Semi-analytical optimal control for spacecraft constrained hovering over tumbling object - Feng, Zhan; Bai, Xue; Jiang, Jun; Zhu, Jun; Xu, Ming (Advances in space research, 2025)
•Two-layer semi-analytical control optimization for constrained hovering over tumbling object.•A direct method utilizing only state variables as optimization variables.•Satisfy state inequality constraints by state transformation of saturation function.•Avoid numerical integration by analytical solution of optimal reconfiguration problem. Spacecraft proximity operations often demand fuel-intensive constrained hovering near tumbling objects, subject to complex path constraints. This paper presents a semi-analytical method for constrained optimal hovering over an arbitrarily tumbling object. The proposed method leverages the analytical solution of the unconstrained optimal reconfiguration problem to achieve an analytical gradient of the energy cost. The proposed method rewrites the optimal hovering problem as a discrete path-planning problem consisting of two layers of optimization that guarantee the optimality. The outer layer is a numerical optimization on the waypoint sequence of the discrete nodes. A bijective transformation using saturation functions is performed to eliminate the constraints on the optimization variables of the outer-layer optimization. The inner layer is to analytically solve the optimal trajectories connecting two adjacent waypoints. The number of optimization variables is reduced compared to the pseudospectral method. Numerical simulations demonstrate that the proposed method achieves significantly higher computational efficiency than the pseudospectral method while maintaining solution accuracy.