Proposed Guidance Law Research Articles

Three‐dimensional cooperative guidance for simultaneous attack with specified impact time based on fixed‐time convergence

AbstractIn this paper, distributed three‐dimensional (3D) cooperative guidance laws are designed for leader–follower multiple missiles to achieve simultaneous attack at a specified time. The guidance laws are derived from the biased proportional navigation guidance (PNG) law. Two fixed‐time distributed algorithms with time‐varying coefficients are proposed to track the state of the leader under undirected and directed topologies, respectively. The upper bounds of convergence times for the tracking algorithms are obtained. The biased guidance terms of followers are designed to track the leader with the proposed algorithms and the biased guidance term of the leader is designed to achieve specified impact time. Then, an auxiliary function is included into the biased guidance terms to meet the field‐of‐view (FOV) constraints. The leading angles' properties and convergence times under the proposed guidance laws are further analyzed. Numerical simulations are given to verify the effectiveness of the proposed cooperative guidance laws.

Integrated entry guidance with no-fly zone constraint using reinforcement learning and predictor-corrector technique

This paper presents an integrated entry guidance law for hypersonic glide vehicles with no-fly zone constraint. Existing methods that employ predictor-corrector technique and lateral guidance logic for both guidance and avoidance, may have limitations in response time and maneuverability when facing sudden threats, because the guidance cycle is limited by computational efficiency and the bank angle magnitude cannot be adjusted according to the urgency of the avoidance. To overcome these challenges, the proposed method divides the entry process into safe flight stages and no-fly zone avoidance stages, and introduces reinforcement learning to develop an intelligent avoidance strategy for the latter. This division reduces the complexity of the learning problem by restricting the state space and increases the applicability in the presence of multiple no-fly zones. The trained avoidance strategy can directly output continuous bank angle command through a single forward calculation, considering both guidance and avoidance requirements. This enables the full utilization of the vehicle’s maneuverability and supports a high command update frequency to effectively handle threats. Additionally, a network trained via supervised learning is employed to generate reference commands, accelerating the training convergence of reinforcement learning. Simulation results demonstrate the effectiveness of the proposed guidance law, highlighting its high computational efficiency, command stability, and robustness. Importantly, the approach offers convenience in extending to multiple no-fly zones and accommodating vast initial state spaces.

Three-dimensional terminal angle constraint guidance law with class [formula omitted] function-based adaptive sliding mode control

This paper investigates the three-dimensional (3-D) interception guidance problem, where the missile is required to intercept the maneuvering target with the desired terminal angles. For the nonlinear relative kinematic model, a class K∞ function-based adaptive sliding mode guidance law is proposed, which ensures that the errors of terminal Line-of-Sight (LOS) angles converge to the small neighborhoods of origin at the time of interception, without relying on information about the target's acceleration. To overcome the challenges of large initial control input and chattering in existing sliding mode guidance laws, two improved control schemes are introduced. The first scheme is to directly impose saturation constraints into the adaptive gain. However, it is important to ensure that the unknown disturbance remains within the prescribed saturation bound. To avoid the limitation, another approach involves introducing auxiliary dynamics to eliminate the reaching phase and slow down the convergence of LOS angles by presetting the convergence time of the sliding mode variables, which helps mitigate excessive initial control inputs. Numerical simulations are conducted using a realistic missile model and considering a 3-DOF point-mass aircraft as the target to evaluate three different guidance laws. The results indicate that the proposed guidance law ensures interception accuracy while substantially reducing the control gain.

Trajectory prediction-based guidance law

This paper proposes a guidance law based on trajectory prediction, aiming to address the difficulty of traditional guidance laws in meeting high-speed and highly maneuverable vehicles. The unscented Kalman filtering (UKF) technique is employed to estimate the target’s motion and predict the virtual impact point using the Singer model and measuring model. The midcourse guidance law is applied to the virtual target, taking into account the constraint of the intersection angle, while the terminal guidance utilizes modified proportional guidance. To mitigate the overload chattering in the transition sections of both midcourse and terminal guidance, the distance is used to modify the transition section of the terminal guidance. Simulation results demonstrate that the proposed guidance law effectively reduces both the encounter angle and the required maneuvering. Furthermore, to minimize midcourse guidance errors, the prediction results of the virtual target are continually updated during the trace process. This method can also be applied to trail other highly maneuverable targets.

Analytical Prescribed Performance Guidance with Field-of-View and Impact-Angle Constraints

Aiming at the impact-angle-control guidance with field-of-view constraint in the three-dimensional space, a novel analytical prescribed performance guidance law is proposed. First, a new prescribed performance function is designed in the relative range domain, and the common drawbacks of most existing prescribed performance functions, such as large overshoot, time dependency, and infinite-time convergence, are avoided. Second, the three-dimensional biased pure proportional navigation guidance frame is selected. The biased term is derived based on the prescribed performance control theory and the optimal error dynamic method, for realizing the terminal impact-angle constraint. After that, the analytical solution of missile lead angle is derived under some linearization approximations, and two methods are respectively developed for obtaining the range of the guidance gain and updating its value to guarantee the satisfaction of the field-of-view constraint during the guidance process. Moreover, for the proposed guidance law and methods, the tracking error could be ensured to remain in the predefined performance boundaries. Finally, numerical simulations are conducted to verify the effectiveness of the new theoretical findings.

Adaptive Fuzzy Quantized Control for a Cooperative USV-UAV System Based on Asynchronous Separate Guidance

This paper focuses predominantly on the multi-tasks carried out by the cooperative unmanned surface vehicle-unmanned aerial vehicle (USV-UAV) system in which the input quantization is considered. The proposed cooperative scheme consists of the asynchronous separate guidance and adaptive fuzzy quantized control algorithm. The proposed guidance law takes full advantage of subsystems whilst considering the maneuverability of these subsystems in order to achieve the goal of executing multi-tasks. In contrast to previous guidance laws, although the same waypoint path is planned, the calculation for guidance law proposed is based on speed rather than time, which in reality is more relevant. As for the controls, an adaptive fuzzy quantized controller was developed to reduce undue exertion on the actuator. By fusing the dynamic surface control (DSC) and fuzzy logic system (FLS), a hysteresis quantizer has been introduced to reduce the transmission load. By properly adjusting the quantization density, the number of quantizations was reduced whilst maintaining a favorable control performance. All of the stated variables are semi-global uniform ultimate bounded (SGUUB) and the stability of the USV-UAV system is proofed through the Lyapunov theorem. Finally, the advantages of the proposed scheme are evaluated by two simulative experiments, exhibiting the favorable tracking accuracy and reduced wear on the actuators.

Fixed-Time Convergent Guidance Law with Angle Constraint and Autopilot Lag Compensation Using Partial-State Feedback

In this paper, by accounting for the angle constraint (AC) and autopilot lag compensation (ALC), a novel fixed-time convergent guidance law is developed based on a fixed-time state observer and bi-limit homogeneous technique. The newly proposed guidance law exhibits three attractive features: (1) unlike existing guidance laws with AC and ALC which can only guarantee asymptotic stability or finite-time stability, the newly proposed guidance scheme can achieve fixed-time stability. Thus, the newly proposed scheme can drive the guidance error to zero within bounded time which is independent of the initial system conditions. (2) To compensate for autopilot lag, existing guidance schemes need the unmeasurable second derivative of the range along line-of-sight (LOS) and second derivative of LOS angle or the derivative of missile’s acceleration. Without using these unmeasurable states, the newly proposed guidance law still can guarantee the fixed-time stability. (3) By using the bi-limit homogeneous technique to construct an integral sliding-mode surface, the proposed scheme eliminates the singular problem without using the commonly-used approximate method in recent fixed-time convergent guidance schemes. Finally, the simulation results demonstrate the effectiveness of the proposed scheme.

Composite Zero-Effort-Miss Guidance with Predictor–Corrector Steps for Ballistic Interception

In this paper, a midcourse guidance law for exoatmospheric interception using a solid-propellant rocket is presented. Existing guidance laws based on the zero-effort-miss concept lack consideration for remaining thrust, potentially resulting in the excessive magnitude and rate of the thrust direction command. To address this issue, the zero-effort-miss concept is combined with an iterative predictor–corrector-based guidance law that is adapted for solid-propellant rockets. To apply the iterative predictor–corrector-based guidance law to the interception problem with a solid-propellant rocket, a composite zero-effort-miss concept is introduced, and the correction step is formulated as an online convex optimization problem. The composite zero-effort-miss consists of two zero-effort-misses. One miss is obtained from current state and the other miss is obtained from predicted state at burnout. Those render the proposed guidance law robust to thrust uncertainty allow for a noniterative approach and eliminate the singularity problem. Also, the proposed guidance law reduces maneuvering during the early part of the midcourse phase, leading to less velocity loss, and resolves intercept performance degradation due to the rate limit of thrust vectoring. Numerical simulations comparing the proposed method with the modified zero-effort-miss guidance demonstrate its effectiveness and robustness.

Event‐triggered cooperative control for moving target encirclement and tracking with time‐varying pattern by UAV formation

AbstractThis paper investigates an event‐triggered cooperative control policy of moving‐target encirclement and tracking with time‐varying radius commands for unmanned aerial vehicle (UAV) formation. Different from the existing works, this study takes into account the relative motion model between the UAVs and the target in order to design a guidance law specifically tailored for moving‐target encirclement and tracking. Additionally, a time‐varying radius command is introduced, allowing the radius of the circular orbit formed by the UAVs around the target to adjust according to the commands. This flexibility and adaptability enhance the UAV formation's performance in complex work scenes and unstructured geometric spaces. To address the concerns of communication and computing costs associated with time‐triggered guidance laws, an event‐triggered method is proposed for dynamic target encirclement and tracking, eliminating the occurrence of Zeno behaviour. The stability of the proposed guidance laws is mathematically proven using the interconnected systems lemma. Finally, the effectiveness of the controllers is verified by some simulations.

Nonlinear three dimensional all-aspect guidance with terminal impact angle constraints

In this paper, a nonlinear three dimensional all-aspect guidance law, to intercept maneuvering target at pre-specified orientation, is presented. Without decoupling the engagement kinematics into two perpendicular planes, the proposed guidance law is derived in three dimensions directly. More importantly, the proposed strategy is an ‘all-aspect’ guidance law, which allows missile to intercept the target at the desired impact angle, even in the presence of very large initial pointing errors. First, in order to design a guidance law with all-aspect interception capability, the collision conditions analysis process is carefully developed and an additional necessary constraint condition is derived. Then, based on chattering reduction sliding mode control, a nonlinear three dimensional terminal impact angle constrained guidance law is derived considering maneuvering targets. After capturability analysis, an additional sliding mode surface and a switching logic are further designed, so that the all-aspect capability is guaranteed. Finally, numerical simulations are provided to demonstrate the effectiveness of the proposed guidance strategy.

Vector field-based integral LOS path following and target tracking for underactuated unmanned surface vehicle

The paper focuses on developing a method that enables the unmanned surface vehicle (USV) to effectively track dynamic objects on the water surface. The integral line-of-sight (LOS) guidance law is improved by introducing the concept of vector field for curved paths and the time-varying lookahead distance with a smoothing control parameter for straight paths. These enhancements facilitate faster convergence to the desired path with reduced oscillations and allow for mitigating the impact of constant external disturbances. The research demonstrates that the proposed guidance law exhibits κ-exponential stability when converging towards a desired path composed of both straight lines and curves. The results presented in the paper demonstrate that the proposed method effectively improves the accuracy of tracking dynamic targets for unmanned surface vehicles while ensuring the safety of docking operations.

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.

Cooperative robust line‐of‐sight guidance law based on high‐gain observers for active defense

SummaryIn this paper, a three‐body confrontation problem of a target‐defender team against an attacker is studied in three dimensions. To eliminate the system deviation that arises from the linearization of the model, a second‐order nonlinear model with normal acceleration as its input is established to describe the relative motion of three vehicles in three‐dimensional space. A high‐gain observer is designed to estimate the line‐of‐sight angular velocity in the case that system states cannot be measured. Based on disturbance rejection technique, a robust line‐of‐sight guidance law is developed in virtue of the estimated information for the target‐defender team so that the defender is able to intercept the attacker. Key features of the developed guidance law lie in that it does not need to know guidance information of the guidance law of the attacker in advance, and is robust to disturbance and uncertainty. Simulation examples are provided to demonstrate the effectiveness of the proposed guidance law.

Synthesis of Suboptimal Guidance Law for Anti-Tank Guided Missile with Terminal Impact Angle Constraint Based on the SDRE Technique

In this paper, the homing-phase guidance law is proposed against a stationary target in the planar engagement scenario. In this problem, two technical criteria that the guidance law must achieve are: first, zero terminal miss distance, and second, satisfying the desired impact angle constraint at the final time. This guidance law is synthesized as a nonlinear optimal control problem with an infinite-time horizon and is solved using the state-dependent Riccati equation (SDRE) method. To obtain a guidance law with a finite-time horizon, a state weighting matrix based on the time-to-go is utilized in the SDRE control scheme. The synthesized guidance law is applied to a new generation anti-tank guided missile class, with specific thrust and drag parameters. Nonlinear simulations are conducted to demonstrate the fundamental properties, applicability, and effectiveness of the proposed guidance law.

Constrained Moving Path Following Control for UAV With Robust Control Barrier Function

This paper studies the moving path following (MPF) problem for fixed-wing unmanned aerial vehicle (UAV) under output constraints and wind disturbances. The vehicle is required to converge to a reference path moving with respect to the inertial frame, while the path following error is not expected to violate the predefined boundaries. Differently from existing moving path following guidance laws, the proposed method removes complex geometric transformation by formulating the moving path following problem into a second-order time-varying control problem. A nominal moving path following guidance law is designed with disturbances and their derivatives estimated by high-order disturbance observers. To guarantee that the path following error will not exceed the prescribed bounds, a robust control barrier function is developed and incorporated into controller design with quadratic program based framework. The proposed method does not require the initial position of the UAV to be within predefined boundaries. And the safety margin concept makes error-constraint be respected even if in a noisy environment. The proposed guidance law is validated through numerical simulations of shipboard landing and hardware-in-the-loop (HIL) experiments.

Distributed observer-based finite-time control of moving target tracking for UAV formation

This paper disseminated two formation control strategies for multiple unmanned aerial vehicles (multi-UAV) system of moving target tracking in a windy environment. The communication among UAVs is modeled by a directed graph. The first control strategy proposes a distributed dynamic error observer and a guidance law to make the system global uniform asymptotic stability when the wind disturbance is a known constant. The second control strategy employs a distributed fixed-time observer and a finite-time stable guidance law to make the system globally finite-time stable with unknown wind disturbances. The stability of both formation control strategies is rigorous demonstrated mathematically. Finally, the excellent performance and reliability of the proposed guidance law for target tracking in a windy environment are verified through several simulation examples.

Impact Angle Control Guidance Considering Seeker’s Field-of-View Limit Based on Reinforcement Learning

This study proposes a computational impact angle control guidance law against a stationary target considering the seeker’s field-of-view (FOV) limit based on a deep reinforcement learning (RL) method. The proposed guidance law generates the acceleration command as a sum of the baseline command and bias command where the bias command is learned through a sequence of learning stages. Each stage trains an RL agent that addresses the impact angle and the FOV limit constraint individually. This approach is favorable in that the succeeding training process tends to preserve the functionality of the guidance law attained in the previous stage. In addition, the proposed method can be easily extended to a missile model with additional elements such as rotational dynamics without the necessity of modifying the algorithm. The proximal policy optimization algorithm is used for training the RL agents. Numerical simulation is carried out under various conditions to analyze the performance and the effects of a design parameter on the performance. The learning strategy proposed in this study provides a way to apply a data-driven method to developing a guidance law under multiple design objectives and more realistic missile models.

Three-dimensional predefined-time impact angle control guidance law with field-of-view limit

In this paper, an impact angle control guidance (IACG) law with predefined convergence time and seeker’s field-of-view (FOV) limit is proposed in three-dimensional (3D) scenario. First, a predefined-time error dynamic is developed whose significance is revealed by comparison with conventional methods. Second, based on coupled engagement dynamics, a 3D predefined-time IACG law is derived by applying the proposed error dynamic. To tackle the FOV limit, two auxiliary functions are introduced into the IACG law. The robustness against disturbances and uncertainties is further improved by utilizing the terminal sliding mode technique. With the proposed guidance law, the impact-angle error can converge to zero exactly at a tunable predefined time. Finally, the effectiveness and performance of the proposed IACG law are shown by several simulations with comparative study.

Homing Guidance Law Design against Maneuvering Targets Based on DDPG

A novel homing guidance law against maneuvering targets based on the deep deterministic policy gradient (DDPG) is proposed. The proposed guidance law directly maps the engagement state information to the acceleration of the interceptor, which is an end-to-end guidance policy. Firstly, the kinematic model of the interception process is described as a Markov decision process (MDP) that is applied to the deep reinforcement learning (DRL) algorithm. Then, an environment of training, state, action, and network structure is reasonably designed. Only the measurements of line-of-sight (LOS) angles and LOS rotational rates are used as state inputs, which can greatly simplify the problem of state estimation. Then, considering the LOS rotational rate and zero-effort-miss (ZEM), the Gaussian reward and terminal reward are designed to build a complete training and testing simulation environment. DDPG is used to deal with the RL problem to obtain a guidance law. Finally, the proposed RL guidance law’s performance has been validated using numerical simulation examples. The proposed RL guidance law demonstrated improved performance compared to the classical true proportional navigation (TPN) method and the RL guidance policy using deep-Q-network (DQN).

Robust guidance law for cooperative aerial target circumnavigation of UAVs based on composite system theory

Unmanned aerial vehicles (UAVs) are widely used in many fields and relevant research is becoming widespread. However, there are still many problems in the control design of multiple UAVs. This paper proposes a new robust guidance law for the cooperative circumnavigation of an aerial target by multiple UAVs. By incorporating an altitude channel, the controlled fixed-wing UAV was modeled as a simplified three-dimensional (3D) nonlinear dynamic system. Unlike existing studies, tracking and cooperation were considered as a composite system, and the coupling of the UAV linear velocity and angular velocity was considered in the design process. The proposed guidance law considers both the input and output constraints, which represent the system uncertainties and output limits, respectively, and are used to verify the robustness of the guidance law. The robust stability of the disturbed cooperative target circumnavigation system in 3D space is ensured through a strict mathematical proof. Finally, the effectiveness and superiority of the proposed robust guidance law are demonstrated by simulations using a UAV unicycle model and a six-degree-of-freedom (6-DOF) model.