Precise impact time and angle guidance strategy under time-varying velocity

In this paper, a new guidance strategy is proposed for achieving precise control of time-varying velocity aircraft with impact time and angle constraints. The traditional guidance law assumes that the velocity of the aircraft is constant, but in the actual scenario, the velocity of the aircraft changes with time, thus affecting the guidance accuracy with impact time and angle constraints. To overcome these difficulties, a guidance strategy consisting of trajectory generation and trajectory tracking is proposed. Firstly, the reference trajectory is constructed based on the Bézier spiral, which naturally satisfies the impact angle constraint. Then, the control problem of the impact time is transformed into an adjustment problem of the trajectory length. The expression of the Bézier spiral that is only related to the curvature is derived, and a new lemma describing the relationship between trajectory length and curvature is found. Furthermore, the differential flatness property of the control system is explored to design a trajectory tracking method for the Bézier spiral trajectory, which applies feedback linearization of the system through higher-order information. Finally, numerical simulations confirm the superiority of the proposed method and validate the analytic findings.