Federated learning offers a natural way for multiple robots to jointly improve manipulation policies without requiring centralized access to training demonstrations. However, non-IID task and environment distributions can induce representation drift and mutually incompatible robot-policy updates, making naive parameter aggregation destructive. We present FedDRMan, a federated subspace-guided distillation framework for heterogeneous robot manipulation. At each communication round, the server model provides a frozen teacher for local behavior cloning, while low-rank multimodal subspace and action-distribution distillation preserve globally useful representation geometry and policy behavior. To address heterogeneous aggregation, FedDRMan groups clients by update compatibility and maintains a persistent model for each cluster. The server then spectrally rebalances each compatible aggregate to mitigate attenuation of weaker task-relevant robot-policy update directions. Extensive experiments on LIBERO across diverse non-IID settings, heterogeneity levels, client participation variation, together with ablations and aggregation analyses, show that FedDRMan substantially improves knowledge transfer and consistently outperforms strong federated baselines achieving a peak mean success rate of 80.7%, 11.6 percentage points above the strongest evaluated federated baseline.

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