1. Instantaneous Impact Point (IIP) Guidance
Instantaneous impact point (IIP) stands for a predicted location on the ground where a rocket is expected to touchdown after free-fall. The IIP remains unchanged during the flight if no external force, such as thrust, is exerted on the rocket. It is a critical metric in rocket operations for safety.
IIP guidance is a steering logic that moves the IIP to the desired location on the ground (see Fig. 1). This research first establishes the IIP dynamics, which describes the behavior of the IIP on the (rotating) ground with respect to the rocket's state and external forces. Based on the dynamics, we derive an acceleration command in an analytic form that ensures the IIP moves along the shortest ground path. Furthermore, we enhance the IIP guidance to address the potential risk on the ground caused by engine cut-off failure (see Fig. 2). This is achieved by incorporating IIP hold guidance and a mode-switching algorithm. The novelty of the proposed algorithms lies in their outstanding performance and computational efficiency. Case studies on Falcon 9 demonstrate the effectiveness of the proposed algorithms.
Fig. 1: IIP guidance
Fig. 2: Engine-cutoff insensitive IIP guidance
2. Midcourse Guidance for a Ballistic Interceptor
A long-range interceptor faces challenges in designing its guidance system due to a coasting phase required to reach a ballistic target. The complexity arises from the fact that the final state is not the target directly, but rather to achieve a specific state that ensures the interceptor reaches the target after the coasting arc.
This study aims to tackle the issue by introducing a novel mid-course guidance algorithm called virtual impact point (VIP) steering. The new algorithm sets a hit altitude at which the interceptor is expected to hit the target and defines a hit sphere. The virtual impact point is where the interceptor and the hit sphere intersect. Based on the equations of motion for the VIP expressed in analytic forms, we derive the closed-form acceleration command. This command enables the VIP to move toward the predicted impact point (PIP) and synchronizes the arrival time of two missiles at the PIP. Additionally, this algorithm is able to effectively control the burn time by adjusting the hit altitude and thus applicable to a solid rocket.
Fig. 3: Concept of the proposed mid-course guidance algorithm
Fig. 4: Concept of boost-back burn
3. Boost-back Guidance for a Reusable Launch Vehicle
The landing sequence of a reusable launch vehicle (RLV) includes three burns for a soft landing: boost-back burn (optional for downrange landing), re-entry burn, and terminal landing burn. The goal of the boost-back burn is to re-orient a reusable stage towards the landing site, which can be interpreted as the change of the IIP to the vicinity of the landing site. Minimizing propellant consumption during this burn leads to significant fuel savings as the total impulse is the greatest among the three burns.
This research proposes two types of guidance algorithms, each has its pros and cons, applicable to the boost-back burn of an RLV: 1) Improve IIP guidance and 2) minimum impulse guidance. We first improve the conventional IIP guidance by adopting a flight path angle rate control scheme to prevent the vehicle from descending which degrades the performance. Subsequently, we develop the minimum impulse guidance whose subroutine calculates the required velocity to target the desired IIP while minimizing the velocity increment. It shows an outstanding performance (the optimality gap is less than 1%) but involves iterative procedures and faces challenges in imposing various constraints. In contrast, while the improved IIP guidance does not involve any iterative procedures and various constraints can be considered, the performance is relatively inferior, and a user-defined parameter is necessary.