Multi-objective trajectory optimization for spaceborne antennas with nonlinear coupling using hp-adaptive pseudospectral discretization

Spaceborne antennas are essential for remote sensing, deep-space communication, and Earth observation, yet their trajectory planning is complicated by nonlinear base-manipulator coupling and antenna flexibility. To address these challenges, this paper proposes a multi-objective trajectory optimization framework. The system dynamics capture both nonlinear rigid-flexible coupling and antenna deformation through a reduced-order formulation. To enhance discretization efficiency, a predictive-terminal hp-adaptive pseudospectral method is employed, assigning collocation density based on task-phase characteristics: finer resolution is applied to dynamic segments requiring higher accuracy, especially near the terminal phase. This enables efficient transcription of the continuous-time problem into a Nonlinear Programming Problem (NLP). The resulting NLP is then solved using a multi-objective optimization strategy based on the nondominated sorting genetic algorithm II, which explores trade-offs among antenna pointing accuracy, energy consumption, and structural vibration. Numerical results demonstrate that the proposed method achieves a reduction of approximately 14.0 % in control energy and 41.8 % in peak actuation compared to a GPOPS-II baseline, while significantly enhancing vibration suppression. The resulting Pareto front reveals structured trade-offs and clustered solutions, offering robust and diverse options for precision, low-disturbance mission planning.