Learning Geometry-Aware Virtual Fixtures From Sparse Demonstrations
Authors: Maximilian Mühlbauer, Marcella Piacentino, Raffaella Mancino, Paolino De Risi, Bernhard Weber, Margarida Campos, Thomas Hulin, Sylvain Calinon, +5 more
Organizations: German Aerospace Center (DLR), Robotics and Mechatronics Center (RMC), Münchener Str. 20, 82234 Weßling, Germany. · Department of Computer Engineering, Technical University of Munich, Friedrich-Ludwig-Bauer-Str. 3, Garching, Germany. · C.R.E.A.T.E. Consorzio di Ricerca per l’Energia, l’Automazione e le Tecnologie dell’Elettromagnetismo, Universit`a degli Studi di Napoli Federico II, Napoli, Italy · Department of Mechanical, Energy, Management and Transportation Engineering (DIME), University of Genova, Genoa, Italy · Department of Electrical Engineering and Information Technology (DIETI), University of Naples Federico II, 80131 Naples, Italy · Instituto Superior T´ecnico, University of Lisbon, Portugal. · Idiap Research Institute, Martigny, Switzerland. · ´Ecole Polytechnique F´edérale de Lausanne (EPFL), Switzerland.
In many teleoperation applications, collecting a large number of demonstrations as required for traditional probabilistic learning from demonstration (LfD) approaches may not be feasible. To still give operators the ability to intuitively create trajectories as Virtual Fixtures (VFs), we propose to leverage a motion prior in the learning process. Particularly, by using Linear Quadratic Tracking (LQT), users are able to define guiding trajectories from the demonstration of just a few via points. To account for orientation guidance, we further reformulate classical LQT on Riemannian manifolds, introducing an additional geometric prior. Through a probabilistic interpretation of the LQT solution, we derive a covariance estimate at each trajectory point which we use to modulate the stiffness of the resulting fixture, resulting in strong guidance around the via points and softer guidance when far away. The covariance information is also used to define a validity region of the fixture, allowing the operator to leave its influence area and conduct unmodeled tasks. We evaluate the proposed Riemannian LQT formulation in a set of toy examples and the full framework on a cutting task requiring high precision in a minimally invasive surgery setting on the da Vinci Research Kit (dVRK).
Figures & tables
Fig. 4 : Plots for writing the letter “B” of the handwriting dataset [ 29 ] on S2 . We fit the GMM using 10 Gaussians and extract 10 via points using GMR for LQT ; all these Gaussians are depicted with their mean and covariance ellipsoid. For the LQT , we furthermore plot its velocity as blue and the command at each time step as green arrows. Note how it passes through the edge of the covariance ellipsoids only for high control cost, trading accuracy for control cost, while approximating the original trajectory more precisely with decreasing control cost.
Fig. 5 : Plots of a circular trajectory for our proposed Riemannian LQT and a STS variant [ 9 ] . Long coordinate systems show via points and their orientation, short coordinate systems those of the prediction. The gray volume shows the predicted covariance of the position part.
Mean
“Skin”
“Blue”
“White”
No Fixture
65.0±13.2
66.8±7.3
65.0±17.9
63.3±13.4
Fixture
65.3±17.4
67.0±18.4
67.0±18.3
62.0±17.1
TABLE I : SUS value (M ± SD) for different phantoms. Higher = better, highlighted in bold.
Mean
“Skin”
“Blue”
“White”
No Fixture
6.27±3.90
5.92±4.20
6.00±3.67
6.88±3.95
Fixture
6.01±2.99
4.99±2.55
6.34±3.03
6.70±3.21
TABLE II : Raw NASA TLX (M ± SD) for different phantoms. First row without, second with fixture, lower = better.
Mean
“Skin”
“Blue”
“White”
No Fixture
43.2±26.3
36.4±19.7
32.3±18.9
60.9±29.9
Fixture
43.9±24.5
37.2±19.9
28.0±14.2
66.6±20.3
TABLE III : Completion time in seconds for different phantoms. Lower = better, highlighted in bold.
Dependent Variable
Factor
df1
df2
F
p (corr.)
Completion Time
Fixture
1
9
0.0684
n.s.
Phantom
2
18
11.8193
<0.001
Fixt. * Phant.
2
18
1.2908
n.s.
TABLE IV : ANOVA comparing completion time results.
Mean
“Skin”
“Blue”
“White”
Flexor
9.9±19.2
16.3±31.5
5.9±3.8
7.4±10.8
w. Fixture
10.3±17.8
15.2±25.1
5.6±3.7
10.2±18.0
Extensor
9.4±4.0
10.5±3.6
9.4±4.5
8.2±3.9
w. Fixture
10.2±4.7
11.6±5.2
9.7±4.5
9.4±4.6
TABLE V : EMG values ( % of MVC ) for different experiments.
Dependent Variable
Factor
df1
df2
F
p (corr.)
Flexor % MVC
Fixture
1
9
1.7881
n.s.
Phantom
2
18
1.6192
n.s.
Fixt. * Phant.
2
18
0.8406
n.s.
Extensor % MVC
Fixture
1
9
6.7434
<.05
Phantom
2
18
3.9399
<.1
Fixt. * Phant.
2
18
0.8200
n.s.
TABLE VI : ANOVA results comparing EMG values.
Mean
“Skin”
“Blue”
No Fixture
1.1±0.7
1.1±0.5
1.1±0.8
Fixture
0.9±0.6
0.9±0.5
0.9±0.7
TABLE VII : Distance between cut and marked line in mm. Lower = better, highlighted in bold.
Mean
“Skin”
“Blue”
No Fixture
1.1±0.9
1.1±0.8
1.1±1.0
Fixture
0.7±0.7
0.9±0.6
0.6±0.7
TABLE VIII : Distance between start / end of cut and marked line start / end in mm. Lower = better, highlighted in bold.
Dependent Variable
Factor
df1
df2
F
p
Cut Offset
Fixture
1
9
4.3675
<.1
Phantom
1
9
0.0377
n.s.
Fixt. * Phant.
1
9
0.0149
n.s.
Cut Length
Fixture
1
9
6.7924
<.05
Phantom
1
9
0.5015
n.s.
Fixt. * Phant.
1
9
0.8161
n.s.
TABLE IX : ANOVA results comparing results with and without fixture, excluding the “white” phantom.
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.
Diana Cuervo Espinosa, Mahathi Anand, Angela P. Schoellig
Chair of Robotics and System Intelligence, Technical University of Munich, Germany · Learning Systems and Robotics Lab, Technical University of Munich, Germany
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.
Wangyi Liu, Dasharadhan Mahalingam, Fanru Gao +2
Department of Mechanical Engineering, Stony Brook University, NY, USA. · Department of Civil Engineering, Stony Brook University, NY, USA.