We introduce GeoSACS, a geometric framework for shared autonomy (SA). In variable environments, SA methods can be used to combine robotic capabilities with real-time human input in a way that offloads the physical task from the human. To remain intuitive, it can be helpful to simplify requirements for human input (i.e., reduce the dimensionality), which create challenges for to map low-dimensional human inputs to the higher dimensional control space of robots without requiring large amounts of data. We built GeoSACS on canal surfaces, a geometric framework that represents potential robot trajectories as a canal from as few as two demonstrations. GeoSACS maps user corrections on the cross-sections of this canal to provide an efficient SA framework. We extend canal surfaces to consider orientation and update the control frames to support intuitive mapping from user input to robot motions. Finally, we demonstrate GeoSACS in two preliminary studies, including a complex manipulation task where a robot loads laundry into a washer.
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