Three-dimensional Guidance Law Research Articles

Three-Dimensional Guidance Laws for Spacecraft Propelled by a SWIFT Propulsion System

This paper discusses the optimal control law, in a three-dimensional (3D) heliocentric orbit transfer, of a spacecraft whose primary propulsion system is a Solar Wind Ion Focusing Thruster (SWIFT). A SWIFT is an interesting concept of a propellantless thruster, proposed ten years ago by Gemmer and Mazzoleni, which deflects, collects, and accelerates the charged particles of solar wind to generate thrust in the interplanetary space. To this end, the SWIFT uses a large conical structure made of thin metallic wires, which is positively charged with the aid of an electron gun. In this sense, a SWIFT can be considered as a sort of evolution of the Janhunen’s E-Sail, which also uses a (nominally flat) mesh of electrically charged tethers to deflect the solar wind stream. In the recent literature, the optimal performance of a SWIFT-based vehicle has been studied by assuming a coplanar orbit transfer and a two-dimensional scenario. The mathematical model proposed in this paper extends that result by discussing the optimal guidance laws in the general context of a 3D heliocentric transfer. In this regard, a number of different forms of the spacecraft state vectors are considered. The validity of the obtained optimal control law is tested in a simplified Earth–Venus and Earth–Mars transfer by comparing the simulation results with the literature data in terms of minimum flight time.

Adaptive Distributed Fixed-Time Cooperative Three-Dimensional Guidance Law for Multimissiles against Manoeuvring Target

The problem of cooperative interception of the manoeuvring target is investigated in this paper. Firstly, in light of fast fixed-time consensus theory, time-to-go, and undirected topologies, adaptive cooperative guidance along the line-of-sight (LOS) direction is proposed to guarantee impact time synchronization. Next, novel nonsingular terminal sliding mode (NTSM) is designed to establish adaptive fixed-time guidance law for steering LOS angular rates to the origin or its small neighbourhood. Without the knowledge of target manoeuvre, the proposed cooperative guidance law can be provided by lateral and longitudinal accelerations of each missile, while more reasonable and rigorous analysis of fixed-time stability is carried out through the Lyapunov theory. Within the specified time, both control tasks of simultaneous attack and the desired impact angles can be completed before the final time of the guidance process. Finally, numerical simulations demonstrate the feasibility and effectiveness of the proposed scheme.

Observer-based robust impact angle control three-dimensional guidance laws with autopilot lag

Considering an air-based missile intercepting maneuvering target with desired impact angles, robust guidance laws with autopilot lag in three-dimensional coupling space are presented in this paper. First, combining the fixed-time stability theory and adaptive sliding mode control technique, a novel dual-layer adaptive fixed-time sliding mode disturbance observer is proposed to estimate the unknown target maneuver. The proposed disturbance observer releases the requirement of information on either the target maneuver or its derivative. To achieve interception with the desired impact angles, a novel guidance law based on the nonsingular terminal sliding mode (NTSM) with an exponent coefficient is provided. The proposed control framework prevents singular problems and ensures the fixed-time stability of the guidance system. In addition, autopilot dynamics are taken into consideration, and the dynamics surface control (DSC) method is used to address the nonlinear static feedback system. Meanwhile, the improved fixed-time differentiator is used to acquire the derivative of virtual control laws. This prevents the inherent “differential explosion” of the backstepping technique. The uniform boundedness of the closed-loop system is demonstrated via the Lyapunov method. Finally, numerous numerical simulations are carried out, and the simulation results verify the effectiveness of the proposed guidance laws.

Optimal guidance for hypersonic vehicle using analytical solutions and an intelligent reversal strategy

This paper presents a novel three-dimensional guidance law to quickly generate optimal commands in the gliding phase. Owing to the complicated trajectory constraints and highly uncertain disturbances, the novel gliding profile is developed for the longitudinal plane. Subsequently, this longitudinal profile is utilized to obtain analytical equations of motion for performance index and path constraints prediction. Moreover, stringent terminal constraints, which comprise the altitude, the flight path angle, and the position of transition from gliding phase to terminal diving phase, are integrated into the longitudinal profile. The proposed analytical expressions simplify the onboard generation of optimal gliding trajectory as it does not involve complicated nonlinear programming problems. In addition, to regulate the terminal velocity onboard and simultaneously eliminate the heading error, two bank-reversal opportunities are used in the lateral profile and determined using a reinforcement learning algorithm. In the proposed guidance law, the terminal deviations are first predicted in real-time using the analytical expressions; and then the three-dimensional trajectory is regenerated by addressing a simple optimization problem and planning bank-reversal positions. The computation of the guidance law is facilitated using analytical solutions and a reinforcement learning method; therefore, the frequency of replanning facilitates the robustness, accuracy, and optimality. We evaluated the effectiveness of our method using some representative scenarios.

Three-dimensional cooperative guidance law for multiple missile based on sliding mode control

Based on the missile-target three-dimensional relative motion model, a multi-missile coordinated three-dimensional guidance law with attack time constraints is designed for attacking stationary targets. The sliding mode variable structure control is adopted in the pitch channel, and the dynamic inverse control is adopted in the yaw channel. By maneuvering in the yaw channel, adjusting the missile's attack time and comparing with the results of using augmented proportional guidance, the simulation results show that the algorithm designed in this article can achieve coordinated attack and high hitting accuracy, which verifies the correctness and superiority of the algorithm.

A Novel Fixed-Time Convergence Three-Dimensional Guidance Law for Intercepting Highly Maneuvering Targets

A Novel Fixed-Time Convergence Three-Dimensional Guidance Law for Intercepting Highly Maneuvering Targets

Three-Dimensional Impact Time Control Guidance Considering Field-of-View Constraint and Velocity Variation

The problem of three-dimensional impact time control guidance considering field-of-view constraints and time-varying velocity is investigated in this study. First, considering the effect of gravity and aerodynamic forces on velocity, a simplified numerical estimation algorithm of flight time with a three-dimensional proportional navigation guidance law is derived. Then, based on the structure of the biased proportional navigation guidance law, the effect of the biased term on flight time is analyzed. The biased term is then designed to achieve impact time and field-of-view constraints considering time-varying velocity. Finally, numerical simulations are performed to demonstrate the effectiveness and superiority of the proposed guidance law.

Unified Method for Field-of-View-Limited Homing Guidance

Homing guidance requires maintaining the target lock-on condition within the seeker’s field of view (FOV). This paper aims at developing a unified FOV-limited guidance framework from which a variety of two-dimensional (2D) and three-dimensional (3D) guidance laws can be derived. First, the unified method for 2D homing guidance is established by augmenting an arbitrary baseline guidance law with a biased command. To mitigate the effect on the baseline guidance law, this biased command is designed in the admissible range that respects the FOV limit and only takes effect when the lead angle approaches the FOV bound. For more practical relevance, the autopilot dynamic of any order is further considered explicitly in the design with a recursive approach. Then, the unified method for 3D homing guidance with coupling nonlinearity is developed by exploiting the geometric relation among space angles. Unlike existing similar results, the proposed design requires neither switch logic nor numerical algorithms, which allows for continuous guidance command and convenient implementation. With the proposed method, various illustrative guidance laws are derived to demonstrate the significance of the unified framework. Finally, numerical simulations with comparative study are conducted to support the analytical findings and show the superiority of the proposed method.

A nonlinear disturbance observer-based adaptive integral sliding mode control for missile guidance system

A novel composite three-dimensional (3D) guidance law based on an adaptive integral sliding mode (AISM) control utilizing a nonlinear disturbance observer (NDOB) technique is proposed for missiles. First, an integral sliding mode control is selected as the guidance law to get rid of the reaching phase of sliding mode control. Second, the switching gains are adjusted by designing an adaptive law. Finally, the NDOB is designed to estimate and compensate for the unknown target accelerations that are considered as the disturbance. Thus the NDOB and AISM law are combined into a novel composite guidance law to improve performance and to reduce the chattering phenomenon. Finally, to verify the effectiveness and robustness, numerical simulations are performed in different scenarios and these results are presented comparatively with the augmented proportional navigation (APN) and the AISM guidance law. Moreover, the proposed law outperforms the other schemes regarding the miss distance and interception time.

Adaptive Fast Fixed-Time Three-Dimensional Guidance Law With Acceleration Saturation Constraints

This paper investigates continuous anti-saturation three-dimensional guidance law against maneuvering target at the desired line-of-sight (LOS) angles. Firstly, in the light of fixed-time stability, fast nonsingular terminal sliding mode is designed without the limitation of odd-ratio fractional order. Then, with the limits of lateral acceleration saturation, continuous guidance law is proposed to guarantee that desired LOS angles are reached and maintained after the specified time, while adaptive law is implemented to estimate the information on maneuver accelerations of the attacking missile. Finally, numerical simulations are presented to validate the effectiveness and rationality of the designed scheme.

Three-Dimensional Optimal Guidance with Lyapunov Redesign for UAV Interception

Three-dimensional guidance laws are designed to intercept non-maneuvering targets and maneuvering targets in this paper. An optimal control approach with constant or time-variant feedback gain is proposed for interception. The cost function is designed with considerations on energy-efficiency and time-efficiency in the transient process. Lyapunov redesign method is applied to treat the target acceleration, where the precise information of target accelerations is not necessarily required. Efficacy of the proposed guidance laws is proved theoretically and verified by simulation results.

Terminal Impact Time Control Cooperative Guidance Law for UAVs under Time-Varying Velocity

Aiming at the problem that multiple Unmanned Aerial Vehicles (UAVs) attack the stationary target cooperatively under time-varying velocity, the cooperative guidance law with finite time convergence on two-dimensional plan and the three-dimensional cooperative guidance laws with impact time constraint are designed separately in this paper. Firstly, based on the relative motion equation between UAV and target on two-dimensional plane, the time cooperative guidance model of multiple UAVs is established. Then based on the consistency theory and graph theory, a distributed time cooperative guidance law is designed, which can ensure that the impact time of all UAVs can be quickly consistent in a limited time. Next, the cooperative guidance problem is expanded from two-dimensional plane to three-dimensional space, the motion model between UAV and target in three-dimensional space is established and the expression of time-to-go estimation under time-varying velocity is derived. Finally, according to whether there is the communication among UAVs under the condition of time-varying velocity, a multiple UAVs three-dimensional cooperative guidance law based on desired impact time and a multiple UAVs three-dimensional cooperative guidance law based on coordination variables are designed, respectively. The simulation results show that the cooperative guidance law with finite time convergence on two-dimensional plan and the three-dimensional cooperative guidance law with impact time constraint proposed in this paper are effective, which can both realize the saturation attack under the time-varying velocity.

Sensor-Based Robust Incremental Three-Dimensional Guidance Law with Terminal Angle Constraint

In this work, a robust incremental three-dimensional (3D) guidance law is proposed considering terminal angle constraint against maneuvering targets. As a stepping stone, the line-of-sight (LOS) tracking error dynamics is employed for the 3D guidance law design. A sliding variable is constructed such that its first-order derivative excludes the relative range in the perturbation, which avoids the unboundedness of system perturbation induced by target maneuvers near collision. A time-varying version of the sliding variable is designed to accelerate convergence of the LOS tracking errors and avoid large initial sliding variables. Then, two guidance laws are derived as a benchmark via the nonlinear dynamic inversion (NDI)-based sliding mode control (NDI-SMC) and NDI-based time-varying sliding mode control (NDI-TVSMC), respectively. To further improve guidance robustness with reduced system perturbation, the sensor-based incremental nonlinear dynamic inversion (INDI) control is used to design the INDI-SMC-based and INDI-TVSMC-based guidance laws. The sensor-based guidance laws exploit the LOS angular acceleration and guidance command output at the latest step, which result in smaller guidance gains to reject the perturbation than the NDI guidance laws. Numerical simulations in various cases and comparison studies are conducted to verify the effectiveness and robustness of the proposed method.

Measurement Compensation for Time-Delay Seeker and Three-Dimensional Adaptive Guidance Law Design.

The time delay of seekers has grown to be a serious issue for tactical missile guidance with the development of flight vehicle technologies. To address the problem, a measurement compensation system for the seeker, with lags and delays based on predictive active disturbance rejection control, is proposed. In addition, to eliminate the effects of target maneuvers to the tactical missile guidance, an adaptive finite-time convergent sliding mode guidance law, based on super-twisting algorithm, is proposed in three-dimensional missile-target engagement kinematics. Specifically, the compensation system consists of a predictive tracking structure and an active disturbance rejection control system, which could follow a virtual measurement without lags and delays. The compensation system has advantages in disturbance rejection and model inaccuracy addressing, compared with existing compensation methods for seeker measurement. As for the sliding mode guidance law design, the proposed approach is based on an improved super-twisting algorithm with fast convergent adaptive gains, which has advantages in addressing unknown but bounded target maneuvers and avoiding chattering of the classical sliding mode control. As a result, the measurement compensation system and the adaptive sliding mode guidance law is verified robust and effective under the proposed constraints by the simulation examples.

Three-dimensional cooperative interception guidance law with impact time constraint

This article proposes a new terminal cooperative guidance law with impact time constraint in three-dimensional (3D) engagement. Two parts are comprised by this guidance scheme to control the impact time and fulfill the interception. The guidance law along the line-of-sight (LOS) direction is first designed based on finite time consensus protocol to share time-to-go values among missiles and reach the consensus. Meanwhile, the guidance law on the LOS normal direction is developed based on the fast finite time control method to achieve the interception. The stability analysis of the proposed guidance law based on the Lyapunov theory is also demonstrated in detail. Moreover, the maneuvering target can be intercepted successfully under the presented control algorithm, and the guidance system can fulfill stability within finite time. Additionally, the effectiveness and applicability of the proposed guidance scheme are explicitly verified through simulation tests.

Fixed-time three-dimensional guidance law with input constraint and actuator faults

This paper investigates the three-dimensional guidance with the impact angle constraint, actuator faults and input constraint. Firstly, an adaptive three-dimensional guidance law with impact angle constraint is designed by using the terminal sliding mode control and nonhomogeneous disturbance observer. Then, in order to solve the problem of the input saturation and actuator faults, an adaptive anti-saturation fault-tolerant three-dimensional law is proposed by using the hyperbolic tangent function based on the passive fault-tolerant control. Finally, the effectiveness of the designed guidance laws is verified by using the Lyapunov function and simulation.

Multiconstraint adaptive three-dimensional guidance law using convex optimization

The traditional guidance law only guarantees the accuracy of attacking a target. However, the look angle and acceleration constraints are indispensable in applications. A new adaptive three-dimensional proportional navigation (PN) guidance law is proposed based on convex optimization. Decomposition of the three-dimensional space is carried out to establish three-dimensional kinematic engagements. The constraints and the performance index are disposed by using the convex optimization method. PN guidance gains can be obtained by solving the optimization problem. This solution is more rapid and programmatic than the traditional method and provides a foundation for future online guidance methods, which is of great value for engineering applications.

A finite-time 3D guidance law based on fixed-time convergence disturbance observer

In order to achieve accurate interception of high-speed maneuvering targets, this paper presents a relative Line-of-Sight (LOS) velocity based finite-time three-dimensional guidance law design framework, and discusses the application of fixed-time convergence disturbance observer in this framework. Firstly, a simple Lyapunov function is provided to show that the coupled terms in the relative kinematics can be ignored in the proposed guidance law design framework. Secondly, the realizations of several classical guidance laws are analyzed with the proposed framework, including TPN guidance law, finite-time Input-to-State Stability (ISS) guidance law, and sliding mode guidance law. Thirdly, fixed-time convergence disturbance observers are introduced to design the composite finite-time 3D guidance law, and Lyapunov method is employed to show the stability of the guidance system. Numerical simulations with different scenarios show that the proposed generalized guidance law performs high interception accuracy.

The approach of partial stabilisation in design of discrete-time robust guidance laws against manoeuvering targets

ABSTRACTIn this paper, a robust three-dimensional guidance law against manoeuvering targets is designed using the approach of discrete-time partial stabilisation. In the proposed method, the equations of the guidance problem are divided into two subsystems where the asymptotic stability is desired only for the first one. The control input of the second subsystem is designed such that the collision to be ensured in a short time. Despite recent advances in technology and implementation of digital controllers, the design of guidance laws with the approach of discrete-time partial stabilisation has not been done, till now. One of the advantages of this paper is to design a discrete-time guidance law even with the difficulties of the discrete-time Lyapunov theorem. Moreover, the Lyapunov function is chosen based on the physics of the guidance problem (making the rate of line of sight (LOS) rotation close to zero), and it is shown that it is not possible to asymptotically stabilise the system in the case of manoeuvering targets. Nevertheless, to guarantee the collision with the target, it is enough to limit the rotation rate of LOS to a small value. Finally, simulation results are given to show the appropriate performance of the proposed guidance law.

Design of Three-Dimensional Guidance Law With Impact Angle Constraints and Input Saturation

This thesis studies the problem of three-dimensional guidance considering maneuvering acceleration and input saturation based on the background of missile intercepting maneuvering target. On the basis of the three-dimensional guidance model with impact angle constraints, a three-dimensional guidance law is designed by using the integral sliding mode control and adaptive control. To solve the problem of input saturation, an adaptive anti-saturation integral sliding mode three-dimensional guidance law is designed by introducing an auxiliary system. The stability of the designed guidance law is proved by Lyapunov theory, which ensures that the sliding mode manifold converges to zero in finite time. The effectiveness of the designed guidance law is verified by simulation analysis.