Adaptive weighting impact angle optimal guidance law considering seeker's FOV angle constraints

In this paper, a new adaptive optimal guidance law with impact angle and seeker’s field-of-view(FOV) angle constraints is proposed. To this end, the generalized optimal guidance law is derived first. A changeable impact angle weighting(IAW) coefficient is introduced and used to modify the guidance law to make it adaptive for all guidance constraints. After integrating the closed-form solution of the guidance command with linearized engagement kinematics, the analytic predictive models of impact angle and FOV angle are built, and the available range of IAW corresponding to constraints is certain. Next, a calculation scheme is presented to acquire the real-time value of IAW during the entire guidance process. When applying the proposed guidance law, the IAW will keep small to avoid a trajectory climbing up to limit FOV angle at an initial time but will increase with the closing target to improve impact position and angle accuracy, thereby ensuring that the guidance law can juggle orders of guidance accuracy and constraints control.

Robust Trajectory and Communication Design for Angle-Constrained Multi-UAV Communications in the Presence of Jammers

This paper studies a multi-unmanned aerial vehicle(UAV)enabled wireless communication system,where multiple UAVs are employed to communicate with a group of ground terminals(GTs)in the presence of potential jammers.We aim to maximize the throughput overall GTs by jointly optimizing the UAVs’trajectory,the GTs’scheduling and power allocation.Unlike most prior studies,we consider the UAVs’turning and climbing angle constraints,the UAVs’three-dimensional(3D)trajectory constraints,minimum UAV-to-UAV(U2U)distance constraint,and the GTs’transmit power requirements.However,the formulated problem is a mixed-integer non-convex problem and is intractable to work it out with conventional optimization methods.To tackle this difficulty,we propose an efficient robust iterative algorithm to decompose the original problem be three sub-problems and acquire the suboptimal solution via utilizing the block coordinate descent(BCD)method,successive convex approximation(SCA)technique,and S-procedure.Extensive simulation results show that our proposed robust iterative algorithm offers a substantial gain in the system performance compared with the benchmark algorithms.

Design of integral sliding mode guidance law based on disturbance observer

With the increasing precision of guidance,the impact of autopilot dynamic characteristics and target maneuvering abilities on precision guidance is becoming more and more significant.In order to reduce or even eliminate the autopilot dynamic operation and the target maneuvering influence,this paper suggests a guidance system model involving a novel integral sliding mode guidance law(ISMGL).The method utilizes the dynamic characteristics and the impact angle,combined with a sliding mode surface scheme that includes the desired line-ofsight angle,line-of-sight angular rate,and second-order differential of the angular line-of-sight.At the same time,the evaluation scenario considere the target maneuvering in the system as the external disturbance,and the non-homogeneous disturbance observer estimate the target maneuvering as a compensation of the guidance command.The proposed system’s stability is proven based on the Lyapunov stability criterion.The simulations reveale that ISMGL effectively intercepted large maneuvering targets and present a smaller miss-distance compared with traditional linear sliding mode guidance laws and trajectory shaping guidance laws.Furthermore,ISMGL has a more accurate impact angle and fast convergence speed.

Missile guidance law design based on free-time convergent error dynamics

To solve the finite-time error-tracking problem in mis-sile guidance,this paper presents a unified design approach through error dynamics and free-time convergence theory.The proposed approach is initiated by establishing a desired model for free-time convergent error dynamics,characterized by its independence from initial conditions and guidance parameters,and adjustable convergence time.This foundation facilitates the derivation of specific guidance laws that integrate constraints such as leading angle,impact angle,and impact time.The theoretical framework of this study elucidates the nuances and synergies between the proposed guidance laws and existing methodologies.Empirical evaluations through simulation comparisons underscore the enhanced accuracy and adaptability of the proposed laws.

An impact angle constraint integral sliding mode guidance law for maneuvering targets interception

An integral sliding mode guidance law(ISMGL)combined with the advantages of the integral sliding mode control(SMC)method is designed to address maneuvering target interception problems with impact angle constraints.The relative motion equation of the missile and the target considering the impact angle constraint is established in the longitudinal plane,and an integral sliding mode surface is constructed.The proposed guidance law resolves the existence of a steady-state error problem in the traditional SMC.Such a guidance law ensures that the missile hits the target with an ideal impact angle in finite time and the missile is kept highly robust throughout the interception process.By adopting the dynamic surface control method,the ISMGL is designed considering the impact angle constraints and the autopilot dynamic characteristics.According to the Lyapunov stability theorem,all states of the closed-loop system are finally proven to be uniformly bounded.Simulation results are compared with the general sliding mode guidance law and the trajectory shaping guidance law,and the findings verify the effectiveness and superiority of the ISMGL.

Extended optimal guidance law with impact angle and acceleration constriants

The extended optima straints of miss distance and Schwartz inequality. To reduce guidance law with terminal conmpact angle is derived by the terminal acceleration and eliminate gravity disturbance absolutely, the object function, which designs the weight of control command to be the power function of time-to-go＇s reciprocal, is given. And the gravity is considered when building the state equation. Based on the parsing express of the guidance command change with varying time and adjoint system analysis method, the command characteristics and the non-dimensional miss distance of the guidance law are analyzed, a design principle of guidance order coefficients is discussed. Finally, based on the requirement of engineering, the method to calculate the guidance condition and maximal required acceleration of the guidance law is given. The simulation demonstrates that not only the guidance law can satisfy the terminal position and impact angle constraints, but also the terminal acceleration can be converged toward zero, which will support a good situation for the terminal angle of attacking control.

Three-dimensional impact angle constrained distributed cooperative guidance law for anti-ship missiles

This paper investigates the problem of distributed cooperative guidance law design for multiple anti-ship missiles in the three-dimensional(3-D)space hitting simultaneously the same target with considering the desired terminal impact angle constraint.To address this issue,the problem formulation including 3-D nonlinear mathematical model description,and communication topology are built firstly.Then the consensus variable is constructed using the available information and can reach consensus under the proposed acceleration command along the line-of-sight(LOS)which satisfies the impact time constraint.However,the normal accelerations are designed to guarantee the convergence of the LOS angular rate.Furthermore,consider the terminal impact angle constraints,a nonsingular terminal sliding mode(NTSM)control is introduced,and a finite time convergent control law of normal acceleration is proposed.The convergence of the proposed guidance law is proved by using the second Lyapunov stability method,and numerical simulations are also conducted to verify its effectiveness.The results indicate that the proposed cooperative guidance law can regulate the impact time error and impact angle error in finite time if the connecting time of the communication topology is longer than the required convergent time.

A trajectory shaping guidance law with field-of-view angle constraint and terminal limits

In this paper, a trajectory shaping guidance law,which considers constraints of field-of-view(FOV) angle, impact angle, and terminal lateral acceleration, is proposed for a constant speed missile against a stationary target. First, to decouple constraints of the FOV angle and the terminal lateral acceleration, the third-order polynomial with respect to the line-ofsight(LOS) angle is introduced. Based on an analysis of the relationship between the looking angle and the guidance coefficient,the boundary of the coefficient that satisfies the FOV constraint is obtained. The terminal guidance law coefficient is used to guarantee the convergence of the terminal conditions. Furthermore, the proposed law can be implemented under bearingsonly information, as the guidance command does not involve the relative range and the LOS angle rate. Finally, numerical simulations are performed based on a kinematic vehicle model to verify the effectiveness of the guidance law. Overall, the work offers an easily implementable guidance law with closed-form guidance gains, which is suitable for engineering applications.

Three-dimensional cooperative guidance law for multiple missiles with impact angle constraint

This paper proposes a cooperative guidance law for attacking a ground target with the impact angle constraint based on the motion camouflage strategy in the line-of-sight(LOS)frame.A dynamic model with the impact angle constraint is established according to the relative motion between multiple missiles and the target.The process of cooperative guidance law design is divided into two stages.Firstly,based on the undirected graph theory,a new finite-time consensus protocol on the LOS direction is derived to guarantee relative distances reach consensus.And the value of acceleration command is positive,which is beneficial for engineering realization.Secondly,the acceleration command on the normal direction of the LOS is designed based on motion camouflage and finite-time convergence,which can ensure the missiles reach the target with the desired angle and satisfy the motion camouflage state.The finitetime stability analysis is proved by the Lyapunov theory.Numerical simulations for stationary and maneuver targets have demonstrated the effectiveness of the cooperative guidance law proposed.

Impact angle constrained fuzzy adaptive fault tolerant IGC method for Ski-to-Turn missiles with unsteady aerodynamics and multiple disturbances

An impact angle constrained fuzzy adaptive fault tolerant integrated guidance and control method for Ski-to-Turn(STT)missiles subject to unsteady aerodynamics and multiple disturbances is proposed.Unsteady aerodynamics appears when flight vehicles are in a transonic state or confronted with unstable airflow.Meanwhile,actuator failures and multisource model uncertainties are introduced.However,the boundaries of these multisource uncertainties are assumed unknown.The target is assumed to execute high maneuver movement which is unknown to the missile.Furthermore,impact angle constraint puts forward higher requirements for the interception accuracy of the integrated guidance and control(IGC)method.The impact angle constraint and the precise interception are established as the object of the IGC method.Then,the boundaries of the lumped disturbances are estimated,and several fuzzy logic systems are introduced to compensate the unknown nonlinearities and uncertainties.Next,a series of adaptive laws are developed so that the undesirable effects arising from unsteady aerodynamics,actuator failures and unknown uncertainties could be suppressed.Consequently,an impact angle constrained fuzzy adaptive fault tolerant IGC method with three loops is constructed and a perfect hit-to-kill interception with specified impact angle can be implemented.Eventually,the numerical simulations are conducted to verify the effectiveness and superiority of the proposed method.

Multiple-stage spatial-temporal cooperative guidance without time-to-go estimation

This paper investigates the spatial-temporal cooperative guidance problem for multiple flight vehicles without relying on time-to-go information.First,a two-stage cooperative guidance strategy,namely the cooperative guidance and the Proportional Navigation Guidance(PNG)stage strategy,is developed to realize the spatial-temporal constraints in two dimensions.At the former stage,two controllers are designed and superimposed to satisfy both impact time consensus and impact angle constraints.Once the convergent conditions are satisfied,the flight vehicles will switch to the PNG stage to ensure zero miss distance.To further extend the results to three dimensions,a planar pursuit guidance stage is additionally imposed at the beginning of guidance.Due to the inde-pendence of time-to-go estimation,the proposed guidance strategy possesses great performance in satisfying complex spatial-temporal constraints even under flight speed variation.Finally,several numerical simulations are implemented to verify the effectiveness and advantages of the proposed results under different scenarios.

An adaptive fast fixed-time guidance law with an impact angle constraint for intercepting maneuvering targets

Sliding mode guidance laws based on a conventional terminal sliding mode guarantees only finite-time convergence, which verifies that the settling time is required to be estimated by selecting appropriate initial launched conditions. However, rapid convergence to a desired impact angle within a uniform bounded finite time is important in most practical guidance applications. A uniformly finite-time/fixed-time convergent guidance law means that the convergence（settling） time is predefined independently on initial conditions, that is, a closed-loop convergence time can be estimated a priori by guidance parameters. In this paper, a novel adaptive fast fixed-time sliding mode guidance law to intercept maneuver targets at a desired impact angle from any initial heading angle,with no problems of singularity and chattering, is designed. The proposed guidance law achieves system stabilization within bounded settling time independent on initial conditions and achieves more rapid convergence than those of fixed-time stable control methods by accelerating the convergence rate when the system is close to the origin. The achieved acceleration-magnitude constraints are rigorously enforced, and the chattering-free property is guaranteed by adaptive switching gains.Extensive numerical simulations are presented to validate the efficiency and superiority of the proposed guidance law for different initial engagement geometries and impact angles.

Three-dimensional time-varying sliding mode guidance law against maneuvering targets with terminal angle constraint

This paper deals with the problem of intercepting maneuvering targets with terminal angle constraints for missiles subjected to three-dimensional non-decoupling engagement geometry.To achieve the finite-time interception and satisfactory overload characteristics, a time varying sliding mode control methodology is developed based on a time base generator function. The main feature of the proposed guidance law guarantees the Line-of-Sight(LOS) angles to converge to small neighborhoods of the desired values at the interception time. First, a fractional power extended state observer is used to estimate the unknown target acceleration, which can significantly reduce the adaptive switching gain. The fractional power extended state observer enjoys the advantage of better noise tolerance. Then, a newly designed sliding mode surface is constructed by introducing a time base generator function and the time-varying sliding mode guidance law is developed based on this time-varying sliding surface. The proposed guidance law significantly reduces the overload magnitudes. Numerical simulations are carried out to verify the performance of the proposed guidance law.

Phase plane design based fast altitude tracking control for hypersonic flight vehicle with angle of attack constraint

In this paper, fast setpoint altitude tracking control for Hypersonic Flight Vehicle(HFV)satisfying Angle of Attack(AOA) constraint is studied with a two-loop structure controller, in the presence of parameter uncertainties and disturbances. For the outer loop, phase plane design is adopted for the simplified model under Bang-Bang controller to generate AOA command guaranteeing fast tracking performance. Modifications based on Feedback-Linearization(FL) technique are adopted to transform the phase trajectory into a sliding curve. Moreover, to resist mismatch between design model and actual model, Fast Exponential Reaching Law(FERL) is augmented with the baseline controller to maintain state on the sliding curve. The inner-loop controller is based on backstepping technique to track the AOA command generated by outer-loop controller. Barrier Lyapunov Function(BLF) design is employed to satisfy AOA requirement. Moreover, a novel auxiliary state is introduced to remove the restriction of BLF design on initial tracking errors. Dynamic Surface Control(DSC) is utilized to ease the computation burden. Rigorous stability proof is then given, and AOA is guaranteed to stay in predefined region theoretically. Simulations are conducted to verify the efficiency and superior performance of the proposed method.

Structural topology optimization subject to overhang angle constraint with overhang length relaxation in additive manufacturing

This paper studies additive manufacturing(AM) oriented structural topology optimization(TO).The minimum compliance design subject to overhang angle constraint with overhang length relaxation and horizontal minimum length control is considered.Although the overhang length relaxation allows additional flexibility for AM product design,there have been very limited studies on it.This paper elucidates that the overhang angle constraint we proposed can identify the lower boundary element that violates the overhang angle constraint.Taking advantage of this fact,we achieve the overhang length relaxation by specifying that the volume fraction of the elements that violate the overhang angle constraint in each local area of the design domain is less than a specified upper bound.A formula for estimating the maximum allowable overhang length of this method is proposed and verified.The horizontal minimum length constraint is also employed in this paper.While controlling the horizontal length size of the structural member,this constraint together with the overhang angle constraint with overhang length relaxation suppresses the hanging feature.The gradient-based optimization algorithm method of moving asymptotic(MMA) is used to solve the TO formulation.Numerical examples show the effectiveness of this method.It is observed that the new constraint alleviates the main issues of traditional overhang angle constraints,i.e.,gray element issue,stress concentration issue,and shattered structure issue.Compared with the strict traditional overhang angle constraint,the new formulation reduces structural compliance.

Robust guidance method with terminal impact angle constraint for autonomous underwater vehicle

Based on robust control design method,a variable structure guidance method is proposed for autonomous underwater vehicle(AUV) during the guiding course with terminal impact angle constraint.Considering the intercept geometry,a sliding mode controller is proposed for controlling the hne of sight angle rate and the impact angle,based on the principle which controls the line of sight angle rate to approach zero and the terminal angle to approach the expected value more quickly as the distance decreases.Simulation results show that,with the application of the proposed method,small miss distance is achieved and the expected impact angle is reached.In addition,the system is robust to the target maneuvering.

Impact time control guidance against maneuvering targets based on a nonlinear virtual relative model

Aiming at the problem of high-precision interception of air-maneuvering targets with impact time constraints,this paper proposes a novel guidance law based on a nonlinear virtual relative model in which the origin is attached to the target.In this way,the original maneuvering target is transformed into a stationary one.A polynomial function of the guidance command in the range domain with two unknown coefficients is introduced into the virtual model,one of the coefficients is determined to achieve the impact time constraint,and the other is determined to satisfy a newly defined virtual look angle constraint.For meeting the terminal constraints simultaneously,the guidance command can finally be obtained.The resulting solution is represented as a combination of proportional navigation guidance-like term which is aimed to meet the zero miss distance constraint,a bias term for impact time control by adjusting the length of the homing trajectory,and an additional term for target maneuvers.Numerous simulations demonstrate that the proposed law achieves an acceptable impact time error for various initial conditions against different types of maneuvering targets and shows more effective performance in comparison with those of other existing guidance laws.

Cooperative guidance strategy for multiple hypersonic gliding vehicles system

Cooperative guidance strategy for multiple hypersonic gliding vehicles system with flight constraints and cooperative constraints is investigated.This paper mainly cares about the coordination of the entry glide flight phase and driving-down phase.Different from the existing results,both the attack time and the attack angle constraints are considered simultaneously.Firstly, for the entry glide flight phase, a two-stage method is proposed to achieve the rapid cooperative trajectories planning, where the control signal corridors are designed based on the quasi-equilibrium gliding conditions.In the first stage, the bank angle curve is optimized to achieve the attack angle coordination.In the second stage, the angle of attack curve is optimized to achieve the attack time coordination.The optimized parameters can be obtained by the secant method.Secondly, for the driving-down phase, the cooperative terminal guidance law is designed where the terminal attack time and attack angle are considered.The guidance law is then transformed into the bank angle and angle of attack commands.The cooperative guidance strategy is summarized as an algorithm.Finally, a numerical simulation example with three hypersonic gliding vehicles is provided for revealing the effectiveness of the acquired strategy and algorithm.

Optimal guidance of extended trajectory shaping

To control missile＇s miss distance as well as terminal impact angle, by involving the timeto-go-nth power in the cost function, an extended optimal guidance law against a constant maneuvering target or a stationary target is proposed using the linear quadratic optimal control theory.An extended trajectory shaping guidance（ETSG） law is then proposed under the assumption that the missile-target relative velocity is constant and the line of sight angle is small. For a lag-free ETSG system, closed-form solutions for the missile＇s acceleration command are derived by the method of Schwartz inequality and linear simulations are performed to verify the closed-form results. Normalized adjoint systems for miss distance and terminal impact angle error are presented independently for stationary targets and constant maneuvering targets, respectively. Detailed discussions about the terminal misses and impact angle errors induced by terminal impact angle constraint, initial heading error, seeker zero position errors and target maneuvering, are performed.