Desired Impact Angle Research Articles

Impact speed and angle constrained guidance law for unpowered gliding vehicle

In this paper, a novel guidance law is proposed which can achieve the desired impact speed and angle simultaneously for unpowered gliding vehicles. A guidance law with only impact angle constraint is used to produce the guidance profile, and its convergence in the varying speed scenario is proved. A relationship between flight states, guidance input and impact speed is established. By applying the fixed-time convergence control theory of error dynamics, an impact speed corrector is built with the above guidance profile, which can implement impact speed correction without affecting the impact angle constraint. Numerical simulations with various impact speed and angle constraints are conducted to demonstrate the performance of the proposed guidance law, and the robustness is also verified by Monte Carlo tests.

Optimal impact angle guidance law with barrier constraint

This paper presents an optimal guidance law for missile to achieve desired impact angles on a stationary target while accommodating the barrier constraint. The proposed guidance law consists of two parts: a baseline guidance command for intercepting the target with desired impact angles, and a bias command to prevent collision with the barrier. Specifically, the baseline guidance command is derived by solving a linearized optimal control problem, and its explicit trajectory solution is also obtained for collision estimation. The bias command is designed using a novel guidance error that is defined based on the geometrical relationship between the barrier and the proposed explicit trajectory solution. The new guidance law can be easily implemented to a variety of practical engagement geometries, resulting in successful collision avoidance and minimal control efforts. Its effectiveness and robustness are demonstrated via extensive numerical simulations.

Polynomial shaping based three-dimensional impact angle and field-of-view constrained guidance

This paper proposes a polynomial-based three-dimensional (3D) impact angle-constrained guidance law considering the seeker's field-of-view (FOV) bound. The guidance laws are derived using nonlinear coupled dynamics of the interceptor-target engagement against stationary as well as constant velocity targets. Line-of-sight (LOS) orientations between the interceptor and the target in both pitch and yaw planes are shaped as two cubic polynomial functions of relative range. An explicit expression for the look angle of the interceptor is acquired in terms of the LOS polynomials. This expression facilitates the embodiment of the FOV constraint in the boundary conditions inflicted on the polynomials. A system of equations with the eight unknown coefficients is obtained by employing the appropriate launch and terminal conditions of the interceptor-target engagement. Reference LOS angle and lead angle profiles are generated using the calculated coefficients, complying to which the interceptor achieves a zero miss distance with desired impact angle and FOV constraints. A tracking controller is then designed using a nonlinear control technique that enables the interceptor to follow reference lead angle profiles in mutually orthogonal planes. Unlike the already existing guidance strategies for 3D impact angle and FOV-constrained target interception, the proposed nonlinear guidance strategy is designed without the use of linearization or decoupling. Moreover, no switching logic or multi-phase guidance structures are employed in the proposed guidance strategy, which eliminates possible jumps in the guidance command. The effectiveness of the proposed guidance law is validated using numerical simulations, along with a comparison study with the existing strategy.

Optimal sliding mode guidance law against maneuvering target with impact angle constraint

In this paper, an optimal sliding mode guidance law with impact angle constraint is proposed against maneuvering targets. Firstly, the impact angle frame for a static target is extended to a maneuvering target. Then, in this impact angle frame, the optimal reaching law of sliding mode is proposed to design an optimal sliding mode guidance law which is robust to target maneuvers and satisfies an impact angle constraint. The optimal sliding mode guidance law with impact angle constraint is also extended to the three-dimensional case. Numerical simulations in different scenarios with a realistic missile model show that the guidance law can intercept a maneuvering target with a desired impact angle, and the control effort is close to the optimal value, which verifies that the proposed optimal sliding mode guidance law has both robustness and optimality.

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.

Integrated guidance and control with impact angle and general field-of-view constraints

This paper investigates the problem of integrated guidance and control (IGC) law design with impact angle and general field-of-view (FOV) constraints. Firstly, the IGC model for intercepting non-maneuvering moving target is parameterized by state-dependent coefficient matrices. The nominal IGC law for intercepting the target with the desired impact angle is obtained by solving the state-dependent Riccati equation. Secondly, since the relative degrees of the general FOV constraints with respect to the IGC model exceed one, the high-order control barrier functions are constructed. The satisfaction of the FOV constraints is equivalent to ensuring that the superlevel sets defined by the barrier functions are forward invariant, which is converted into affine constraints on the control input. The nominal IGC law is modified in a minimally invasive way by quadratic programming. Then, the proposed method is extended to the case of intercepting maneuvering target by leveraging a relative coordinate frame. Finally, numerical simulations are conducted to verify the effectiveness of the proposed method.

Sinusoidal Guidance

This work presents a novel three-point guidance strategy that simultaneously achieves a desired impact angle, launch angle, impact time, and maximum lateral acceleration against a stationary target. The guidance strategy uses four sinusoidal harmonics of different amplitudes to construct an interceptor trajectory that satisfies all the mission specifications. A new geometric constant G for sinusoids is proposed, which requires only the interceptor’s line-of-sight angles from the launcher and the target for computation. Correspondingly, a geometric rule is developed—the interceptor follows the desired sinusoidal trajectory by maintaining G=0 throughout the engagement. A trajectory design algorithm to determine the desired sinusoidal trajectory based on the mission specifications is presented. A proportional-derivative controller is applied to implement the proposed geometric rule, and analytical expressions for the controller gains are defined. The efficacy of the guidance strategy is investigated via various simulation scenarios. It is shown that the developed guidance law is robust to the initial heading errors and interceptor dynamics.

Three-dimensional field-of-view-constrained guidance law against maneuvering target with intercept angle control

Most existing three-dimensional (3D) impact angle guidance laws against maneuvering target focus on terminal-angle-constrained guidance without considering the field-of-view (FOV) limit. In this study, a 3D nonsingular FOV-constrained guidance strategy with the desired impact angles is proposed. The analytical expression between the desired impact angles and terminal light-of-sight angles is derived by integrating the transition matrix in the interception time with the collision triangle theory. A novel fixed-time sliding mode surface is presented and, based on it, guidance commands are generated. The radial basis function neural networks are combined with composite intelligent learning to improve the approximation precision of target maneuvering. Furthermore, a barrier Lyapunov function is used in the pitch plane to satisfy the FOV constraint. For the capturability analysis, the analytical achievable impact sets are calculated. Simulations are demonstrated to verify the effectiveness and robustness of the proposed guidance strategy.

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.

Distributed observer‐based fixed‐time cooperative guidance law against maneuvering target

SummaryThis paper presents a fixed‐time cooperative guidance law for leader‐following missiles, comprising one leader missile with the target seeker and several seeker‐less follower missiles. The aim is to achieve a simultaneous attack on a maneuvering target at desired impact angles. First, a guidance law with impact angle control for the leader missile against a maneuvering target is proposed based on nonsingular fast terminal sliding mode (NFTSM) control algorithm. Then, the design of cooperative guidance law for the follower missiles is composed of two parts: along the follower‐to‐leader line of sight (LOS) direction, the guidance command derived from bi‐homogeneous property is designed to ensure that the follower‐leader ranges keep proportional consensus with the range‐to‐go of the leader missile, thus avoiding the estimation of time‐to‐go (); in the normal follower‐to‐leader LOS direction, considering the relative impact angle constraints which is determined by the leader LOS angle, the guidance command is proposed based on predefined‐time sliding mode control method. What's more, a distributed fixed‐time observer is designed for the follower missiles to compensate for unobtainable leader missile information. The fixed‐time stability of the proposed methods is demonstrated using the Lyapunov theory and bi‐homogeneous property. Finally, simulation results confirm the effectiveness and superiority of the proposed fixed‐time cooperative guidance law with leader‐following strategy.

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.

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.

Three-dimensional event-triggered fixed-time cooperative guidance law against maneuvering target with the constraint of relative impact angles

In order to improve the flexibility and reduce the energy consumption of cooperative guidance laws considering the impact angle constraint, this paper proposes a three-dimensional event-triggered fixed-time cooperative guidance law with the constraint of relative impact angles. First, for the purpose of avoiding the precision degradation due to the estimation error of time-to-go especially facing a maneuvering target, the range-to-go and velocity along the line-of-sight (LOS) are taken as the coordination variables for achieving time-cooperative guidance. Secondly, instead of assigning specific desired impact angles for each missile, only the consensus errors of relative impact angles are utilized as the coordination variables for achieving space-cooperative guidance, which can avoid continually maneuvering for maintaining the constant desired impact angles, thus reducing the fuel consumption. Next, the guidance laws along the LOS and perpendicular to the LOS are developed, and the event-triggering mechanisms are designed to reduce the update frequency of cooperative guidance commands, thus further reducing the energy consumption. To guarantee the convergence rate, the fixed-time control theory is adopted and the stability of proposed event-triggered cooperative guidance laws are rigorously proved. In addition, it is also proved that there is no Zeno behavior when implementing the proposed event-triggered cooperative guidance laws. Finally, numerical simulations indicate that the strictly simultaneous attack is achieved and the constraint of relative impact angles is satisfied. Comparative studies demonstrate that the computation burden of cooperative guidance commands is relaxed and the fuel consumption is reduced by the proposed event-triggered cooperative guidance laws with the constraint of relative impact angles.

Impact Angle Controlled Integrated Guidance and Control with Input and State Constraints

A novel integrated guidance and control scheme is derived for STT missile with strict constraints as desired impact angle, input saturation, and partial system state in three- dimensional space. The backstepping technique and command filter are adopted for achieving input constraints, and the improved compensation signals are constructed to correct tracking errors. The integral barrier Lyapunov function is introduced to prevent the partial system states from exceeding a predefined interval. A modified extended state observer is employed to strengthen the robustness of the system further. Theoretically, the required properties of a closed-form system are proved by Lyapunov theory in detail. Numerical simulations are conducted to exhibit the performance and robustness of the IGC scheme fully.

Three-Dimensional Impact Angle and Time Control Guidance Law Based on Two-Stage Strategy

In this article, a 3-D nonlinear guidance law is developed for attacking a stationary target with desired impact angle and time. The guidance law is divided into two stages—impact angle control guidance (IACG) and proportional navigation guidance (PNG). In the IACG stage, a sliding-mode guidance law is established to guarantee the satisfaction of the impact angle constraint, and in the second stage, the 3-D PNG law is applied to ensure zero miss distance. The switch between the IACG and the PNG stages is determined by a guidance parameter related to the impact time constraint. By the virtue of Newton iteration method, an appropriate guidance parameter is obtained by solving an implicit nonlinear equality after a small number of iterations. Several numerical simulations are conducted to verify the feasibility and effectiveness of the proposed guidance law under different scenarios.

Analytic Solution for Nonlinear Impact-Angle Guidance Law with Time-Varying Thrust

This paper presents an impact-angle guidance law of unmanned aerial vehicles (UAVs) with time-varying thrust in a boosting phase. Most current research on impact-angle guidance law assumes that UAV speed is constant in terms of controlled thrust. However, the UAV speed and the acceleration in a boosting phase keep changing because of time-varying thrust. Environmental factors and manufacturing process error may prohibit accurately predicting vehicle-thrust profiles. We propose a nonlinear impact-angle guidance law by analytically solving second-order error dynamics with nonlinear time-varying coefficients. The proposed analytic solution enables one to update guidance gains according to initial and current states so that desired impact angle is met while the miss-distance error is reduced. We prove the finite-time error convergence of the proposed guidance law with the Lyapunov stability theory. Various simulation studies are performed to verify the proposed guidance law.

High-precision computational guidance in terminal phase with impact angle, lead angle and lateral acceleration constraints

This paper proposes a high-precision three-dimensional nonlinear optimal computational guidance law in the terminal phase of an interceptor that ensures near-zero miss-distance as well as the desired impact angle. Additionally, it achieves these ambitious objectives while ensuring that the lead angle and lateral acceleration constraints are not violated throughout its trajectory. This ensures (i) the target does not escape the field of view of its seeker at any point in time (a state constraint) and (ii) it does not demand unreasonable lateral acceleration that cannot be generated (a control constraint). The guidance problem is formulated and solved using newly proposed Path-constrained Model Predictive Static Programming (PC-MPSP) framework. All constraints, both equality and inequality, are equivalently represented as linear constraints in terms of the errors in the control history, thereby reducing the complexity and dimensionality of the problem significantly. Coupled with a quadratic cost function in control, the problem is then reduced to a standard quadratic optimization problem with linear constraints, which is then solved using the computationally efficient interior-point method. Results clearly demonstrate the advantage of the proposed guidance scheme over the conventional Biased PN as well as the recently proposed GENeralized EXplicit (GENEX) guidance techniques. Numerical simulations with variation in initial conditions and Monte–Carlo simulations with parametric uncertainty demonstrate the robustness of the proposed guidance scheme.

Field-of-View Constrained Three-Dimensional Impact Angle Control Guidance for Speed-Varying Missiles

This article develops a three-dimensional (3-D) impact angle control guidance law with the field-of-view (FOV) constraint. The impact error is defined as the difference between the predicted impact angle by proportional navigation guidance and the desired impact angle. The derived guidance command enables the impact angle error trajectory to follow a desired impact angle error dynamic. It can guarantee that the impact error converges to zero before the time of interception. Meanwhile, zero terminal guidance command is achieved, and the FOV constraint is always met during the guidance process. Furthermore, the trajectory of a guided missile is not affected by the variation of missile speed even under the FOV constraint, which reveals that the impact angle control performance is independent of time-varying missile speed. Numerical simulations are conducted to demonstrate the effectiveness of the proposed guidance law.

Sliding mode control based impact angle constrained guidance with predefined convergence time

This paper proposes predefined-time convergent guidance schemes that can drive the pursuer on a collision course corresponding to the target interception from a pre-specified impact direction, irrespective of initial engagement geometries. The target interception at the desired impact angle is first transformed into a problem of controlling the line-of-sight angle and its rate. Then, guidance commands are derived using sliding mode control (SMC) to ensure the convergence of corresponding errors to zero within a predefined time. A nonlinear disturbance observer is used to estimate the target’s maneuver, and the estimation error is treated as an uncertainty while rejecting its effect by virtue of SMC. Guidance commands are also derived for the case where the target maneuver is completely unknown except for its upper bound. It was shown that the gain could be selected based on the maximum bound on target maneuver to enforce sliding mode on the chosen surface, and thus guarantees target interception at a pre-specified impact angle, provided the closing speed of the engagement is positive. Owing to the use of a nonlinear framework while deriving pursuer guidance commands, the proposed guidance strategies remain valid even for engagements with large initial deviations where schemes based on linearized dynamics may fail or have degraded performance. The efficacy of the proposed guidance methods is validated through simulations for the pursuers having constant speed and time-varying speed, for various engagement geometries. The results of proposed strategies are compared with those of existing guidance and shown to be superior.

Impact angle-based engagement classification and nonlinear guidance against targets with a speed advantage

In this paper, we propose Lyapunov theory-based nonlinear guidance scheme to achieve an angle-constrained interception of a high-speed target (targets with speed advantage). An impact angle based classification between head-on and head-pursuit interception geometries is first proposed to uniquely match a desired impact angle to a corresponding desired line-of-sight (LOS) angle for successful target interception. The proposed guidance scheme comprises two phases, namely orientation and LOS tracking phases. The orientation phase corrects the interceptor's lead angle based on the desired interception geometry whenever required. The LOS tracking phase then enables the tracking of desired LOS angle by enforcing the error is LOS angle to converge onto a manifold with finite-time convergent properties. The applicability of the proposed guidance strategy is validated using numerical simulations for various engagement geometries, in the presence of autopilot, for constant speed as well as time-varying speed interceptors. The performance of the proposed guidance scheme is also compared with existing ones against high-speed targets, and is found to be superior.