Proposed Guidance Law Research Articles

Coordinated Formation Guidance Law for Fixed-Wing UAVs Based on Missile Parallel Approach Method

This paper presents a classic missile-type parallel-approach guidance law for fixed-wing UAVs in coordinated formation flight. The key idea of the proposed guidance law is to drive each follower to follow the virtual target point. Considering the turning ability of each follower, the formation form adopts the semi-perfect rigid form, which does not require the vehicle positions form a rigid formation, and the orientations keep consensus. According to the mission characteristics of the follower following a leader and the leader following a route, three guidance laws for straight, turning, and circling flight are designed. A series of experiments demonstrate the proposed guidance law’s improved response and maneuvering stability. The results of hardware-in-the-loop simulations and real flight tests prove that the proposed guidance law satisfies the practical UAV formation flight control demands.

Predictive Differential Game Guidance Approach for Hypersonic Target Interception Based on CQPSO

In the descent phase of the hypersonic target flight trajectory, the hypersonic speed of the target makes the reaction time shorter. Due to overload restrictions, it is challenging for the interceptor to achieve successful interception. To address this problem, a predictive differential game guidance approach based on dynamic optimization algorithm is proposed to relax the interceptor acceleration requirements. Two-dimensional kinematics and dynamics engagement mode for hypersonic target interception is formulated as a nonlinear differential control model in the presence of matched uncertainties. The nonlinear differential model is transformed into a differential game model by combining a performance index. The performance index is positively correlated with the Line-Of-Sight (LOS) rate and control effort of interceptor and negatively correlated with the target maneuver. The Chaotic Quantum Particle Swarm Optimization (CQPSO) algorithm is utilized to address the nonlinear differential game problem to generate the instantaneous and predicted guidance commands for the interceptor and target. Numerical examples are given to verify the performance of the proposed guidance law in various engagement scenarios, including different target maneuvers, initial heading angles and target overload. Moreover, the performance of the algorithm is validated comparing with traditional and state-of-the-art guidance laws.

Optimal Cooperative Line-of-Sight Guidance for Defending a Guided Missile

This correspondence proposes an optimal cooperative guidance law for protecting a target from a guided missile. The linearized three-body kinematics using the line-of-sight (LOS) triangle concept is formulated, and a new concept called error distance is introduced. A generalized linear quadratic optimization problem is formulated in minimizing weighted energy consumption while regulating the error distance. The analytic guidance command is derived by solving the optimization problem formulated. The main feature of the proposed guidance law lies in that it helps reduce the maneuver capability demand of the defender. Extensive numerical simulations are carried out to demonstrate the effectiveness of the proposed solution.

Avoiding Obstacles via Missile Real-Time Inference by Reinforcement Learning

In the contemporary battlefield where complexity has increased, the enhancement of the role and ability of missiles has become crucial. Thus, missile guidance systems are required to be further developed in a more intelligent and autonomous way to deal with complicated environments. In this paper, we propose novel missile guidance laws using reinforcement learning, which can autonomously avoid obstacles and terrains in complicated environments with limited prior information and even without the need of off-line trajectory or waypoint generation. The proposed guidance laws are focused on two mission scenarios: the first is with planar obstacles, which is used to cope with maritime operations, and the second is with complex terrain, which is used to cope with land operations. We present the detailed design processes for both scenarios, including a neural network architecture, reward function selection, and training method. Simulation results are provided to show the feasibility and effectiveness of the proposed guidance laws and some important aspects are discussed in terms of their advantages and limitations.

An event‐triggered optimal cooperative guidance law for simultaneous attacks with impact angle constraints

This article proposes a multimissile cooperative guidance law for simultaneous attacks with impact angle constraints based on an event-triggered strategy. The guidance law has two parts. One part is derived from optimal control to satisfy impact angle constraints, and the other is a cooperative term to perform simultaneous attacks. An event-triggered strategy is introduced to reduce communication frequency and save energy. The consensus is proved by the Lyapunov theory. Efficacy of the proposed guidance law is verified by numerical simulations.

Three-dimensional field of view and impact angle constrained guidance with terminal speed maximization

A three-dimensional strap-down seeker based multi-constrained guidance law for an interceptor is proposed in this paper to achieve near zero miss distance with minimal control effort (lateral acceleration) and interception time. When the interceptor is guided based on strap-down seeker measurements, the field of view limit throughout the flight trajectory is one of the major concerns to guarantee tracking of the target. To enhance the capability of warhead while approaching a target, the interceptor needs to ensure the desired impact angles and maximum speed at terminal time as well as various path inequality constraints throughout the trajectory, such as lateral acceleration limit and field of view limit. To meet these requirements, the proposed guidance is designed using a new extended version of the computationally efficient, suboptimal generalized model predictive static programming (GMPSP) technique in an unspecified final time framework. In addition, to make all the states available, to estimate parameter uncertainties and to filter out the sensor measurement noises, an extended Kalman filter based state and parameter estimation is incorporated with this proposed guidance law. Using simulation studies, the efficacy of the proposed GMPSP based suboptimal guidance method is shown and compared with that of the Chebyshev pseudo-spectral method as well. The extensive simulation results also demonstrate that the proposed robust suboptimal guidance design can perform well, in the presence of aerodynamic parameter uncertainties and sensor noises.

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.

Gravity-compensated guidance for impact-angle interception of a moving target

This paper proposes an impact-angle control guidance (IACG) law for anti-ship and anti-tank missiles in which the command converges to zero at the point of interception, even in a gravity field. The desired line-of-sight (LoS) angle that satisfies the terminal impact-angle and acceleration constraints is first defined. The guidance command is then derived as a solution that realizes the convergence of the actual LoS angle to the desired LoS angle during the terminal stage of homing in on a target. Gravity is considered when designing the guidance law such that the desired terminal constraints are accurately satisfied, even under realistic pitch-axis engagement. We also investigated whether the proposed law is optimal for minimizing the total expense of maneuvering while performing IACG in a gravity field. The results of the numerical simulations included in this study demonstrate that the proposed guidance law achieves accurate impact-angle interception with the command converging to zero at the end of homing.

Terminal Impact Angle Control Guidance Law Considering Target Observability

The problem of the terminal impact angle control guidance law, considering the target observability for passive guidance with bearing-only measurement, is investigated in this paper. Modified line-of-sight (LOS) angle error dynamics and their closed-loop analytical solution are developed to enhance the target observability, and then their characteristics are studied, which makes the LOS angular rate oscillate in the early stage. The terminal impact angle control guidance law with the global sliding mode is designed to eliminate the approaching stage of sliding mode control, which makes the system robust throughout the entire process of control. Finally, numerical simulations are presented to demonstrate the performance of the proposed guidance law under various conditions, which achieves the desired results.

A hybrid proportional navigation based two-stage impact time control guidance law

To improve applicability and adaptability of the impact time control guidance (ITCG) in practical engineering, a two-stage ITCG law with simple but effective structure is proposed based on the hybrid proportional navigation, namely, the pure-proportional-navigation and the retro-proportional-navigation. For the case with the impact time error less than zero, the first stage of the guided trajectory is driven by the retro-proportional-navigation and the second one is driven by the pure-proportional-navigation. When the impact time error is greater than zero, both of the stages are generated by the pure-proportional-navigation but using different navigation gains. It is demonstrated by two-and three-dimensional numerical simulations that the proposed guidance law at least has comparable results to existing proportional-navigation-based ITCG laws and is shown to be advant-ageous in certain circumstances in that the proposed guidance law alleviates its dependence on the time-to-go estimation, consumes less control energy, and adapts itself to more boundary conditions and constraints. The results of this research are expected to be supplementary to the current research literature.

Vector field guidance for standoff target tracking

This work presents a guidance algorithm for standoff target tracking by unmanned aerial vehicles using the traditional Lyapunov guidance vector field framework. Unlike the past work, this guidance law is the function of the minimum radius of curvature, and, hence, it can act more flexibly for different maneuverable vehicles. Moreover, normalized even and odd functions are proposed here as circulation and convergence terms to improve performance in terms of optimality. The presence of wind is also considered for real world applications. As the proposed guidance law generates paths of continuous curvature, the designed path is flyable by fixed-wing unmanned vehicles. Simulation results are presented to validate the proposed guidance law.

Three-dimensional prescribed performance cooperative guidance law with spatial constraint for intercepting manoeuvring targets

This paper proposes three-dimensional cooperative guidance laws with prescribed performance. To avoid degradation in performance due to error in the estimation of the time-to-go, the relative distance between the missiles and the target is chosen as a coordination variable, and a fixed-time cooperative guidance law along the direction of the line-of-sight (LOS) is proposed. The guidance laws with prescribed performance for the elevation and direction of the azimuth of the LOS are then developed by combining the LOS angle tracking error with a performance constraint function to formulate a transformed error function. The problem of prescribed performance control is transformed into that of the boundedness of the transformed error function. A fixed-time convergence disturbance observer is designed to discuss the problem whereby information on aggregate uncertainty, including on the target, is unavailable. The results of simulations show that the proposed guidance laws are effective.

Finite-Time Distributed Leaderless Cooperative Guidance Law for Maneuvering Targets under Directed Topology without Numerical Singularities

A new distributed leaderless cooperative guidance algorithm is suggested for multi-directional saturation strikes against maneuvering targets. First, the finite-time disturbance observer (FDO) is used to estimate the target’s unknown maneuvers. After that, the guidance laws along the line-of-sight (LOS) direction and the LOS normal direction are designed separately based on the finite-time consensus theory. The proposed guidance law could satisfy both impact time and LOS angle constraints. Numerical singularities due to feedback linearization are avoided by nonlinear stability analysis. Finally, the effectiveness of the proposed cooperative guidance law is proved by numerical simulation arithmetic.

A New Guidance Law for Impact Angle Constraints with Time-Varying Navigation Gain

AbstractIn this study, a new impact angle control guidance law is proposed against a stationary target in the three-dimensional (3D) plane. A time-varying navigation gain is derived to achieve the specific terminal angle in a longitudinal plane without phased or adding a bias term. A proportional guidance law is also adopted in the lateral plane to achieve an accurate strike. The monotonicity of the look angle and the convergence of the acceleration are analysed and proven to support the proposed method. For the proposed guidance law, estimating time-to-go or giving a switch strategy is unnecessary; the navigation is continuous, which would not result in sudden changes in control input, and is convenient to implement. Extensive simulations, including autopilot lag or real missile model, are performed to validate the efficiency of the proposed method.

Three-dimensional prescribed performance sliding mode guidance law for intercepting maneuvering target

This article describes three-dimensional sliding mode guidance laws with prescribed performance. The proposed guidance laws can ensure that the line of sight (LOS) angle converges according to the prescribed performance, and the convergence rate, the steady-state error and the maximum overshoot can be preset in advance. By combining the LOS tracking error with the performance constraint function, a new error variable function is designed, and then the prescribed performance control problem is transformed into that of the boundedness of the error variable function. The key concept in this approach is to design a new sliding mode surface to ensure that the error variable function is bounded, so as to ensure that the system state converges according to the prescribed performance. Additionally, this article discusses the problem whereby the upper bound of the aggregate uncertainty, including the target information, is unavailable. An adaptive guidance law is presented for this scenario. Finally, simulations comparisons are conducted with other forms of guidance laws. Simulation results show that the guidance laws proposed in this article achieve effective performance.

A Distributed Control for Ground Target Tracking of Nonlinear Unmanned Aerial Vehicles Formation

This paper investigates a circular formation control strategy for multiple unmanned aerial vehicles (multi-UAV) formation for ground moving target tracking. Each UAV obtains the observation value of target information through sensors and exchanges data with its neighbors. Since the formation cannot get the parameter of the target directly, we proposed a distributed error observer. A new guidance law based on the error value obtained has been designed, and it was proved through the interconnection system that it was consistent with Lyapunov stability. Finally, a simulation example is used to illustrate the effectiveness of the proposed guidance law.

Optimal Guidance Laws for a Hypersonic Multiplayer Pursuit-Evasion Game Based on a Differential Game Strategy

The guidance problem of a confrontation between an interceptor, a hypersonic vehicle, and an active defender is investigated in this paper. As a hypersonic multiplayer pursuit-evasion game, the optimal guidance scheme for each adversary in the engagement is proposed on the basis of linear-quadratic differential game strategy. In this setting, the angle of attack is designed as the output of guidance laws, in order to match up with the nonlinear dynamics of adversaries. Analytical expressions of the guidance laws are obtained by solving the Riccati differential equation derived by the closed-loop system. Furthermore, the satisfaction of the saddle-point condition of the proposed guidance laws is proven mathematically according to the minimax principle. Finally, nonlinear numerical examples based on 3-DOF dynamics of hypersonic vehicles are presented, to validate the analytical analysis in this study. By comparing different guidance schemes, the effectiveness of the proposed guidance strategies is demonstrated. Players in the engagement could improve their performance in confrontation by employing the proposed optimal guidance approaches with appropriate weight parameters.

Impact time and angle constrained guidance via range‐based line‐of‐sight shaping

AbstractIn this article, impact time and angle constrained guidance law is proposed using a range‐based line‐of‐sight (LOS) shaping strategy. The relative motion of missile and target is described in a polar coordinate, where the LOS angle can be shaped as a polynomial function of range‐to‐go. The order of the polynomial function is selected according to the number of constraints. Coefficients of the polynomial function are determined by the boundary conditions and solved through a simple integral equation, which facilitates the onboard implementation. Guidance command is designed in a state feedback form to track the shaped trajectory. The proposed guidance law shows some advantages over several similar polynomial shaping based guidance laws. Multiple simulation studies demonstrate the effectiveness of the proposed guidance law.

Rapid Homing Guidance Using Jerk Command and Time-Delay Estimation Method

For certain engagements against small and fast-moving targets at higher altitude, an available total flight time during the terminal homing phase is short due to the limited performance of onboard seekers to detect and track the target, and the autopilot performance of an aerodynamically controlled missile can degrade due to low air density and low dynamic pressure. To increase the lethality of warheads, sometimes terminal zero acceleration, corresponding to zero angle of attack at the instant of interception, is also required. This article proposes a new rapid homing guidance law, which can achieve the terminal zero miss-distance and zero-acceleration response under these severe engagements mentioned earlier. For deriving state feedback form commands that can be implemented to arbitrary order autopilot systems, the polynomial-function-based guidance design method and time-delay estimation method are adopted by introducing a jerk command and more general autopilot dynamics. The characteristics and performance of the proposed guidance law are demonstrated by performing various numerical linear simulations and adjoint simulations, including model uncertainties.

Fractional-Order Sliding Mode Guidance Law for Intercepting Hypersonic Vehicles

This paper addresses the problem of a low-speed missile intercepting a hypersonic vehicle in the longitudinal plane. Firstly, based on the concept of the zero of the angular rate of the line-of-sight (LOS) angle, the guidance system is established by defining the LOS angular rate as the state variable. Secondly, in view of the difficulty of precisely measuring the external disturbance caused by the hypersonic vehicle’s maneuver in the guidance system, a non-homogeneous disturbance observer is designed to precisely estimate the disturbance information. Then, by introducing the fractional-order operator into the sliding surface, a fractional-order fast power reaching (FOFPR) guidance law is proposed based on the fast power reaching law. Simulation examples are carried out in two different maneuver modes of the hypersonic vehicle: the bang-bang maneuver mode and sinusoidal maneuver mode. Besides, comparative experiments are conducted with the proportional navigation (PN) and the integer-order fast power reaching (IOFPR) guidance laws. Finally, the simulation results demonstrate the superiority of the effectiveness of the proposed guidance law.