Identifying an appropriate task space that simplifies control solutions is important for solving robotic manipulation problems. One approach to this problem is learning an appropriate low-dimensional action space. Linear and nonlinear action mapping methods have trade-offs between simplicity on the one hand and the ability to express motor commands outside of a single low-dimensional subspace on the other. We propose that learning local linear action representations that adapt based on the current configuration of the robot achieves both of these benefits. Our state-conditioned linear maps ensure that for any given state, the high-dimensional robotic actuations are linear in the low-dimensional action. As the robot state evolves, so do the action mappings, ensuring the ability to represent motions that are immediately necessary. These local linear representations guarantee desirable theoretical properties by design, and we validate these findings empirically through two user studies. Results suggest state-conditioned linear maps outperform conditional autoencoder and PCA baselines on a pick-and-place task and perform comparably to mode switching in a more complex pouring task.

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