Multiple Impedance Control (MIC) in Space Free-Flying Robot (SFFR) is necessary to ensure simultaneous accurate tracking and safe interactions; however, the computation related to grasp in these interactions has become a computational bottleneck, which intensifies with increasing Degrees of Freedom (DoF) and makes on-line control and real-time implementation difficult. Although Machine Learning-based Multiple Impedance Control (ML-MIC) has partly reduced this computational burden, the design of the Machine Learning (ML) network still relies on trial-and-error and does not guarantee optimal reduction of computations. In this paper, an Optimal Machine Learning-based Multiple Impedance Control (OML-MIC) is presented, in which the explicit computation related to the grasp matrix is replaced with a nonlinear approximation based on a Radial Basis Function Neural Network (RBFNN), and the network architecture is optimized using a Genetic Algorithm (GA) to minimize computational cost under accuracy constraints. The proposed method systematically determines the optimal network structure and, while preserving the physical dynamics of the grasp, eliminates the need for heavy linear-algebra operations.

Simulation results for planar manipulation of an object by a dual-arm SFFR show that, while meeting the MIC control specifications, OML-MIC reduces the number of multiplication operators by 73.15%, the number of addition operators by 41.27%, and the hidden-layer computations of ML-MIC by 50%. As a result of the structured optimal design, error analysis with statistical quantitative metrics confirms that accuracy remains within the safe-interaction range. These results indicate that integrating architecture optimization with learning-based control provides a reliable path to precise, real-time interaction on robotic platforms with limited resources.