Iterative Guidance Scheme for a Satellite Launch Vehicle along a Three-Dimensional Trajectory

The guidance laws are commonly designed to yield as small a miss distance as possible, harmonious with the missile’s acceleration capability. In recent decades, the concept of optimized guidance law is well understood in applications where information concerning the target range and line-of-sight angle is available. Researchers' efforts have been continually made to apply modern control theory to conventional and adaptive autopilot designs, even though the classical theory is still applicable to autopilots. It can be noted that it is desirable to perform a detailed computer-aided feasibility study within the context of a realistic missile-target engagement model. Development and evaluation of guidance and control laws for simplified missile-target engagement scenarios are extended and adapted to the air-to-air missile situation and implemented in a complete three-dimensional engagement model. Thus, this study proposed a computational method for constructing an optimal midcourse guidance law, which is based on the optimal control theory and initial boundary conditions. This proposed guidance law is derived from an optimal control theory with the boundary conditions such as allowed relative distance between missile and target at the final time, low line-of-sight rate. A numerical simulation verifies the performance of this guidance law with the impact of harmonic wind. The simulation results demonstrate that the quality of effectiveness as well as the applicability of this proposed algorithm.

Introduction: Aircrew equipment assemblies are life critical equipment worn by the aircrew to ensure protection from various life-threatening environmental conditions that may occur in nominal or off-nominal flight conditions. It is important for the sizing system of body worn aircrew equipment to be divided into different size classes such that it is as representative of existing groups in the population as feasible. Machine learning techniques provide a powerful tool to develop efficient sizing systems that are representative of actual body types existing in the population. The objective of the study was to use machine learning clustering techniques to identify naturally existing body types to formulate an optimal sizing system for an aircrew helmet. Material and Methods: The standard sizing schedule of an aircrew helmet using head length and head breadth was studied. An iterative semi-supervised machine learning protocol called K-means clustering was used to identify naturally occurring clusters of head types within the population. The cluster boundaries were identified to develop the final sizing schedule. Analysis of variance (ANOVA) with post hoc analysis was carried out on the four head lengths and head breadths. Results: Four clusters of head type were identified using K-means clustering. This led to a sizing schedule which can be descriptively called “Short-Narrow,” “Short-Broad,” “Long-Narrow,” “Long-Broad.” ANOVA showed a statistically significant difference between the four clusters for both head length and head breadth. Conclusion: Consideration of several variables in sizing schedules often fails to meet desired fitment. Standard sizing methods use linear partitions on individual control parameters. In reality, the proportional variation between parameters is not linear. Machine learning tools help in identification of naturally occurring clusters within the database considering several variables at the same time. This study uses machine learning techniques to identify existing groups in a population and develop a final sizing schedule. Similar analysis for other aircrew equipment assemblies can be carried out to determine sizing schedules which assist in design and fitment.

Optimal explicit guidance for three-dimensional launch trajectory

Adaptive Impact Time Control Via Look-Angle Shaping Under Varying Velocity

This paper presents a survey of the most recent literature developments in the field of computational guidance and control for space applications. In recent years, the space sector has changed significantly, shifting towards solutions requiring increased performance and autonomy. This change has also been accelerated by the technical and economic needs of the new space approach. However, traditional guidance and control techniques cannot always meet the increasing requirements of autonomy and performance. For this reason, computational guidance and control has become of increasing interest to the aerospace sector. In contrast to traditional guidance and control, computational guidance and control generates commands in real time by using on-board numerical computation. It represents, therefore, a fundamental step on the way to system autonomy and autonomous operations, with the potential to increase system capabilities and reduce operational costs. On-board computation introduces, however, a series of challenges, including the need to develop algorithms which are computationally efficient, reliable and robust. The literature has classified computational guidance and control techniques into two major categories, namely model-based and data-based. The model-based category encompasses all techniques in which the guidance and control laws are explicitly related to the system dynamic and kinematic models. On the contrary, data-based techniques infer guidance and control laws from a set of data, derived from the models, but do not explicitly use such models in the algorithm itself. Model-based guidance and control includes optimal control, model predictive control and convex optimisation. For the specific case of space attitude re-orientation manoeuvres, additional techniques are path planning and artificial potential functions. The general concept behind the Model Predictive Control (MPC) framework is to solve an optimal control problem repeatedly, for example whenever new measurements are available. The MPC implements only the first element of the returned solution, and the process is then repeated. By doing so, the system is better able to cope autonomously with model uncertainties, failures, or errors. For spacecraft with limited on-board capability, having to repeatedly solve an optimisation problem on-board could represent a challenge. In this case, explicit implementations of the MPC have been proposed, in which the guidance and control laws are precomputed offline and implemented on-board using look-up tables or simple functions. If the optimal control problem of the MPC is convex, or if it can be convexified, convex optimisation can be used directly. If the problem cannot be convexified, the solution can be found by sequentially solving a convex approximation of the original non-convex problem. Convex optimisation can be used either repeatedly in the context of an MPC framework, or as a single function call to generate guidance and control laws, e.g. at the beginning of an attitude re-orientation manoeuvre. Convex optimisation has received increased attention in recent years, also due to its suitability to on-board implementation. In fact, if the optimal control problem is convex, it can be solved reliably and efficiently on-board. Convex optimisation has been successfully applied to the space sector with the notable examples of the SpaceX rocket booster landing and of the Mars pinpoint landing demonstration aboard the Masten Xombie sounding rocket. Model-based guidance techniques, not based on optimisation, have been increasingly explored in recent years, as guidance strategies employed in other engineering fields, such as robotics, are being applied to spacecraft. Among these strategies, of particular importance are path planning and artificial potential field methods, due to their applicability to spacecraft autonomous attitude manoeuvres. Path planning algorithms have been applied for decades to ground vehicles and robotic manipulators. These algorithms consist of techniques to find the best route between two points of a graph representing the search space of a problem. For spacecraft re-orientation applications, the literature has proposed different attitude representation conventions and various cost functions associated to the graph search algorithm. Each approach comes with advantages and disadvantages, which will be analysed in the paper. Along with path planning, Artificial Potential Function (APF) techniques have been developed in the field of robotics, and are now also considered for space applications, to track or maintain a specific reference under a set of constraints. The main idea behind these methods is to synthetise the controller using a potential function. This function is specifically built to grant asymptotic stability to the system, according to Lyapunov’s second stability theorem. This formulation grants flexibility to accommodate system constraints, in a computationally light-weight and efficient manner. Data-based guidance and control laws are mainly based on Artificial Intelligence (AI) technologies, and generate guidance commands after training an algorithm with a large set of data. The interest of the space sector towards AI has accelerated in the last years due to the greater maturity of the technology. Some of the most powerful examples lie in the area of machine learning, like reinforcement learning, supervised learning and deep learning. These algorithms are used to extract patterns from large amounts of data derived from complex nonlinear dynamical and kinematical models. Examples of such data can be numerical solutions of an optimal control problem. The patterns extracted from the data allow the system to identify, in a short computational time, the critical parameters needed to relate the state and control variables. Creating a sufficiently large dataset for training the algorithm requires a considerable computational effort, though, and for certain methods optimality cannot be guaranteed due to the lack of theoretical support derived from the optimality conditions. Advancements made in the last years span several research directions and open a wide variety of opportunities and challenges, which need to be examined to guide further exploration. In this paper, both model-based and data-based techniques and applications are presented. The considered techniques include model predictive control, convex optimisation and machine learning. In addition, for the implementation of autonomous attitude manoeuvres, path planning methods and artificial potential function methods are analysed. These techniques have been applied, in the literature, to a range of different applications. The applications discussed in this paper include, in addition to attitude manoeuvres, powered descent landing guidance, low-thrust orbital transfers, proximity operations and station keeping.

Terminal guidance law against the maneuvering target is always the focal point. Most of the literatures focus on estimating the acceleration of target and time to go in guidance law, which are difficult to acquire. This paper presents a terminal guidance law based on receding horizon control strategy. The proposed guidance law adopts the basic framework of receding horizon control, and the guidance process is divided into several finite time horizons. Then, optimal control theory and target motion prediction model are used to derive guidance law for minimum time index function with continuous renewal of original conditions at the initial time of each horizon. Finally, guidance law performs repeated iteration until intercepting the target. The guidance law is of subprime optimal type, requiring less guidance information, and does not need to estimate the acceleration of target and time to go. Numerical simulation has verified that the proposed guidance law is more effective than traditional methods on constant and sinusoidal target with bounded acceleration.

Conventional proportional navigation or augmented proportional navigation guidance laws are widely used for intercepting maneuverable targets; however, they are effective only in intercepting a target with a constant velocity or a known acceleration. In this paper, a continuous second-order sliding mode guidance law is designed to intercept a highly maneuverable target in connection with the super-twisting algorithm. Meanwhile, the target maneuver information, regarded as unpredictable disturbance, is coped with by an extended state observer (ESO) and then is compensated in the guidance law. In the proposed guidance scheme, no information about target motion is needed. The closed-loop error can be guaranteed to be bounded by using Lyapunov method. The simulation results demonstrate the effectiveness and robustness of the proposed guidance method against a highly maneuverable target.

Optimal impact angle control guidance law and its variants for intercepting a maneuvering target are introduced in this paper. The linear quadratic(LQ) optimal control theory is reviewed first to setup framework of guidance law derivation, called the sweep method. As an example, the inversely weighted time-to-go energy optimal control problem to obtain the optimal impact angle control guidance law for a fixed target is solved via the sweep method. Since this optimal guidance law is not applicable for a moving target due to the angle mismatch at the impact instant, the law is modified to three different biased proportional navigation(PN) laws: the flight path angle control law, the line-of-sight(LOS) angle control law, and the relative flight path angle control law. Effectiveness of the guidance laws are verified via numerical simulations.

This paper gives an overview of guidance laws that can be applied for planar motion control purposes. Considered scenarios include target tracking, where only instantaneous information about the target motion is available, as well as path scenarios, where spatial information is available a priori. For target-tracking purposes, classical guidance laws from the missile literature are reviewed. These laws encompass guidance principles such as line of sight, pure pursuit, and constant bearing. For the path scenarios, enclosure-based and look-ahead-based guidance laws are presented. Considered paths include straight lines (zero curvature), circles (constant curvature), as well as general, regularly parameterized paths (variable curvature). Also, relations between the guidance laws are discussed, as well as interpretations toward saturated control.

A novel two-stage missile guidance law for impact time and angle control is proposed. This guidance law is derived based on the nonlinear engagement dynamics without using small angle assumption. In order to control both impact time and impact angle, a two-stage scheme is developed. This scheme is composed of a nonsingular sliding mode guidance law for the first stage and a switching target strategy for the second stage. The guidance law is switched from the first stage to the second stage when the switching condition is attained, which can ensure that the guidance law is switched at the right time to satisfy impact time constraint. The switching target strategy in the second stage can achieve impact angle control with high accuracy. Impact time and angle can be controlled simultaneously under this two-stage scheme. Numerical simulations are performed to demonstrate the performance of the proposed method.

This paper describes the results of an attempt to develop a modelling and simulation environment for the closed-loop dynamics of the NASA Intelligent Flight Control System F-15 aircraft. Emphasis was placed on the modelling of fault tolerance capabilities for the aircraft flight control system. Failures of the primary control surfaces are simulated for the most common failure scenarios, which are actuator blockage with and without a missing portion of the control surface. The controller featured in the flight control system has an optimal “feedforward and feedback” architecture to provide desirable handling qualities at nominal flight conditions while retaining good performance at post-failure conditions. The parameters within the control laws are updated using an online real-time parameter identification scheme based on the Fourier Transform Regression method. The desirable performance and utility of the entire scheme are illustrated through numerical simulations in the event of stabilator failure.

This paper proposes an optimal impact angle control guidance law for homing missiles with a narrow field-of-view of the seekers. As groundwork for designing a guidance law, we first present a general guidance structure that can achieve any terminal constraint of the line-of-sight rate based on the optimal control theory. We configure the desired profile of the line-of-sight rate using a saturation function whose exact form is determined to satisfy the required boundary conditions. By combining the line-of-sight rate profile with the optimal guidance structure, we develop a guidance law that achieves an impact angle interception with the field-of-view constraint. Herein, as the entire guidance structure is derived based on exact kinematics without any approximation, the proposed law ensures the accurate impact angle interception for various engagement scenarios. This precise consideration of the engagement kinematics also accurately ensures the energy optimality of preventing the excessive use of control inputs when homing. To evaluate the performance of the proposed method, numerical simulations with various engagement scenarios are conducted, and the results demonstrate that the proposed law allows missiles to accurately intercept their targets with the desired impact angles and without violating the prescribed field-of-view constraint.

In this paper, we study the differential game cooperative guidance law for multiple missiles to combat single intelligent targets in future air warfare. First, we derive the differential game guidance law between the single missile and the single target through optimal control theory. On the basis of this, we design the cooperative guidance law using the leader-followers framework, in which the differential game guidance law is applied to the leader. We design the cooperative guidance law of followers by using a kind of second-order nonlinear system. Finally, simulation result are shown to assert the potency of the designed guidance law.KeywordsDifferential gameCooperative guidance lawOptimal control theory

In this paper, a suboptimal guidance law with the terminal constraints on impact angle, acceleration, and time-derivative of acceleration (jerk) is presented. The proposed homing guidance problem is an over-determined problem, i.e., the number of constraints is much larger than the order of system. Since it is difficult to solve the problem by using the conventional optimal control theory, we newly introduce the control input which consists of an additional feed-forward command and the optimal feedback command. The additional feed-forward command is defined as a polynomial function of time-to-go with two degree-of-freedoms. Here, the coefficients of the function in the feed-forward command are determined to satisfy the constraints on terminal acceleration and jerk. The optimal feedback command in consideration of a feed-forward command is determined by Schwartz inequality. The guidance command obtained from the proposed scheme shows a similar form of the biased proportional navigation (BPN) guidance obtained by the optimal control theory. However, the proposed guidance law is less sensitive to the time-to-go estimation error than the BPN law, and it can be easily implemented in the real system. Furthermore, since the coefficients of time-to-go in the feed-forward command remain as design parameters, the proposed guidance law provides more flexibility in application aspect such as trajectory shaping. The characteristics of the proposed guidance law is studied and its performance is also evaluated through numerical simulation.

Guidance and control law design for missiles traveling at hypersonic speeds is an extremely difficult task due to the inherently coupled nonlinear nature of the system dynamics. The controller designs are further complicated by model uncertainty and unmodeled disturbances, which are inevitable in practical application. Beyond the challenges inherent in the system dynamics, additional complications arise in the design of hypersonic missile control laws, where terminal constraints are imposed in order to optimize target penetration. In this research, a robust nonlinear control technique is combined with an optimal control method to develop a control law for air-breathing hypersonic missiles in the presence of model uncertainty and unmodeled, nonlinear exogenous disturbances. The control law presented in this paper is designed to be computationally inexpensive, requiring no observers, online adaptive laws, or function approximators. One of the contributions of this research is detailed theoretical analysis of the performance characteristics of the proposed tracking control design. In addition, maximum target penetration is achieved by generating an optimal desired trajectory that incorporates terminal constraints in the cost function. Specifically, the trajectory optimization routine is designed to minimize angle of attack (AoA) and inertial angle of obliquity (AoO) at impact. A Lyapunov-based stability analysis is utilized to prove global asymptotic trajectory tracking, and high-fidelity numerical simulation results are provided to verify the practical performance of the proposed guidance law design.