• Journal of the Korean Society for Precision Engineering
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• v.15 no.6
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• pp.97-106
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• 1998

In this Paper, a fuel minimizing closed loop explicit inertial guidance algorithm for orbit injection of a rocket is developed. In the formulation, the fuel burning rate and magnitude of thrust are assumed constant. The motion of rocket is assumed to be subject to the average inverse-square gravity, but negligible effects from atmosphere. The optimum thrust angle to obtain a given velocity vector in the shortest time with minimizing fuel consumption is first determined, and then the additive thrust angle for targeting the final position vector is determined by using Pontryagin's maximum principle. To establish real time processing, many algorithms of onboard guidance software are simplified. The explicit guidance algorithm is simulated on the 2nd-stage flight of the N-1 rocket developed in Japan. The results show that the explicit guidance algorithm works well in the presence of the maximum $\pm$10% initial velocity and altitude errors, and exhibits better performance than the open-loop program guidance. The effects of the guidance cycle time are also examined.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.36 no.9
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• pp.874-883
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• 2008

This study considers powered explicit guidance, one of the closed-loop guidance laws for satellite launch vehicles. The guidance algorithm employed here does not include the iterative procedure of the original algorithm. Also, the single-target algorithm to treat the general time-varying thrust profiles is described. The computer simulations for the 6-DOF launch vehicle model are performed to investigate the orbit injection accuracy of the guidance algorithm in the nominal/off-nominal flight conditions.

• Journal of Institute of Control, Robotics and Systems
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• v.7 no.2
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• pp.173-182
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• 2001

Ascent trajectory optimization and optimal explicit guidance problems for a satellite launch vehicle in a 2-dimensional pitch plane are studied. The trajectory optimization problem with boundary conditions is formulated as a nonlinear programming problem by parameterizing the pitch attitude control variable, and is solved by using the SQP algorithm. The flight constraints such as gravity-turn are imposed. An optimal explicit guidance algorithm in the exoatmospheric phase is also presented, the guidance algorithm provides steering command and time-to-go value directly using the current states of the vehicle and the desired orbit insertion conditions. To verify the optimality and accuracy of the algorithm simulations are performed.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.40 no.10
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• pp.853-861
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• 2012

This paper considers one of the explicit guidance algorithms, which has been proposed by Jaggers, to determine the closed-loop guidance algorithm for upper stages of a 3-staged space launch vehicle. Its commanded thrust vector is closer to the optimal solution when compared with that obtained by using the well-known Powered Explicit Guidance (PEG), which has been developed through the Space Shuttle program. Its performance is evaluated here by applying for guidance of the launcher during the second and third stages. Furthermore, to generate more precise guidance commands, it is attempted not to use the approximate formulas for the derivation of the original guidance law, and it is shown that performance is improved in comparison with the original.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10a
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• pp.419-424
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• 1991

In this paper, a fuel minimizing closed loop explicit inertial guidance algorithm for the orbit injection of a rocket is developed. In this formulation, the fuel burning rate and magnitude of thrust are assumed constant, and the motion of a rocket is assumed to be subject to the average inverse-square gravity, but with negligible atmospheric effects. The optimum thrust angle for obtaining the given velocity vector in the shortest time with minimizing fuel consumption is first determined, and then the additive thrust angle for targeting the final position vectors is determined by using Pontryagin's Maximum Principle. To establish the real time processing, many algorithms of the onboard guidance software are simplified. Simulations for the explicit guidance algorithm, for the 2nd-stage flight of the N-1 rocket, are carried out. The results show that the guidance algorithm works well in the presence of the maximum .+-.10 % initial velocity and altitude error. The effects of the guidance cycle time is also examined.

• Advances in aircraft and spacecraft science
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• v.9 no.5
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• pp.433-447
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• 2022

This work deals with an explicit guidance and control architecture for autonomous lunar ascent and orbit injection, i.e., the locally-flat near-optimal guidance, accompanied by nonlinear reduced-attitude control. This is a new explicit guidance scheme, based on the local projection of the position and velocity variables, in conjunction with the real-time solution of the associated minimum-time problem. A recently-introduced quaternion-based reduced-attitude control algorithm, which enjoys quasi-global stability properties, is employed to drive the longitudinal axis of the ascent vehicle toward the desired direction. Actuation, based on thrust vectoring, is modeled as well. Extensive Monte Carlo simulations prove the effectiveness of the guidance, control, and actuation architecture proposed in this study for precise lunar orbit insertion, in the presence of nonnominal flight conditions.

• Journal of Institute of Control, Robotics and Systems
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• v.8 no.7
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• pp.613-623
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• 2002

Ascent trajectory optimization and explicit guidance problems for a satellite launch vehicle with yaw maneuver in a 3-dimension are considered. The trajectory optimization problem with boundary conditions is formulated as a nonlinear programming problem by parameterizing the inertial pitch and yaw attitude control variables, and is solved by using the SQP algorithm. The flight constraints such as gravity-turn and range safety conditions are imposed. An explicit inertial guidance algorithm in the exoatmospheric phase is also presented. The guidance algorithm provides steering command and time-to-go value directly using the current states of the vehicle and the desired orbit insertion conditions. The liquid propelled Delta 2910 launch vehicle is used as a numerical model.

• Aerospace Engineering and Technology
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• v.11 no.1
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• pp.169-177
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• 2012

This paper considers the explicit guidance algorithm to determine the closed-loop guidance law applicable to upper stages of a given space launch vehicle. It has the advantage of very simple forms derived from the flat earth assumption, which is appropriate for its on-board application. However the simple time-to-go prediction equation produces the degraded guidance performance of the launcher because of its inaccuracy. To overcome the problem, the elaborate prediction equations, which have been employed in Saturn and H-II, are attempted here. Finally, the simulation results show that the simple guidance approach requires the more accurate time-to-go prediction and gravity integrals for its broad application.

• Aerospace Engineering and Technology
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• v.10 no.1
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• pp.89-97
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• 2011

This paper considers improved IGM (Iterative Guidance Mode), one of the explicit guidance algorithms, to determine the guidance algorithm for upper stages of a space launch vehicle. IGM, which has been employed successfully for the Saturn to put its payload into the parking orbit and lunar transfer orbit, is applied here for guidance of the launcher during the second and third stages. The orbit injection accuracy is evaluated through the 3-DOF computer simulations and an accurate prediction method, which can eliminate the prediction error of the downrange position at the orbit injection, is also proposed here.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.3
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• pp.327-364
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• 2015

In this paper, a generalized guidance law with an arbitrary pair of guidance coefficients for impact angle control is proposed. Under the assumptions of a stationary target and a lag-free missile with constant speed, necessary conditions for the guidance coefficients to satisfy the required terminal constraints are obtained by deriving an explicit closed-form solution. Moreover, optimality of the generalized impact-angle control guidance law is discussed. By solving an inverse optimal control problem for the guidance law, it is found that the generalized guidance law can minimize a certain quadratic performance index. Finally, analytic solutions of the generalized guidance law for a first-order lag system are investigated. By solving a third-order linear time-varying ordinary differential equation, the blowing-up phenomenon of the guidance loop as the missile approaches the target is mathematically proved. Moreover, it is found that terminal misses due to the system lag are expressed in terms of the guidance coefficients, homing geometry, and the ratio of time-to-go to system time constant.