GeoSACS: Geometric Shared Autonomy via Canal Surfaces

TL;DR

GeoSACS presents a geometric shared-autonomy approach that encodes robot trajectories as canal surfaces learned from as few as two demonstrations, and allows users to apply 2D corrections on cross-sections to steer 6-DOF motion in real time. By integrating orientation data and introducing correction frames aligned with a global axis, it addresses the data-efficiency and input-mapping challenges of traditional LfD-SA methods. The method is demonstrated in two preliminary tasks (targeted object relocation and laundry loading), showing feasible execution with modest demonstration requirements and correction-time budgets, and highlights orientation benefits and backtracking for repetitive tasks. This work provides a practical framework for intuitive, low-data shared autonomy in everyday robotic assistance, with potential impact on home-care and assistive robotics.

Abstract

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.

Figures (6)

• Figure 1: GeoSACS proposes a SA framework to encode robot motions as canal surfaces while allowing users to provide corrections on the cross-sections of the canal to change the way the robot navigates the canal. Using GeoSACS, users can control robots in real task of daily living, such as filling a laundry machine.
• Figure 2: Circular cross-section canal surfaces with the same directrix curve and different radii functions. The cross-section is fixed to a circular shape, and the radii can change along the directix as shown in (b) and (c).
• Figure 3: Frame evolution of Bishop frames (left) and our correction frames (right) along a curve with tangent vector illustrated in yellow. Highlighted points illustrate how our correction frames exhibit increased consistency and reduced directional changes compared to Bishop frames.
• Figure 4: Visual representation of the trajectory reproduction phase from frame $s{-}1$ to frame $s$.
• Figure 5: Applying a correction on $C_{s}$ (blue arrow marked on the joystick control pad). The x and y axes marked on the joystick control pad control the corrections on $C_{s}$ along $\textbf{x}_{s}$ and $\textbf{y}_{s}$ respectively. The blue arrows marked on $C_{s}$ indicate how the input of the joystick affects $p_{s}$ to reach $p^{'}_{s}$.