수를 이용하여 수식전개를 단순화하였다. 또한 각 스텝에서 계산된 제어입력은 서로 독립적이기 때문에 Lyapunov 함수를 이용한 안정성을 증명하였다. 최종적으로 제안된 이론을 이용한 시뮬레이션을 수행하였다. The precise landing technology is required under the presence of the navigation error that was occurred during passing through the Martian atmosphere. In this paper, the precise landing guidance for Mars is suggested based on the model predictive control theory that performs optimization process at each time step. The drawback of the theory that cannot guarantee the global optimum is resolved by using convex optimization. Additionally, the formulation is simplified using Laguerre function. For independent control inputs obtained by independent optimization process, the stability is proved by Lyapunov stability. Finally, the simulation results are represented for the proposed guidance.
Convex 최적화를 이용한 화성착륙 유도제어 알고리즘 연구
강상욱,변수영,김호영,방효충 한국항공우주학회 2013 한국항공우주학회 학술발표회 논문집 Vol.2013 No.11
화성탐사의 성공적인 임무수행을 위해서는 화성 착륙선을 정해진 목표지점에 정확히 착륙시키는 것이 매우 중요하다. 본 연구에서는 Convex optimization을 이용하여 목표지점까지 착륙선을 유도제어할 수 있는 추력하강단계의 착륙알고리즘에 관해 연구를 수행하였다. 미리 정해진 목표지점과 최소의 착륙 오차를 갖는 궤적을 생성한 후 연료소모를 최소화하는 궤적을 설계하였다. 착륙오차를 최소화하는 궤적은 추력벡터의 크기가 0이 아닌 하한값을 갖기 때문에 nonconvex 문제이다. 따라서 이 문제를 convex 최적화 문제로 변형하여 전역영역에서의 최적화 궤적을 찾는 알고리즘을 소개하였다. 이 연구는 실제 화성탐사시 실시간으로 적용할 수 있는 추력단계에서의 착륙알고리즘 개발에 많은 도움이 될 것이다. To perform the Mars mission successfully, it is important to land the lander precisely on the target of Mars surface which is determined in advance. In this study, powered descent guidance algorithm to guide lander on target was investigated using convex optimization. Minimum landing error trajectory is generated before designing trajectory of minimum fuel consumption for this study. the problem of minimum landing error trajectory is noconvex optimal control problem because of nonzero lower bound on the magnitude of thrust vector. So it is introduced to solve the optimal trajectory in global domain after converting this problem to convex optimal control problem. This study will be helped on development of powered descent guidance algorithm to apply on real time implementation for Mars mission.
Mars precision landing guidance based on model predictive control approach
Jung, Youeyun,Bang, Hyochoong SAGE Publications 2016 Proceedings of the Institution of Mechanical Engin Vol.230 No.11
<P>A precision landing guidance design for the Mars powered descent phase is proposed based on model predictive control (MPC) approach. Dynamics model used for the formulation are convexificated and linearized to adopt the convex optimization technique, which has been suggested by researchers of Jet Propulsion Laboratory. To employ the receding horizon frame and reduce the number of control inputs, the convex optimization problem is augmented with Laguerre functions. To represent the minimum fuel consumption or minimum landing error precisely unlike the optimal control theory, new cost function is designed by combining them with weighting factors. Moreover, the stability of the proposed guidance design for the independent control inputs calculated from each time step is verified by using Lyapunov stability analysis. Finally, numerical simulations are conducted to examine the suggested guidance formulation and to compare the performance with an optimal solution.</P>
An optimal trajectory design for the lunar vertical landing
Leeghim, Henzeh,Cho, Dong-Hyun,Kim, Donghoon SAGE Publications 2016 Proceedings of the Institution of Mechanical Engin Vol.230 No.11
<P>A research for designing the optimal lunar vertical landing trajectory to reduce the total energy or mass of propellant is addressed in this paper. Most of these problems can be divided into two phases: breaking and approach phase. The optimal landing trajectory in general does not consider the pitch-up motion so that the landing problem has been only solved in the breaking phase. For this reason, there are some attempts to find the optimal trajectory including the final vertical landing phase by including the equations of angular motion of the vehicle. However, the optimal solution using this approach depends on the scale factor of a cost function because the cost function consists of two different mechanical parameters such as the final mass and total control torque. The final control constraints are augmented for vertical lunar landing instead of the equations of angular motion. The obtained optimal trajectory has an additional positive effect of the image acquisition as well as the final vertical landing.</P>