This paper presents a nonlinear three-dimensional (3D) guidance law for homing missiles with field-of-view (FOV) constraint to achieve impact time and angle control against a stationary target. Specifically, a guidance error vector and its nonlinear error dynamics are first developed. The desired impact time and angle can be satisfied as long as the guidance error converges to zero before the interception. The proposed nonlinear error dynamics is then enhanced with an auxiliary function to address the FOV constraint, and the prescribed-time control technique is employed to obtain a feedback guidance law. The guidance framework in this paper is rigorously derived under the original 3D missile-target kinematics model, without decoupling the engagement geometry into two mutually orthogonal planes. Furthermore, different from existing similar studies, the proposed guidance law does not require explicit time-to-go estimation and numerical iterations, which avoids estimation error and allows for convenient implementation.

A major challenge in homing guidance is that accurately predicting the time to go for missiles is generally difficult, which limits the practical application of a certain class of guidance laws with impact-time constraints or cooperative capabilities. To address this issue, a generalized method referred to as the time-to-go inversion guidance is presented, where the time to go is first specified as an explicit function and then the corresponding guidance law is inversely derived. By employing this new method, a variety of guidance laws and their globally accurate time-to-go solutions can be developed, regardless of whether the impact-angle constraint is considered or not. Different from all existing studies, the proposed method addresses the problem of time-to-go estimation without relying on any linearizing approximations or numerical iterations. To enhance the practicality of the proposed method, it is augmented with bias commands to result in either the impact time control guidance law or the impact time and angle control guidance law. Numerical simulation results demonstrate the higher accuracy, larger feasible solution region, and lower computational demand of the proposed guidance laws even for the missiles with nonconstant speeds.

One major challenge for autonomous attitude takeover control for on-orbit servicing of spacecrafts is that an accurate dynamic motion model of the combined vehicles is highly nonlinear, complex and often costly to identify online, which makes traditional model-based control impractical for this task. To address this issue, a recursive online sparse Gaussian Process (GP)-based learning strategy for attitude takeover control of noncooperative targets with maneuverability is proposed, where the unknown dynamics are online compensated based on the learnt GP model in a semi-feedforward manner. The method enables the continuous use of on-orbit data to successively improve the learnt model during online operation and has reduced computational load compared to standard GP regression. Next to the GP-based feedforward, a feedback controller is proposed that varies its gains based on the predicted model confidence, ensuring robustness of the overall scheme. Moreover, rigorous theoretical proofs of Lyapunov stability and boundedness guarantees of the proposed method-driven closed-loop system are provided in the probabilistic sense. A simulation study based on a high-fidelity simulator is used to show the effectiveness of the proposed strategy and demonstrate its high performance.

This paper introduces a new methodology for designing guidance laws that directly shape the pattern of the heading error as desired. To this end, the concept of generalized finite-time convergence error dynamics is introduced. By leveraging this specific error dynamics, the proposed guidance laws can ensure that the heading error decreases according to the desired pattern while guaranteeing finite-time convergence. The resulting guidance laws take the form of proportional navigation guidance laws, but with a previously unexplored time-varying gain. The paper conducts a theoretical analysis to examine the properties of the proposed guidance laws, including the closed-form solutions of the heading error and acceleration command. Compared to existing methods, the proposed guidance laws provide a more direct and versatile approach to addressing various guidance operational goals. Accordingly, several illustrative examples are presented to demonstrate the process of designing guidance laws using the proposed approach. Furthermore, numerical simulations are conducted to validate the characteristics of the designed guidance laws.