Biased Proportional Navigation Guidance Law Research Articles

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.

Distributed target-encirclement guidance law for cooperative attack of multiple missiles

The target-encirclement guidance problem for many-to-one missile-target engagement scenario is studied, where the missiles evenly distribute on a target-centered circle during the homing guidance. The proposed distributed target-encirclement guidance law can achieve simultaneous attack of multiple missiles in different line-of-sight directions. Firstly, the decentralization protocols of desired line-of-sight angles are constructed based on the information of neighboring missiles. Secondly, a biased proportional navigation guidance law that can arbitrarily designate the impact angle is cited. The missiles can achieve all-aspect attack on the target in an encirclement manner by combining the biased proportional navigation guidance law and dynamic virtual targets strategy. Thirdly, the consensus protocol of simultaneous attack is designed, which can guarantee that all missiles’ time-to-go estimates achieve consensus asymptotically, and the convergence of the closed-loop system is proved strictly via the Lyapunov stability theory. Finally, numerical simulation results demonstrate the performance and feasibility of the proposed distributed target-encirclement guidance law in different engagement situations.

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.

Coverage-based cooperative guidance strategy against highly maneuvering target

Considering highly maneuvering target, a novel cooperative guidance strategy, which aims to make multiple missiles' joint reachable sets cover the target evasion region, is proposed. The assumed engagement scenario is that multiple missiles separate with each other at the beginning of homing phase and then cooperatively intercept the highly maneuvering target which cannot be intercepted by single missile due to insufficient maneuverability. Firstly, for biasing the reachable sets of different missiles to cover different subintervals of target maneuvering range as expected, a biased proportional navigation guidance law (BPN) is designed by introducing the virtual aiming point. Secondly, for the missile-team without communication capability, the minimum relative maneuverability superiority and minimum team size for covering the whole target maneuvering range are derived based on the BPN respectively, and one open-loop cooperative guidance strategy is proposed with an acceptable assumption about the handover errors of midcourse guidance. While for the missile-team with communication capability, a novel coordinating variable is designed and the corresponding closed-loop guidance strategy is proposed. Numerical simulations with different target maneuver modes are presented to verify the guidance performance of the proposed cooperative guidance strategy.

Generalized optimal impact-angle-control guidance with terminal acceleration response constraint

To study the optimal impact-angle-control guidance problem with multiple terminal constraints, a generalized optimal impact-angle-control guidance law with terminal acceleration response constraint (GOIACGL-TARC) is proposed. In the deriving, a time-to-go − nth power weighted object function is adopted to derived the GOIACGL-TARC and a general expression of GOIACGL-TARC is presented. Based on the general expression of GOIACGL-TARC, three guidance laws, GOIACGL-TARC1/TACC0/TACC1 are proposed and the inheritance relationship between GOIACGL-TACC0/TACC1/TARC1 and the conventional optimal guidance law with impact angle constraint is demonstrated. Performance analysis of the proposed guidance laws shows that in the case of GOIACGL-TACC0, the terminal acceleration is not zero at n = 0 and only as n > 0, the terminal acceleration converges to zero; in the case of GOIACGL-TACC1 and GOIACGL-TARC1, GOIACGL-TARC1 can guarantee the acceleration response to reach the exactly zero value but GOIACGL-TACC1 cannot, which can only guarantee the acceleration command to reach the exactly zero value. It is pointed out that compared with the biased proportional navigation guidance law, GOIACGL-TARC1 has an outstanding guidance performance in acceleration response, miss distance, and terminal impact angle error.

Biased PNG With Terminal-Angle Constraint for Intercepting Nonmaneuvering Targets Under Physical Constraints

A biased proportional navigation guidance law, considering the seeker's look angle and acceleration capability limits, for impact-angle-control against nonmaneuvering targets is proposed. The proposed law consists of two time-varying biases: One is to achieve the desired impact angle within the command limit; the other is to keep the look angle constant for not exceeding the boundary value. Under physical constraints, the maximum achievable impact angle is obtained for practical implementation. The performance of the proposed law is demonstrated through nonlinear simulations.

Midcourse Guidance Law Based on High Target Acquisition Probability Considering Angular Constraint and Line-of-Sight Angle Rate Control

Random disturbance factors would lead to the variation of target acquisition point during the long distance flight. To acquire a high target acquisition probability and improve the impact precision, missiles should be guided to an appropriate target acquisition position with certain attitude angles and line-of-sight (LOS) angle rate. This paper has presented a new midcourse guidance law considering the influences of random disturbances, detection distance restraint, and target acquisition probability with Monte Carlo simulation. Detailed analyses of the impact points on the ground and the random distribution of the target acquisition position in the 3D space are given to get the appropriate attitude angles and the end position for the midcourse guidance. Then, a new formulation biased proportional navigation (BPN) guidance law with angular constraint and LOS angle rate control has been derived to ensure the tracking ability when attacking the maneuvering target. Numerical simulations demonstrates that, compared with the proportional navigation guidance (PNG) law and the near-optimal spatial midcourse guidance (NSMG) law, BPN guidance law demonstrates satisfactory performances and can meet both the midcourse terminal angular constraint and the LOS angle rate requirement.

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 direction control, is designed in the line-of-sight (LOS) rotation coordinate system. The theoretical analysis 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.

A biased proportional navigation guidance law with large impact angle constraint and the time-to-go estimation

For large impact angle control problem (here, the “large impact angle” means the impact angle in the closed interval from −180° to 180°), estimating the time-to-go accurately is the key of impact time and impact angle control guidance (ITIACG). The objectives of this paper are to construct a new impact angle control guidance (IACG) law suitable for large impact angle control and present a time-to-go estimation procedure for the new IACG law suitable for designing ITIACG law. The constructed IACG law is a biased proportional navigation guidance law with large impact angle constraint, the rule of the cosine of the lead angle in the biased term is to guarantee that the lead angle remains in the open interval from −90° to 90°, which is required in the development of time-to-go estimation procedure. To estimate the time-to-go, by introducing a self-convergent angle named as alfa, the closed equations of motion are transformed to a different form, which can be solved conveniently under the assumption of small lead angle. For the case of large lead angle, the time interval of time-to-go is partitioned into n segments, the maximum increment of lead angle is supposed to be a small angle in each segment, the transformed closed equations of motion can be expressed as function of alfa angle and solved analytically. A geometric approach is proposed to determine conservatively a suitable alfa angle to guarantee that the maximum increment of lead angle is a small angle in each segment. The time-to-go estimation procedure for the new IACG law are illustrated. Simulations are performed to verify the effectiveness of the proposed IACG law and the accuracy of the time-to-go estimation procedure.