Optimal 6-DOF Control for Servicing and Assembly at Sun–Earth L2

This paper presents a six-degree-of-freedom (6-DOF) fuel-optimal trajectory optimization framework using indirect methods, where both translational and rotational motions are governed by thruster-based actuation. The formulation couples translational and rotational dynamics, which guarantees local optimality of the spacecraft’s roto-translational motion. A representative thruster configuration is used to simulate various mission scenarios, including nominal operations and thruster failure cases. The methodology is demonstrated in the context of a hypothetical large-aperture space telescope in-space servicing and assembly (ISA) mission in a Sun–Earth L2 halo orbit. The paper also introduces an optimal attitude control strategy for the evolving space structure using the thrusters of a distributed multi-agent CubeSat swarm as attitude control actuators. Time-varying inertial properties and no-thrust time interval constraints are incorporated into the optimal attitude control formulation using smooth time-triggered activation functions and continuation. Angular constraints are also incorporated, using additional Lagrange multipliers, to prevent solar exposure of sensitive instruments. Simulation results demonstrate that the proposed 6-DOF formulation achieves fuel-optimal solutions under nominal conditions and generates feasible trajectories under prescribed thruster failure scenarios. The attitude control framework also successfully maintains the orientation of the evolving space structure while satisfying the prescribed constraints, thereby ensuring safe assembly and operations in deep-space ISA missions.