Sinusoidal Guidance

Abstract

This work presents a novel three-point guidance strategy that simultaneously achieves a desired impact angle, launch angle, impact time, and maximum lateral acceleration against a stationary target. The guidance strategy uses four sinusoidal harmonics of different amplitudes to construct an interceptor trajectory that satisfies all the mission specifications. A new geometric constant G for sinusoids is proposed, which requires only the interceptor’s line-of-sight angles from the launcher and the target for computation. Correspondingly, a geometric rule is developed—the interceptor follows the desired sinusoidal trajectory by maintaining G=0 throughout the engagement. A trajectory design algorithm to determine the desired sinusoidal trajectory based on the mission specifications is presented. A proportional-derivative controller is applied to implement the proposed geometric rule, and analytical expressions for the controller gains are defined. The efficacy of the guidance strategy is investigated via various simulation scenarios. It is shown that the developed guidance law is robust to the initial heading errors and interceptor dynamics.