Convex Optimization for Spacecraft Attitude Alignment of Laser Link Acquisition Under Uncertainties

This paper addresses the critical multiple-uncertainty challenge in laser link acquisition for space gravitational wave detection missions—a key bottleneck where spacecraft attitude alignment for laser link establishment is perturbed by inherent random disturbances in such missions, while also needing to balance ultra-high attitude precision, fuel efficiency, and compliance with engineering constraints. To tackle this, a convex optimization-based attitude control strategy integrating covariance control and free terminal time optimization is proposed. Specifically, a stochastic attitude dynamics model is first established to explicitly incorporate the aforementioned random disturbances. Subsequently, an objective function is designed to simultaneously minimize terminal state error and fuel consumption, with three key constraints (covariance constraints, pointing constraints, and torque saturation constraints) integrated into the convex optimization framework. Furthermore, to resolve non-convex terms in chance constraints, this study employs a hierarchical convexification method that combines Schur’s complementary theorem, second-order cone relaxation, and Taylor expansion techniques. This approach ensures lossless relaxation, renders the optimization problem computationally tractable without sacrificing solution accuracy, and overcomes the shortcomings of traditional convexification methods in handling chance constraints. Finally, numerical simulations demonstrate that the proposed method adheres to engineering constraints while maintaining spacecraft attitude errors below 1 μrad under environmental uncertainties. This study provides a convex optimization solution for laser link acquisition in space gravitational wave detection missions considering uncertainty conditions, and its framework can be extended to the optimal design of other stochastically uncertain systems.