Deep-space exploration missions typically span many years and demand substantial financial and operational resources. Enhancing these missions with opportunistic encounters of additional small bodies, such as asteroids or comets, can significantly increase their overall scientific return with limited incremental cost. As the catalog of known minor bodies in the Solar System rapidly expands, the incentive to enable additional flybys, even for missions with unrelated primary objectives, is becoming increasingly compelling.

Mathematically, a flyby appears as an interior-point equality constraint in an optimal control problem, enforcing coincidence between the spacecraft state and the small body’s ephemeris. In the augmented system, Pontryagin’s Minimum Principle (PMP) implies that such a constraint induces a discontinuity (a “jump”) in the position costate. Conventional forward-shooting schemes must explicitly guess this jump vector, for which no physically grounded prior information is available, thereby increasing the sensitivity of the resulting two-point boundary value problem (TPBVP) and often leading to divergence. Despite their clear relevance for space-mission design, optimal control problems with interior-point equality constraints thus remain classically difficult, particularly within indirect, shooting-based approaches.

To address this limitation, this paper develops a PMP-based forward–backward shooting framework that reformulates the interior constraint through a rigorous re-derivation of the necessary conditions for optimality. The trajectory is partitioned into two phases that meet at the flyby epoch, and the coupled boundary conditions, including the costate discontinuities, are derived explicitly from Pontryagin’s theory. The first phase is integrated forward from departure, and the second backward from arrival, while the spacecraft state is constrained to match the target body’s ephemeris at the interface, thereby enforcing the interior constraint by construction. In this formulation, the position costates are allowed to be discontinuous at the interface without explicit parameterization of the jump vector. The transversality and matching conditions emerge then naturally from the re-derived optimality system, so the interior-point constraint is satisfied without introducing additional optimization variables and without increasing the dimensionality of the original forward–backward TPBVP.

We show that the proposed forward–backward shooting framework applies to a broad class of dynamical models and performance indices, thereby providing a general treatment of interior costate-jump conditions in optimal control. The theoretical formulation is complemented by numerical simulations for both fuel-optimal electric-propulsion trajectories and time-optimal solar-sail trajectories inspired by the fictitious “Altaira” planetary system introduced by JPL in the context of the 13th edition of the Global Trajectory Optimization Competition. The results indicate that the forward–backward scheme achieves higher convergence rates than conventional single-shooting and multiple forward-shooting strategies, while substantially reducing the sensitivity associated with costate discontinuities. This reveals a robust and practically viable pathway to implicitly enforcing interior-point equality constraints in optimal control problems without explicit jump parametrization.