Acceleration Profile Shapeable Catenary-based Guidance with Arbitrary Impact Time and Angle Constraints

Guidance poses a significant issue in aerospace vehicle development. Simultaneous impacts and higher lethality necessitate constraints on impact time and angles, posing a substantial obstacle to effective guidance law design. Similarly, the flexibility and maneuverability of aerospace vehicles, which require a designable acceleration profile, are equally essential issues in guidance law design. Therefore, to overcome the limited selectable constraint ranges and the challenges of shaping acceleration profiles in existing guidance laws, without sacrificing their penetration and cooperation capabilities, a three-stage catenary-based guidance law is proposed that considers constrained impact and robustness to external disturbances. To begin with, the desired launch angle and initial velocity direction of the catenary are enforced during the first stage, which uses a circular arc. Subsequently, the impact time constraint is met in the second catenary-based stage, and the final stage employs an additional circular arc to enforce the desired impact angle. Using the proposed analytical geometric rules, trajectory parameters are determined explicitly. Meanwhile, a robust guidance law is developed, with all constraints met. The proposed guidance law requires no numerical calculations, nonlinear model linearization, or reliance on time-to-go error estimation, making it convenient to implement. Furthermore, the proposed guidance law extends the range of available time constraints from the minimum to infinity and the range of angle constraints from 0 degrees to 360 degrees, thereby addressing the issue of a wide range of spatiotemporal multi-constraints. The adaptability issue arising from an extensive range of impact time constraints and arbitrary angle constraints is addressed by a shapeable acceleration profile, enabling the maximum acceleration value or peak time to be adjusted to meet mission requirements. Various disturbed-engagement scenarios are simulated, and numerous analyses are conducted to evaluate the effectiveness and robustness of the proposed sliding mode control guidance law.