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About this book

This book presents a comprehensive overview of the recent advances in the domain of optimal guidance, exploring the characteristics of various optimal guidance algorithms and their pros and cons. Optimal guidance is based on the concept of trajectory optimization, which minimizes the meaningful performance index while satisfying certain terminal constraints, and by properly designing the cost function the guidance command can serve as a desired pattern for a variety of mission objectives. The book allows readers to gain a deeper understanding of how optimal guidance law can be utilized to achieve different mission objectives for missiles and UAVs, and also explores the physical meaning and working principle of different new optimal guidance laws. In practice, this information is important in ensuring confidence in the performance and reliability of the guidance law when implementing it in a real-world system, especially in aerospace engineering where reliability is the first priority.

Table of Contents

Frontmatter

Chapter 1. Introduction of Optimal Guidance

Abstract
Guidance is one of the key parts of modern aerospace vehicles since it enables improved autonomy by guiding the vehicle to approach a specific stationary/dynamic position. Optimal control theory is known as a valuable and systematic tool in the design and development of guidance algorithms. We explore the characteristics of classical proportional navigation guidance and present the motivation of the development of new optimal guidance laws in this chapter. The overall aim of this book is then summarized and the organization of the entire book, together with some highlights of each chapter, are presented.
Shaoming He, Chang-Hun Lee, Hyo-Sang Shin, Antonios Tsourdos

Optimal Guidance in Missile Applications

Frontmatter

Chapter 2. Optimal Error Dynamics in Missile Guidance

Abstract
This chapter investigates the optimal convergence pattern of the tracking error that frequently appears in missile guidance problems and proposes an optimal error dynamics for guidance law design to achieve various operational objectives. The proposed optimal error dynamics is derived by solving a linear quadratic optimal control problem through Schwarz’s inequality approach. The properties of the proposed optimal error dynamics are discussed. The significant contribution of the proposed result lies in that it can provide a link between existing nonlinear guidance laws and optimal guidance laws for missile systems. Therefore, the advantages of both techniques can be fully exploited by using the proposed approach: existing nonlinear guidance laws can be converted to their optimal forms and the physical meaning of them can then be easily explained. Four illustration examples, including zero zero-effort-miss (ZEM) guidance, impact angle guidance, impact time control, impact angle control as well as impact angle and impact time control, are provided to show how the proposed results can be applied to missile guidance law design. The performance of the new guidance laws is demonstrated by numerical simulation.
Shaoming He, Chang-Hun Lee, Hyo-Sang Shin, Antonios Tsourdos

Chapter 3. Optimal Trajectory Shaping Guidance Law with Seeker’s Field-of-View Constraint

Abstract
This chapter proposes a new trajectory shaping guidance law for impact time control and impact angle control with seeker’s field-of-view (FOV) limit. The proposed guidance law is derived by using the concept of biased PNG (BPNG). The guidance law developed leverages a nonlinear function to ensure the boundedness of velocity lead angle to cater for seeker’s FOV constraint. The finite-time convergence of the impact time error and impact angle error is theoretically analyzed. By investigating the optimality of the biased command, the physical meaning of the proposed trajectory shaping guidance law is revealed to support practical applications. Numerical simulations clearly demonstrate the effectiveness of the proposed formulation.
Shaoming He, Chang-Hun Lee, Hyo-Sang Shin, Antonios Tsourdos

Chapter 4. Linear Observability-Enhancement Optimal Guidance Law

Abstract
This chapter proposes a new optimal guidance law to enhance target observability for passive guidance with bearing-only measurement. A performance index that considers terminal miss distance, control effort and target observability criterion in an integrated manner is proposed first. The proposed guidance law is then derived analytically by solving the optimization problem formulated. Under certain conditions, it is proved that the guidance law developed gradually switches from retro PNG to classical PNG as time goes. The closed-form solutions of ZEM and guidance command are also derived to provide better insights of the proposed guidance law. Nonlinear numerical simulations are conducted to support the analytical findings.
Shaoming He, Chang-Hun Lee, Hyo-Sang Shin, Antonios Tsourdos

Chapter 5. Optimal Proportional-Integral Guidance Law

Abstract
This chapter proposes a new optimal guidance law based on PI concept to reduce the sensitivity to unknown target maneuvers. By augmenting the integral ZEM as a new system state, a linear quadratic optimization problem is formulated and then the proposed guidance law is analytically derived through optimal control theory. The closed-form solution of the proposed guidance law is presented to provide better insight of its properties. Additionally, the working principle of the integral command is investigated to show why the proposed guidance law can be utilized to reduce the sensitivity to unknown target maneuvers. The analytical results reveal that the proposed optimal guidance law is exactly the same as an instantaneous direct model reference adaptive guidance law with a specified reference model. The potential significance of the obtained results is that it can provide a point of connection between PI guidance laws and adaptive guidance laws. Therefore, it allows us to have better understanding of the physical meaning of both guidance laws and provides the possibility in designing a new guidance law that takes advantages of both approaches. Finally, the performance of the guidance law developed is demonstrated by nonlinear numerical simulations with extensive comparisons.
Shaoming He, Chang-Hun Lee, Hyo-Sang Shin, Antonios Tsourdos

Chapter 6. Gravity-Turn-Assisted Optimal Guidance Law

Abstract
This chapter proposes a new optimal guidance law that directly utilizes, instead of compensating, the gravity for accelerating missiles. The desired collision triangle that considers both gravity and vehicle’s axial acceleration is analytically derived based on geometric conditions. The concept of instantaneous zero-effort-miss is introduced to allow for analytical guidance command derivation. The proposed optimal guidance law is derived by using the optimal error dynamics proposed in Chap. 2. The relationships of the proposed formulation with conventional PNG and guidance-to-collision (G2C) are analyzed and the results show that the proposed guidance law encompasses previously suggested approaches. The significant contribution of the proposed guidance law lies in that it ensures zero final guidance command and enables energy saving with the aid of utilizing gravity turn. Nonlinear numerical simulations clearly demonstrate the effectiveness of the proposed approach.
Shaoming He, Chang-Hun Lee, Hyo-Sang Shin, Antonios Tsourdos

Chapter 7. Gravity-Turn-Assisted Optimal Intercept Angle Guidance Law

Abstract
This chapter develops a new optimal gravity-turn-assisted intercept angle guidance law for an exo-atmospheric interceptor. The analytical guidance command is derived as a solution of a finite-time optimal regulation problem by using the Lagrange multiplier approach. The convergence of the instantaneous ZEM and intercept angle error is theoretically analyzed based on the instantaneous linear time-invariant system concept. We also reveal that existing optimal impact angle constrained guidance laws are the special cases of the proposed formulation. Numerical simulations with some comparisons clearly demonstrate the effectiveness of the proposed guidance law.
Shaoming He, Chang-Hun Lee, Hyo-Sang Shin, Antonios Tsourdos

Optimal Guidance in UAV Applications

Frontmatter

Chapter 8. Minimum-Effort Waypoint-Following Guidance Law

Abstract
This chapter addresses the problem of minimum-effort waypoint-following guidance with/without arrival angle constraints of a UAV. By utilizing a linearized kinematics model, the proposed guidance laws are derived as the solutions of a linear quadratic optimal control problem with an arbitrary number of terminal boundary constraints. Theoretical analysis reveals that both optimal proportional navigation guidance and trajectory shaping guidance are special cases of the proposed guidance laws. The key feature of the proposed algorithms lies in their generic property. For this reason, the guidance laws developed can be applied to general waypoint-following missions with an arbitrary number of waypoints and an arbitrary number of arrival angle constraints. Nonlinear numerical simulations clearly demonstrate the effectiveness of the proposed formulations.
Shaoming He, Chang-Hun Lee, Hyo-Sang Shin, Antonios Tsourdos

Chapter 9. Energy-Optimal Waypoint-Following Guidance Law Considering Autopilot Dynamics

Abstract
This chapter addresses the problem of energy-optimal waypoint-following guidance for a UAV with the consideration of a general autopilot dynamics model. The proposed guidance law is derived as a solution of a linear quadratic optimal control problem in conjunction with a linearized kinematics model. The algorithm developed integrates path planning and following into a single step and is able to be applied to a general waypoint-following mission. Theoretical analysis reveals that previously suggested optimal point-to-point guidance laws are special cases of the proposed approach. Nonlinear numerical simulations clearly demonstrate the effectiveness of the proposed formulations.
Shaoming He, Chang-Hun Lee, Hyo-Sang Shin, Antonios Tsourdos

Chapter 10. Optimal Integrated Waypoint Following and Obstacle Avoidance Guidance Law

Abstract
This chapter addresses the problem of energy-optimal waypoint-following guidance for an UAV with the consideration of arbitrary number of obstacles. The proposed guidance law is derived as a solution of a linear quadratic optimal control problem in conjunction with convex parameter optimization. The algorithm developed integrates path following and obstacle avoidance into a single step and is able to be applied to a general waypoint-following mission. Several particular cases of the proposed guidance law are presented to provide better insights of the proposed algorithm. Nonlinear numerical simulations clearly demonstrate the effectiveness of the proposed formulations.
Shaoming He, Chang-Hun Lee, Hyo-Sang Shin, Antonios Tsourdos
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