Desired Impact Angle Research Articles

Modified Generalized Explicit Guidance for Midcourse with Near-Zero Lateral Acceleration in Terminal Phase

By appropriately modifying the generalized explicit guidance and developing it further, an optimal midcourse guidance law is proposed in this paper to ensure terminal impact angle constrained engagement of missiles with near-zero lateral acceleration in the terminal phase. This guidance law generates a desired intermediate point in space as well as the desired angles which needs to be achieved at the end of the midcourse. By reaching this intermediate point with the desired intermediate angles, it ensures that the missile will intercept the target with very less (near zero) acceleration demand in terminal phase with desired impact angles. When both the terminal impact angles are specified, the guidance law solves the constraint equations and find out the intermediate point along with the angles, whereas if only one terminal angle is specified (or both are left free), it generates the intermediate point with missing angle (both angles) which can lead to minimum control effort and then solves that problem.

Sliding mode control based guidance law with impact angle constraint

The terminal guidance problem for an unpowered lifting reentry vehicle against a stationary target is considered. In addition to attacking the target with high accuracy, the vehicle is also expected to achieve a desired impact angle. In this paper, a sliding mode control (SMC)-based guidance law is developed to satisfy the terminal angle constraint. Firstly, a specific sliding mode function is designed, and the terminal requirements can be achieved by enforcing both the sliding mode function and its derivative to zero at the end of the flight. Then, a backstepping approach is used to ensure the finite-time reaching phase of the sliding mode and the analytic expression of the control effort can be obtained. The trajectories generated by this method only depend on the initial and terminal conditions of the terminal phase and the instantaneous states of the vehicle. In order to test the performance of the proposed guidance law in practical application, numerical simulations are carried out by taking all the aerodynamic parameters into consideration. The effectiveness of the proposed guidance law is verified by the simulation results in various scenarios.

Terminal Impact Angle Constrained Guidance Laws Using Variable Structure Systems Theory

In this brief, variable structure systems theory based guidance laws, to intercept maneuvering targets at a desired impact angle, are presented. Choosing the missile's lateral acceleration (latax) to enforce sliding mode, which is the principal operating mode of variable structure systems, on a switching surface defined by the line-of-sight angle leads to a guidance law that allows the achievement of the desired terminal impact angle. As will be shown, this law does not ensure interception for all states of the missile and the target during the engagement. Hence, additional switching surfaces are designed and a switching logic is developed that allows the latax to switch between enforcing sliding mode on one of these surfaces so that the target can be intercepted at the desired impact angle. The guidance laws are designed using nonlinear engagement dynamics for the general case of a maneuvering target.

Sliding-Mode Guidance and Control for All-Aspect Interceptors with Terminal AngleConstraints

In this paper, sliding-mode-control-based guidance laws to intercept stationary, constant-velocity, and maneuvering targets at a desired impact angle are proposed. The desired impact angle, which is defined in terms of a desired line-of-sight angle, is achieved in finite time by selecting the missile's lateral acceleration to enforce terminal sliding mode on a switching surface designed using nonlinear engagement dynamics. The conditions for capturability are also presented. In addition, by considering a three-degree-of-freedom linear-interceptor dynamic model and by following the procedure used to design a dynamic sliding-mode controller, the interceptor autopilot is designed as a simple static controller to track the lateral acceleration generated by the guidance law. Numerical simulation results are presented to validate the proposed guidance laws and the autopilot design for different initial engagement geometries and impact angles.

Optimal impact angle control guidance law considering the seeker’s field-of-view limits

A new optimal guidance problem with impact angle constraint and seeker’s field-of-view limits is investigated for a missile with a strapdown seeker. Impact angle control to satisfy the terminal flight path angle constraint causes missile trajectories to be very curved. Since a strapdown seeker has a narrower field-of-view than a gimbaled seeker, a missile with a strapdown seeker using the impact angle control guidance law can miss its target within the field-of-view during the homing phase, leading to the failure of the mission. Therefore, considering the seeker’s field-of-view limits is a key issue for missiles with strapdown seekers when implementing the impact angle control guidance law. To handle the seeker’s field-of-view limits in the homing guidance problem, a look angle, which is defined as the angle between the velocity vector and the line-of-sight, is considered as an inequality constraint. Based on the optimal control theory with a state variable inequality constraint, the optimal impact angle control guidance law with the seeker’s field-of-view limits is designed. The proposed guidance law is made up of three types of optimal acceleration commands: the first command is to reach the maximum look angle of the seeker, the second is to keep the seeker look angle constant on the constraint boundary, and the third is to intercept the target with the desired impact angle. Nonlinear simulations are performed to validate the proposed approach. In addition, comparisons with other guidance laws considering the limitation of the seeker look angle are carried out via nonlinear simulations, and the results show that the proposed guidance law is more efficient in terms of the control energy.

A Nonlinear Optimal Guidance Law with Terminal Impact Angle Constraint

State-dependent Riccati equation (SDRE) techniques are rapidly emerging as general design methods for nonlinear controllers. A nonlinear optimal guidance law with impact angle constraint is derived for planar engagements to attack stationary targets. The guidance problem is formulated as an infinite horizon nonlinear regulator problem whose equilibrium state is zero. It is solved by SDRE technique and the state weight matrix is chosen as a function of time-to-go. Performance of the guidance law is tested numerically with different initial firing conditions for a realistic GPS/INS guided artillery rocket model with low available lateral acceleration. A reasonable launch angle is helpful to reduce the control effort, and it is acquired by trajectory optimization using genetic algorithm. Results show negligible errors for miss-distance and the desired impact angle. The proposed guidance law is a choice for the guided artillery rocket.

Integrated guidance and control design for missile with terminal impact angle constraint based on sliding mode control

Aimed at the guidance requirements of some missiles which attack targets with terminal impact angle at the terminal point, a new integrated guidance and control design scheme based on variable structure control approach for missile with terminal impact angle constraint is proposed. First, a mathematical model of an integrated guidance and control model in pitch plane is established, and then nonlinear transformation is employed to transform the mathematical model into a standard form suitable for sliding mode control method design. A sufficient condition for the existence of linear sliding surface is given in terms of linear matrix inequalities (LMIs), based on which the corresponding reaching motion controller is also developed. To verify the effectiveness of the proposed integrated design scheme, the numerical simulation of missile is made. The simulation results demonstrate that the proposed guidance and control law can guide missile to hit the target with desired impact angle and desired flight attitude angle simultaneously.

Impact Angle Constrained Guidance Against Nonstationary Nonmaneuvering Targets

G UIDANCE laws with terminal impact angle constraints are widely reported in the literature [1–7]. Proportional navigation guidance (PNG) has been used for deriving impact angle constrained guidance laws for stationary and moving targets. Lu et al. [8] have used PNG in an adaptive guidance law for a hypervelocity impact angle constrained hit at a stationary target. Satisfying impact angle constraint by varying the navigation constant N of the PNG is addressed by Ratnoo and Ghose [9]. In their work [9], a two-stage PNG law is proposed for achieving all impact angles against stationary targets in surface-to-surface engagements. A biased PNG (BPNG) law proposed by Kim et al. [3] has an extra term for annulling the terminal impact angle error together with the conventional line-of-sight rate term for the lateral acceleration command. BPNG law expands the capture region of existing guidance laws against moving targets. However, the performance of BPNG law deteriorates with tail-chase kinds of engagements. The problem of achieving all impact angles against moving targets is addressed here. The idea of a two-stage PNG law, proposed by Ratnoo and Ghose [9], is further investigated and developed for nonstationary nonmaneuvering targets. It should be noted that for different values of N, the PNG law results in a set of impact angles against a moving target. However, studies on classical PNG law [10] reveal that the value of N should be greater than a minimum value for the terminal lateral acceleration demand to be bounded. The achievable set of impact angles is derived for PNG law, with the values of N satisfying the previously mentioned constraint. To achieve the remaining impact angles, an orientation guidance scheme is proposed for the initial phase of the interceptor trajectory. The orientation guidance law is also PNG law, withN being a function of the initial engagement geometry. It is proven that, following the orientation trajectory, the interceptor can switch to N 3 and achieve any desired impact angle in a surface-to-surface engagement scenario.

Nonlinear Model Predictive Spread Acceleration Guidance with Impact Angle Constraint for Stationary Targets

A new technique named as model predictive spread acceleration guidance (MPSAG) is proposed in this paper. It combines nonlinear model predictive control and spread acceleration guidance philosophies. This technique is then used to design a nonlinear suboptimal guidance law for a constant speed missile against stationary target with impact angle constraint. MPSAG technique can be applied to a class of nonlinear problems, which leads to a closed form solution of the lateral acceleration (latax) history update. Guidance command assumed is the lateral acceleration (latax), applied normal to the velocity vector. The new guidance law is validated by considering the nonlinear kinematics with both lag-free as well as first order autopilot delay. The simulation results show that the proposed technique is quite promising to come up with a nonlinear guidance law that leads to both very small miss distance as well as the desired impact angle.

Guidance law to control impact time and angle

This paper proposes a new guidance law to control both impact time and impact angle for a flight vehicle's homing problem, which can be applied for an efficient salvo attack of antiship missiles or a cooperative mission of unmanned aerial vehicles (UAVs). The proposed law can lead vehicles to home on a target at a designated impact time with a prescribed impact angle. It comprises a feedback loop and an additional control command, the first to achieve the desired impact angle with zero miss distance, and the second to control the impact time. Numerical simulations demonstrate the performance of the proposed law in the accuracy of impact angle and impact time

Optimal Guidance Law for Impact Angle Control

In this paper, a set of optimal guidance laws to achieve zero a miss distance as well as a desired impact angle is presented. Each of optimal impact angle control guidance laws is the solution of a linear quadratic optimal control problem in consideration of proper time-varying weighting function into the cost function. This approach is the same way of obtaining “optimal” PNG law with various navigation constants. Proposed optimal impact angle control guidance laws are closely related to the navigation constant of PNG. A simple and practical time-to-go calculation method in consideration of the curved missile trajectory caused by the impact angle control is proposed. Basic properties including error characteristics of proposed laws are also investigated.