Fuel-optimal Boost-Back Guidance via Successive Convexification with a Terminal Constraint for ReusableLaunch Vehicles
Abstract
This paper proposes a fuel-optimal boost-back guidance algorithm for reusable launch vehicles using successive convexification (SCvx). The guidance problem is formulated as a free-final-time optimal control problem with a terminal instantaneous impact point (IIP) constraint. This constraint depends only on the burnout position and velocity and enforces that the predicted ballistic impact point coincides with the target under a spherical-Earth, central-gravity model. By handling the coast analytically, the formulation confines trajectory discretization to the powered phase, reduces the problem size, and explicitly represents the bang-off structure. It also avoids the accumulation of discretization defects over the long coast and the need to resolve the burn-coast transition on a single-phase grid. Two terminal constraint formulations are considered: the closed-form Keplerian IIP and the eccentric-anomaly-based F&G solution. Their Jacobians are evaluated using complex-step differentiation. The algorithm is validated in a return-to-launch-site case study based on the Falcon 9 CRS-10 mission. Comparisons with a single-phase full-trajectory formulation, a closed-form guidance law incorporating the flight path angle rate, and an offline trajectory optimization benchmark assess the trade-off between computational cost and optimality. The results demonstrate near-optimal propellant consumption with reduced computational cost.
Related
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- On the convexification of a bilinearly constrained set with a common variable
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BibTeX
@misc{kim2026fueloptimal,
title = {{Fuel-optimal Boost-Back Guidance via Successive Convexification with a Terminal Constraint for ReusableLaunch Vehicles}},
author = {Mingyeom Kim and Changhyun Kang and Dohyun Lee and Byeong-Un Jo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28759},
eprint = {2609.28759},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28759},
}
RIS
TY - UNPB
TI - Fuel-optimal Boost-Back Guidance via Successive Convexification with a Terminal Constraint for ReusableLaunch Vehicles
AU - Mingyeom Kim
AU - Changhyun Kang
AU - Dohyun Lee
AU - Byeong-Un Jo
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28759
UR - https://arxiv.org/abs/2609.28759
AB - This paper proposes a fuel-optimal boost-back guidance algorithm for reusable launch vehicles using successive convexification (SCvx). The guidance problem is formulated as a free-final-time optimal control problem with a terminal instantaneous impact point (IIP) constraint. This constraint depends only on the burnout position and velocity and enforces that the predicted ballistic impact point coincides with the target under a spherical-Earth, central-gravity model. By handling the coast analytically, the formulation confines trajectory discretization to the powered phase, reduces the problem size, and explicitly represents the bang-off structure. It also avoids the accumulation of discretization defects over the long coast and the need to resolve the burn-coast transition on a single-phase grid. Two terminal constraint formulations are considered: the closed-form Keplerian IIP and the eccentric-anomaly-based F&G solution. Their Jacobians are evaluated using complex-step differentiation. The algorithm is validated in a return-to-launch-site case study based on the Falcon 9 CRS-10 mission. Comparisons with a single-phase full-trajectory formulation, a closed-form guidance law incorporating the flight path angle rate, and an offline trajectory optimization benchmark assess the trade-off between computational cost and optimality. The results demonstrate near-optimal propellant consumption with reduced computational cost.
ER -