Optimal midcourse trajectory planning considering the capture region

An optimal midcourse trajectory planning approach that considers the capture region（CR） of the terminal guidance is proposed in this article based on the Gauss pseudospectral method（GPM）. Firstly, the planar CR of the proportional navigation in terminal guidance is analyzed and innovatively introduced in the midcourse trajectory planning problems, with the collision triangle（CT） serving as the ideal terminal states parameters of the midcourse phase, and the CR area serving as the robustness against target maneuvers. Secondly, the midcourse trajectory planning problem that considers the path, terminal and control constraints is formulated and the well-developed GPM is used to generate the nominal trajectory that meets the CR demands. The interceptor will reshape the trajectory only when the former CR fails to cover the target, which has loosened the critical demand for frequent trajectory modification. Finally, the simulations of four different scenarios are carried out and the results prove the effectiveness and optimality of the proposed method.

Capturability of 3D RTPN guidance law against true-arbitrarily maneuvering target with maneuverability limitation

The capturability of the Three-Dimensional(3D)Realistic True Proportional Navigation(RTPN)guidance law is thoroughly analyzed.The true-arbitrarily maneuvering target is considered,which maneuvers along an arbitrary direction in 3D space with an arbitrary but upperbounded acceleration.The whole nonlinear relative kinematics between the interceptor and target is taken into account.First,the upper-bound of commanded acceleration of 3D RTPN is deduced,using a novel Lyapunov-like approach.Second,the reasonable selection range of navigation gain of3D RTPN is analyzed,when the maneuver limitation of interceptor is considered.After that,a more realistic definition of capture is adopted,i.e.,the relative range is smaller than an acceptable miss-distance while the approaching speed is larger than a required impact speed.Unlike previous researches which present Two-Dimensional(2D)capture regions,the inequality analysis technique is utilized to obtain the 3D capture region,where the three coordinates are the closing speed,transversal relative speed,and relative range.The obtained capture region could be taken as a sufficient-but-unnecessary condition of capture.The new theoretical findings are all given in explicit expressions and are more general than previous results.

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.

New Result on Interception of Stationary Targets at Arbitrary Time-Varying Speed

This paper develops a novel approach and some main results on the varying-speed missile guided by pure proportional navigation(PPN)against a stationary target in the planar interception problem.The missile kinematic equation is established in the arc-length domain based on the differential geometry theory,which eliminates the influence of time-varying missile speed.Then,the closed-form solutions of line-of-sight(LOS)rate,leading angle,closing speed,and curvature command are derived in the arc-length domain.The performance of the varyingspeed missile is analyzed,including the maximum relative distance,maximum curvature command,accurate path-to-go,and curvature increment.Additionally,the capture region is obtained considering the missile maneuvering acceleration limit.These new theoretical results could be extended to improve the performance of existing guidance laws designed under the constant-speed assumption.