Generalized circular impact time guidance

To effectively control impact time and ensure terminal acceleration converges to zero under the look angle constraint, this paper proposes a generalized circular impact time guidance law, providing a deeper insight into circular guidance. The proposed guidance law is formulated based on a generalized circular guidance equation that offers an explicit solution for the time to go. The convergence of both miss-distance and terminal acceleration to zero is proven using Bernoulli number theory. Impact time control is achieved by employing a fixed-time convergent controller that guides the look angle to track desired values. Additionally, the look angle constraint is addressed by incorporating a well-designed function into the acceleration. The proposed guidance law does not require estimated time to go and small-angle assumptions for its implementation. By predicting the mean speed, the proposed guidance law remains valid for missiles with varying speeds. Furthermore, the planar results are extended to three-dimensional scenarios by adopting the concept of the engagement plane. Nonlinear simulations demonstrate the effectiveness, advantages, and robustness of the proposed guidance law in the presence of disturbances and autopilot lag.