Learning Geometry-Aware Virtual Fixtures From Sparse Demonstrations

Learning from demonstratins (LfD) is usually performed over Euclidean spaces, while the robot state, e.g. orientation, naturally evolves over curved spaces. Therefore, to ensure natural, complex motion generation, we investigate learning from demonstrations over Riemannian manifolds that are capable of encoding both position and orientation data. Here, geodesic paths provide for natural motion between two arbitrary points within the manifold. We propose to numerically estimate geodesics via neural ordinary differential equations, mitigating large computational overhead of existing approaches. Finally, these geodesics can be decoded back into the original task space before deploying on the robot. In this extended abstract, we discuss the architecture of our framework, provide some initial insights from our simulation experiments, including comparison to other geodesic computation mechanisms, and discuss the challenges and prospects for future work.

We present STT-LfD, a unified Learning from Demonstration (LfD) framework that integrates motion learning with control for unknown Euler-Lagrange systems. Unlike traditional decoupled approaches that track a fixed reference, the proposed method treats demonstrations as a data-driven safety specification. Using heteroscedastic Gaussian Processes, STT-LfD learns Spatiotemporal Tubes (STTs) as an intent envelope that capture time-varying precision requirements of a task. A closed-form feedback controller then enforces these learned constraints while respecting actuator limits, without requiring explicit system identification. The approach preserves the temporal structure of demonstrations, remains computationally efficient, and avoids explicit system identification. Hardware experiments on a mobile robot and a 7-DOF manipulator show that it outperforms baselines in robustness to disturbances and computational speed.

In this paper, we study the problem of manipulation skill acquisition for performing construction activities consisting of repetitive tasks (e.g., building a wall or installing ceiling tiles). Our approach involves setting up a simulated construction activity in a Virtual Reality (VR) environment, where the user can provide demonstrations of the object manipulation skills needed to perform the construction activity. We then exploit the screw geometry of motion to approximate the demonstrated motion as a sequence of constant screw motions. For performing the construction activity, we generate the sequence of manipulation task instances and then compute the joint space motion plan corresponding to each instance using Screw Linear Interpolation (ScLERP) and Resolved Motion Rate Control (RMRC). We evaluate our framework by executing two representative construction tasks: constructing brick walls and installing multiple ceiling tiles. Each task is performed using only a single demonstration, a pick-and-place action for the bricks, and a single ceiling tile installation. Our experiments with a 7-DoF robot in both simulation and hardware demonstrate that the approach generalizes robustly to arbitrarily long construction activities that involve repetitive motions and demand precision, even when provided with just one demonstration. For instance, we can construct walls of arbitrary layout and length by leveraging a single demonstration of placing one brick on top of another.