From Chemical Reaction to Orbital Assembly: Fast Cost Evaluation and Global Energy Minimization

The high computational complexity of target assignment and trajectory planning in on-orbit assembly tasks limits its development. This paper develops a cross-scale framework for target assignment and global energy optimization inspired by chemical reactions. Aiming at the target assignment problem, according to the theory of molecular graph energy, an innovative rapid cost evaluation method based on the configuration transfer matrix energy is proposed. The method directly quantifies the difference in energy consumption of the assignment strategies by calculating the traces of sparse matrices, avoiding the redundant trajectory optimization costing iterations in traditional methods. For the trajectory planning problem, this paper draws on the idea of manifold dimension reduction for the minimum energy path of a chemical reaction to map the cluster configuration to the manifold space. The high-dimensional trajectory optimization problem is transformed into an energy-optimal path solution on the manifold. The effectiveness of the target assignment cost evaluation method is proved by theoretical derivation and simulation calculation. Finally, the advantages of the manifold algorithm in terms of low energy consumption, low initial guessing dependence, and fast computation are verified by comparative analysis.