This paper proposes a feedback guidance algorithm for a rocket to change its instantaneous impact point (IIP) to a desired location under the uncertainty on the engine cutoff time. The proposed guidance law consists of three phases: 1) IIP change phase, 2) mode switching phase, and 3) IIP maintaining phase. The IIP change phase moves the IIP toward the desired IIP to minimize the fuel consumption. Analytic expressions describing the change in IIP due to the external acceleration (e.g., thrust) is derived and used for this phase. Solely using this phase can cause the miss targeting under the uncertainty on engine cut-off time (e.g., delay in engine cut-off). This issue can be dealt with by introducing the IIP maintaining guidance that keeps the IIP in the current position in the presence of the thrust. The acceleration command for maintaining the IIP is about 90 degree tilted relative to the command obtained in the IIP change phase. The mode switching phase makes the necessary transition between the two acceleration commands associated with the two different objectives (i.e., IIP change and the IIP maintaining) while taking the angular rate limitation of the rocket into account. The developed algorithm is demonstrated by implementing the algorithm in the first stage of a reusable launch vehicle and comparing the results with the open-loop optimal solution.
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