Optimal impact time and angle control guidance with limited speed

This paper proposes a three-dimensional (3-D) impact time and angle control guidance (ITACG) considering the limit of vehicle's speed to realize the spatio-temporal interception against a moving target. Firstly, a relative coordinate system with its origin attached on the target is constructed, based on which the engagement kinematics is formulated. Then, the guidance law is designed based on the prediction-correction concept in the reference frame, naturally decoupling into normal and tangential directions for impact angle and time constraint, respectively. In the normal channel, the final impact angle of PN guidance is predicted, and then the deviation between the predicted and expected angle is eliminated by leveraging the optimal control theory. Simultaneous strike is guaranteed from transforming the predetermined attack time to the desired relative velocity considering the speed limit. Employing the principles of the optimal control theory, the optimal analytical solutions for both normal and tangential control are derived. In addition, the allowed impact time that considers the vehicle’s speed limit is calculated to judge whether the desired attack time is feasible. The proposed guidance law is proved its feasibility and effectiveness by numerical simulation and comparison in various engagements.