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The purpose of this paper is to study the closed-loop guidance algorithm for launch vehicles in an atmospheric ascent phase and present a numerical trajectory reconstruction algorithm to satisfy the real-time requirement of generating the guidance commands.

An optimal control model for an atmospheric ascent guidance system is established directly; following that, the detailed process for necessary conditions of the optimal control problem is re-derived based on the calculus of variations. As a result, the trajectory optimization problem can be reduced to a root-finding problem of algebraic equations based on the finite element method (FEM). To obtain an accurate solution, the Newton method is introduced to solve the roots in a guidance update cycle.

The presented approach can accurately and efficiently solve the trajectory optimization problems. A moderate number of unknowns can yield a good optimal solution, which is well suited for the open-loop guidance. To meet the requirements of the rapidity and accuracy for the close-loop guidance, the fewer number of unknowns is artificially chosen to reduce the calculation time, and the on-board trajectory planning strategy can increase the precision of the optimal solution along with the decrease of time-to-go.

The closed-loop guidance algorithm based on an FEM can be found in this paper, which can solve the optimal ascent guidance problems for launch vehicles in the atmospheric flight phase rapidly, accurately and efficiently.

This paper re-derives the necessary conditions of the optimal solution in a different way compared to the previous work, and the closed-loop guidance algorithm combined with the FEM is also a new thought for the optimal atmospheric ascent guidance problems.

The purpose of this paper is to devise a new approach to synthesize closed‐loop feedback guidance law for online thrust‐insensitive optimal trajectory generation utilizing neural networks.

The proposed methodology utilizes an open‐loop variational formulation that initially determines optimal launch/ascent trajectories for various scenarios of known uncertainties in the thrust profile of typical solid propellant engines. These open‐loop optimized trajectories will then provide the knowledge base needed for the subsequent training of a neural network. The trained network could eventually produce thrust‐insensitive closed‐loop optimal guidance laws and trajectories in flight.

The proposed neuro‐optimal guidance scheme is effective for online closed‐loop optimal path planning through some measurable and computable engine and flight parameters.

Determination of closed‐loop optimal guidance law for non‐linear dynamic systems with uncertainties in system and environment has been a challenge for researchers and engineers for many years. The problem of steering a solid propellant driven vehicle is one of these challenges. Even though a few researchers have worked in the area of non‐linear optimal control and thrust‐insensitive guidance, this paper proposes a new strategy for the determination of closed‐loop online thrust insensitive guidance laws leading to optimal flight trajectories for solid propellant launch and ascent vehicles.

To devise a new technique to synthesise optimal feedback control law for non‐linear dynamic systems through fuzzy logic.

The proposed methodology utilizes the open‐loop optimal control solutions (OCSs) of the non‐linear systems for the training of the fuzzy system in the process of developing closed‐loop fuzzy logic guidance (FLG). This is achieved through defining a set of non‐dimensionalised variables related to the system states.

FLG is capable of generating closed‐loop control law for the non‐linear problem investigated. Since the proposed fuzzy structure is independent of the system equations, the approach is potentially applicable to other non‐linear system. Introduction of the non‐dimensional variables in place of the regular states has effectively increased the fuzzy training performance and greatly reduced the number of fuzzy rule bases required to produce accurate solutions for other untrained scenarios.

There exist many complex non‐linear problems in guidance and control of aerospace vehicles. Determination of optimal control laws for such systems is usually a difficult task even in an open‐loop form and in a noise‐free off‐line environment. On the other hand, closed‐loop OCSs are highly desirable for their robust characteristics in actual operating environments, so are more suitable for online applications, but can seldom be realized for complex non‐linear systems. Even though a few researchers have worked in the area of non‐linear optimal control and application of fuzzy logic on such systems, non‐have dealt with closed‐loop optimal fuzzy controllers. This research proposes a new strategy for the determination of optimal feedback control laws for non‐linear systems, which can be utilized in many spacecraft mission applications.

The purpose of this paper is to propose a hybrid optimization approach with high level of solving precision and efficiency for endo-atmospheric ascent trajectory planning of launch vehicles.

Based on the indirect method of optimal control problems, the optimal endo-atmospheric ascent problem with path constraints and final condition constraints is transformed into a Hamiltonian two point boundary value problem (TPBVP). An advanced Gauss pseudo-spectral method is applied to change the Hamiltonian TPBVP into a system of nonlinear algebraic equations, which is solved by a modified Newton method. To guarantee the convergence of the solution, analytical initial guess technology and homotopy technology are also introduced. At last, simulation tests are made.

The hybrid approach for optimal endo-atmospheric ascent trajectory planning has both fast convergence rate and high solution precision. The simulation results indicate that not only the proposed method is feasible but also it is better than the indirect method, which is a most popular approach for solving the optimal endo-atmospheric ascent problem. Given the same degree of solution accuracy, the new method consumes quite less time on the CPU than that of the indirect method.

The new optimization approach has high level of both solution accuracy and efficiency. It can be used in rapid trajectory designing, on-line trajectory planning and closed-loop guidance of launch vehicles. Also, the proposed Gauss pseudo-spectral method in this paper is a new and efficient method for solving general TPBVPs.

The paper provides a new hybrid optimization method for rapid endo-atmospheric ascent trajectory planning of launch vehicles.

The purpose of this paper is to present fusion of inertial navigation system (INS) and global positioning system (GPS) for estimating position, velocities, attitude and heading of an unmanned aerial vehicle (UAV).

A 15-state extended Kalman filter (EKF) and a split architecture consisting of six-state nonlinear complementary filter (NCF) and nine-state EKF are investigated in detail. In both these fusion architectures GPS and inertial measurement unit consisting of three axis accelerometers, three axis rate gyros and three axis magnetometer have been fused in open loop fashion (loosely coupled) to estimate the navigation states.

These architectures have been implemented in MATLAB/SIMULINK environment and evaluated in closed loop guidance of Black-Kite MAV with software-in-the-loop-simulation (SILS) setup. Furthermore, both the algorithms are validated with flight test data obtained from on-board data logger using an off-the shelf autopilot board (Ardupilot Mega APM-2.5) on SLYBIRD UAV.

The proposed architectures are of high value to accomplish INS/GPS fusion, which plays a vital role in autonomous guidance and navigation of an UAV.

The purpose of this paper is to propose a new guidance algorithm for launching a satellite using an expendable rocket from an equatorial site to an equatorial low‐Earth orbit.

Guidance during endoatmospheric portion is based on a nominal trajectory computed prior to take‐off. A set of updating computations begins anew at the time instant t_g of transition from endoatmosphere to exoatmosphere. The updating computations determine a guidance trajectory and an associated control law for the remainder of path by taking into account the rocket state at time t_g. Thus, the overall guidance involves both initial and midcourse operations, and it has both open‐ and closed‐loop aspects.

Viability and performance in terms of speed, precision, and effectiveness of the proposed scheme is demonstrated through three‐dimensional simulations and comparisons to other methods.

The updating computations and the fashion in which they are incorporated into the entire guidance process constitute the novel features of the proposed algorithm.

The purpose of this paper is to develop a novel solution for the predicted error and introduces a systematic method to develop optimal and explicit guidance strategies for different missions.

The predicted error is derived from its basic definition through analytical dynamics. The relations are developed for two classes of systems. First, for systems in which the acceleration commands are truncated at a specified time. Second, for systems in which the corrective maneuvers are cut off at a specified time. The predicted error differential equation is obtained in a way that allows for derivation of several optimal and explicit guidance schemes.

The effect of tangential acceleration in conjunction with autopilot dynamics can be realized in guidance gain and the predicted error. The differential equation of velocity‐to‐be‐gained is obtained assuming the gravitational acceleration to be given as a vectorial function of time. The relations for different velocity profiles are obtained and discussed including the effective navigation ratio.

The guidance/control system is modeled as a linear time‐varying dynamic and of arbitrary‐order. The gravitational acceleration is assumed as a given vectorial function of time.

The presented schemes are applicable to both midcourse and terminal guidance laws with/without velocity constraints.

Providing a new analytical solution of predicted errors with final position and velocity constraints and their differential equations considering the thrust/drag acceleration and autopilot dynamics in the presence of gravity.

This paper aims to develop a novel trajectory optimization algorithm which is capable of producing high accuracy optimal solution with superior computational efficiency for the hypersonic entry problem.

A two-stage trajectory optimization framework is constructed by combining a convex-optimization-based algorithm and the pseudospectral-nonlinear programming (NLP) method. With a warm-start strategy, the initial-guess-sensitive issue of the general NLP method is significantly alleviated, and an accurate optimal solution can be obtained rapidly. Specifically, a successive convexification algorithm is developed, and it serves as an initial trajectory generator in the first stage. This algorithm is initial-guess-insensitive and efficient. However, approximation error would be brought by the convexification procedure as the hypersonic entry problem is highly nonlinear. Then, the classic pseudospectral-NLP solver is adopted in the second stage to obtain an accurate solution. Provided with high-quality initial guesses, the NLP solver would converge efficiently.

Numerical experiments show that the overall computation time of the two-stage algorithm is much less than that of the single pseudospectral-NLP algorithm; meanwhile, the solution accuracy is satisfactory.

Due to its high computational efficiency and solution accuracy, the algorithm developed in this paper provides an option for rapid trajectory designing, and it has the potential to evolve into an online algorithm.

The paper provides a novel strategy for rapid hypersonic entry trajectory optimization applications.