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.

Movement primitives are trainable parametric models that reproduce robotic movements starting from a limited set of demonstrations. Previous works proposed simple linear models that exhibited high sample efficiency and generalization power by allowing temporal modulation of move-ments (reproducing movements faster or slower), blending (merging two movements into one), via-point conditioning (constraining a movement to meet some particular via-points) and context conditioning (generation of movements based on an observed variable, e.g., position of an object). Previous works have proposed neural network-based motor primitive models, having demonstrated their capacity to perform tasks with some forms of input conditioning or time-modulation representations. However, there has not been a single unified deep movement primitive's model proposed that is capable of all previous operations, limiting neural movement primitive's potential applications. This paper proposes a deep movement primitive architecture that encodes all the operations above and uses a Bayesian context aggregator that allows a more sound context conditioning and blending. Our results demonstrate our approach can scale to reproduce complex motions on a larger variety of input choices compared to baselines while maintaining operations of linear movement primitives provide.