Learning State Conditioned Linear Mappings for Low-Dimensional Control of Robotic Manipulators

Identifying an appropriate task space can simplify solving robotic manipulation problems. One solution is deploying control algorithms in a learned low-dimensional action space. Linear and nonlinear action mapping methods have trade-offs between simplicity and the ability to express motor commands outside of a single low-dimensional subspace. We propose that learning local linear action representations can achieve both of these benefits. Our state-conditioned linear maps ensure that for any given state, the high-dimensional robotic actuation is linear in the low-dimensional actions. As the robot state evolves, so do the action mappings, so that necessary motions can be performed during a task. These local linear representations guarantee desirable theoretical properties by design. 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.