We present a sampling-based approach to reasoning about the caging-based manipulation of rigid and a simplified class of deformable 3D objects subject to energy constraints. Towards this end, we propose the notion of soft fixtures extending earlier work on energy-bounded caging to include a broader set of energy function constraints, such as gravitational and elastic potential energy of 3D deformable objects. Previous methods focused on establishing provably correct algorithms to compute lower bounds or analytically exact estimates of escape energy for a very restricted class of known objects with low-dimensional configuration spaces, such as planar polygons. We instead propose a practical sampling-based approach that is applicable in higher-dimensional configuration spaces but only produces a sequence of upper-bound estimates that, however, appear to converge rapidly to actual escape energy. We present 8 simulation experiments demonstrating the applicability of our approach to various complex quasi-static manipulation scenarios. Quantitative results indicate the effectiveness of our approach in providing upper-bound estimates for escape energy in quasi-static manipulation scenarios. Two real-world experiments also show that the computed normalized escape energy estimates appear to correlate strongly with the probability of escape of an object under randomized pose perturbation.

Soft fixtures are a novel concept designed to restrain both rigid and deformable objects within high-dimensional configuration spaces. As an extension to the notion of caging, a soft fixture describes that an object is constrained within a bounded path-component of a sublevel set defined by a suitable constraint function. In the paper, we propose energy function constraints, such as gravitational and elastic potential energy of 3D deformable objects. As illustrated below in a 2D C-space case, an object in a soft fixture (x_init) corresponds to, for example, a point in a "valley" of an energy function E, and is bounded by a level set (E(x) = 1.8). 

Escape energy refers to a measure of the minimum energy required for an object to escape from a given configuration space to arbitrarily far away. The escape energy is estimated using sampling-based algorithms that densely sample the configuration space and retrieve a finite number of escape paths to approximate an upper bound of the minimum energy cost. 

Soft fixture scenarios in the course of (1) scooping a fish with a shovel, (2) wearing a mask with two fingers, (3) catching a starfish with a bowl, (4) hooking a frozen fish with a fishing hook, (5) grasping a rope loop of blood bags, (6) manipulating a Rubik cube with two grippers, (7) tying a bunch of radishes with a rubber band, (8) snap lock mechanisms.

(1) and (2) are detailed in the paper, while the others are shown as below:

To demonstrate the usefulness of our proposed algorithm in describing the robustness of a caging-based grasp, we implement an evaluation experiment on a Franka Emika Panda robot arm.

The paper is based on our workshop contribution [PDF][Video] in 3rd Workshop on Representing and Manipulating Deformable Objects @ ICRA2023

Please contact Yifei Dong at yifeid@kth.se or Assoc. Prof. Florian Pokorny at fpokorny@kth.se

The authors are with the division of Robotics, Perception and Learning, KTH Royal Institute of Technology, 100 44 Stockholm, Sweden. Funded by the European Commission under the Horizon Europe Framework Programme project SoftEnable, grant number 101070600.

We are thankful to Rafael Cabral and Wenjie Yin for their valuable suggestions for the first draft of the paper, as well as to Zahid Muhammad and other colleagues at RPL for the support of hardware, etc.

All CAD models used in this research are either hand-crafted or downloaded from online. For the latter ones, they have been unchanged or slightly modified for the purpose of this research. There is no commercial purposes.

1. All models below used under CC BY 4.0.

• The background model of the radish example by anastasiaremezova.

• The wooden floor texture by JennyB. 

• The left hand model by kevinruiz. 

• The kitchen cabinets model by jimbogies. 

• The wok kitchen model by 3D Tudor. 

• The medical mask model by Léonard_Doye / Leoskateman. 

• The fish model by Yimit. 

• The girl's head model by mkultraviolence. 

• The antique kitchen model by Stas_SayHallo. 

• The right hand model by kevjumba. 

• The blood bag model by Liam Moffitt. 

2. All models below used under CC BY-NC-SA 4.0.

• • The fish shovel model by shuvalov.di. 

  • The bowl model by Minneapolis Institute of Art. 

3. The following used under CC BY-NC 4.0.

• The hospital model by ChrisRE. 

4. All models below used under the sketchfab license.

• • The starfish model by Drakery. 

  • The fish hook model by HQ3DMOD. 

5. The model below used under the cgtrader license.

• The radish model by 3dlowpoly. 

Details of the licenses above can also be found here. Apologies if any model is used in the paper but an attribution is missing. Please kindly contact the authors in such cases.