Geometric skill learning paradigm for cellular space robots: Achieving cross-task and cross-configuration generalization

Cellular Space Robots (CSRs) function as self-reconfigurable systems with variable topologies and possess great potential for spatial non-cooperative target acquisition. However, task uncertainty and large workspaces pose significant challenges to control strategy generalization. Traditional reinforcement learning often designs policies for specific configurations, which can cause limited transferability across configurations and tasks. To address this issue, an innovative geometric skill learning paradigm is proposed, which construct a configuration-independent capability space using spinor theory, decouple the robot’s physical capabilities from its configurations, and decompose tasks into atomic skill primitives. The Bellman operator of the geometric skill is formulated using optimal transport theory, and its contraction mapping property is rigorously proven to ensure the algorithmic convergence and uniqueness of the optimal policy. On this basis, a task-independent performance bound theorem is derived and further extended to configuration and task generalization theory. The quadratic generalization error of this method is substantially lower than that of traditional algorithms under cross-configuration and zero-sample transfer conditions. The proposed method enabled universal control with only a few training samples. The simulation results indicate that it is effectively applied to 7-DOF and 5-DOF CSRs, achieving capture success rates of 96.3 % and 93.6 %, and significantly exceeds baseline algorithms in zero-shot generalization across tasks and configurations. This study establishes a complete framework from geometric distribution learning to generalization theory, providing a theoretical foundation for self-reconfigurable robotic applications and promoting the transition of robot learning from behavioral imitation to capability acquisition with substantial application potential.