Spatial-temporal cooperative guidance without active speed control

The spatial-temporal coordinated strike is an extremely challenging task, which becomes more prominent when autonomous speed adjustment is not achievable. In this paper, a high-precision spatial-temporal collaborative guidance law is designed for the class of vehicles unable to control speed actively, such as ballistic and boost-glide vehicles. Firstly, a flight-time control term is added to the biased proportional navigation guidance (BPNG) with impact angle constraints. The dynamic model for the impact time error is developed under the small-angle assumption. A nonlinear disturbance observer is designed to estimate and actively compensate for unmodeled errors resulting from the small-angle assumption. A finite-time convergent cooperative guidance (FTCCG) is developed to achieve impact time cooperation in finite time. The accuracy of time cooperation depends on the precision of the estimated remaining flight time, which can be obtained from the high-precision remaining flight time estimator based on neural networks proposed in this paper. Finally, the correctness, effectiveness, and superiority of the proposed methods are verified through simulation experiments. The spatial-temporal cooperative guidance proposed has a spatial cooperation error of less than 0.002 s, a temporal cooperation error of less than 0.05°, and an off-target distance of less than 0.099 m. Compared with existing methods, it achieves comparable spatial coordination accuracy, while its temporal coordination accuracy is improved by one order of magnitude.