Proportional Navigation Guidance Law with Variable Coefficient Gravity Compensation

Based upon a discussion on the merits and limitations of proportional navigation（PN）guidance law in which constant gravity compensation is included as a part,a counterpart having varying compensations,which changes with pitching angle and line-of-sight angle,is substituted.Flight trajectory simulation over a submissile model is conducted,resulting in increased impact angle,shorter miss distance,smaller maximum normal overload and narrower terminal angle of attack.

Design of Closed Loop Optimal Guidance Law Using Neural Networks

It is generally impossible to obtain the analytic optimal guidance law for complex nonlinear guidance systems of homing missiles,and the open loop optimal guidance law is often obtained by numerical methods,which can not be used directly in practice.The neural networks are trained off line using the optimal trajectory of the missile produced by the numerical open loop optimal guidance law,and then,the converged neural networks are used on line as the feedback optimal guidance law in real time.The research shows that different selections of the neural networks inputs,such as the system state variables or the rate of LOS(line of sight),may have great effect on the performances of the guidance systems for homing missiles.The robustness for several guidance laws is investigated by simulations,and the modular neural networks architectures are used to increase the approximating and generalizing abilities in the large state space.Some useful conclusions are obtained by simulation results.

A novel biased proportional navigation guidance law for close approach phase

A novel biased proportional navigation guidance （BPNG） law is proposed for the close approach phase, which aims to make the spacecraft rendezvous with the target in specific relative range and direction. Firstly, in order to describe the special guidance requirements, the concept of zero effort miss vector is proposed and the dangerous area where there exists collision risk for safety consideration is defined. Secondly, the BPNG, which decouples the range control and direc- tion control, is designed in the line-of-sight （LOS） rotation coordinate system. The theoretical anal- ysis proves that BPNG meets guidance requirements quite well. Thirdly, for the consideration of fuel consumption, the optimal biased proportional navigation guidance （OBPNG） law is derived by solving the Schwartz inequality. Finally, simulation results show that BPNG is effective for the close approach with the ability of evading the dangerous area and OBPNG consumes less fuel compared with BPNG.

Impact time control using biased proportional navigation for missiles with varying velocity

A feasible guidance scheme with impact time constraint is proposed for attacking a stationary target by missiles with time-varying velocity.The main idea is to replace the constant velocity with the future mean velocity;therefore, the existing time-to-go estimation algorithm of the proportional navigation guidance law can be improved to adapt to varying conditions.In order to obtain the prediction of the velocity profile, the velocity differential equation to the downrange is derived, which can be numerically integrated between the current downrange and the target position by the on-board computer.Then, a third-order polynomial is introduced to fit the velocity profile in order to calculate the future mean velocity.At the beginning of each guidance loop, the future mean velocity is predicted and the time-to-go information is updated, based on which a novel biased proportional navigation guidance law is established to achieve the impact time constraint.Finally,numerical simulation results verified the effectiveness of the time-to-go estimation algorithm and the proposed law.

Guidance law with impact time and impact angle constraints

A novel closed-form guidance law with impact time and impact angle constraints is pro- posed for salvo attack of anti-ship missiles, which employs missile＇s normal acceleration （not jerk） as the control command directly. Firstly, the impact time control problem is formulated as tracking the designated time-to-go （the difference between the designated impact time and the current flight time） for the actual time-to-go of missile, and the impact angle control problem is formulated as tracking the designated heading angle for the actual heading angle of missile. Secondly, a biased proportional navigation guidance （BPNG） law with designated heading angle constraint is constructed, and the actual time-to-go estimation for this BPNG is derived analytically by solving the system differential equations. Thirdly, by adding a feedback control to this constructed BPNG to eliminate the time-to-go errorthe difference between the standard time-to-go and the actual time-to-go, a guidance law with adjustable coefficients to control the impact time and impact angle simultaneously is developed. Finally, simulation results demonstrate the performance and feasibility of the proposed approach.

Aerial vehicle guidance based on passive machine learning technique

Purpose-The purpose of this paper is to develop a new guidance scheme for aerial vehicles based on artificial intelligence.The new guidance scheme must be able to intercept maneuvering targets with higher probability and precision compared to existing algorithms.Design/methodology/approach-A simulation setup of the aerial vehicle guidance problem is developed.A model-based machine learning technique known as Q-learning is used to develop a new guidance scheme.Several simulation experiments are conducted to train the new guidance scheme.Orthogonal arrays are used to define the training experiments to achieve faster convergence.A wellknown guidance scheme known as proportional navigation guidance(PNG)is used as a base model for training.The new guidance scheme is compared for performance against standard guidance schemes like PNG and augmented proportional navigation guidance schemes in presence of sensor noise and computational delays.Findings-A new guidance scheme for aerial vehicles is developed using Q-learning technique.This new guidance scheme has better miss distances and probability of intercept compared to standard guidance schemes.Research limitations/implications-The research uses simulation models to develop the new guidance scheme.The new guidance scheme is also evaluated in the simulation environment.The new guidance scheme performs better than standard existing guidance schemes.Practical implications-The new guidance scheme can be used in various aerial guidance applications to reach a dynamically moving target in three-dimensional space.Originality/value-The research paper proposes a completely new guidance scheme based on Q-learning whose performance is better than standard guidance schemes.

Vision-based bio-inspired guidance law for small aerial vehicle

During predation, a flying insect can form a stealth flight path. This behavior is called motion camouflage. Based on the study results of this behavior, the perception and neurology of flying insects, a novel bio-inspired guidance law is proposed for the terminal guidance for small aerial vehicle with charge-coupled device imaging seekers. The kinematics relationship between a small aerial vehicle and target is analyzed, and a two-dimensional guidance law model is established by using artificial neural networks. To compare with the proportional guidance law, the numerical simulations are carried out in the vertical plane and in the horizontal plane respectively. The simulation results show that the ballistic of the small aerial vehicle is straighter and the normal acceleration is smaller by using the bio-inspired guidance law than by using the proportional guidance law. That is to say, the bio-inspired guidance law just uses the information of the target from the imaging seeker,but the performance of it can be better than that of the proportional guidance law.

Ideal proportional navigation for exoatmospheric interception

Ideal proportional navigation （IPN） is a natural choice for exoatmospheric interception for its mighty capture capability and ease of implementation. The closed-form solution of two- dimensional ideal proportional navigation was conducted in previous public literature, whereas the practical interception happens in the three-dimensional space. A novel set of relative dynamic equations is adopted in this paper, which is with the advantage of decoupling relative motion in the instantaneous rotation plane of the line of sight from the rotation of this plane. The dimension-reduced IPN is constructed in this instantaneous plane, which functions as a three-dimensional guidance law. The trajectory features of dimension-reduced IPN are explored, and the capture regions of dimension-reduced IPN with limited acceleration against nonmaneuvering and maneuvering targets are analyzed by using phase plane method. It is proved that the capture capability of IPN is much stronger than true proportional navigation （TPN）, no matter the target maneuvers or not. Finally, simulation results indicate that IPN is more effective than TPN in exoatmospheric interception scenarios.

Coning motion instability of spinning missiles induced by the delay of strap-down seeker

The strap-down seeker,which combines the seeker's and the onboard gyro's measurements to obtain the target information,has been extensively applied by spinning missiles.The response delay of the strap-down seeker,a novel factor that could result in crosscoupling between the acceleration commands in the pitch and yaw channels and subsequently cause the significant deterioration in dynamic stability of the spinning missile equipped with a rate loop,is noted in this paper.The sufficient and necessary stability conditions are also analytically established based on the system equation with complex coefficient,which are further verified by numerical simulations.It could be indicated that the response delay of the strap-down seeker will greatly deteriorate the dynamic stability of the whole guidance system designed by the conventional method.It is also noticed from analysis that the stable region of the combined guidance coefficient is shrunken significantly with the increase of the spinning rate.