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To address the issue of intercepting maneuvering targets at a specific time, a polynomial guidance method for impact-time control is proposed in this paper. Based on the relative virtual framework and the classical differential geometry curve theory, such method is divided into two parts: 1) the design of the relative trajectory-length-control (RTLC) guidance law against virtual stationary targets, and 2) the design of the prediction algorithms based on the guidance law or its characteristics. The former realizes RTLC, and the latter establishes the relationship between the desired relative trajectory length-to-go and the desired time-to-go, thus implementing impact-time control. Furthermore, based on the analytical properties of the guidance law in the relative arc-length domain, its performance, characteristics, and allowable impact time are analyzed. Finally, the effectiveness of the proposed guidance method and the validity of the theoretical findings are verified by numerical simulations results.

To improve the autonomous flight capability of endo-atmospheric flight vehicles, such as cruise missiles, drones, and other small, low-cost unmanned aerial vehicles (UAVs), a novel minimum-effort waypoint-following differential geometric guidance law (MEWFDGGL) is proposed in this paper. Using the classical differential geometry curve theory, the optimal guidance problem of endo-atmospheric flight vehicles is transformed into an optimal space curve design problem, where the guidance command is the curvature. On the one hand, the change in speed of the flight vehicle is decoupled from the guidance problem. In this way, the widely adopted constant speed hypothesis in the process of designing the guidance law is eliminated, and, hence, the performance of the proposed MEWFDGGL is not influenced by the varying speed of the flight vehicle. On the other hand, considering the onboard computational burden, a suboptimal form of the MEWFDGGL is proposed to solve the problem, where both the complexity and the computational burden of the guidance law dramatically increase as the number of waypoints increases. The theoretical analysis demonstrates that both the original MEWFDGGL and its suboptimal form can be applied to general waypoint-following tasks with an arbitrary number of waypoints. Finally, the superiority and effectiveness of the proposed MEWFDGGL are verified by a numerical simulation and flight experiments.

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 varying-speed 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.