### Abstract:

This works has been made in the context of Claytronics Project, which aim is to build spherical micro-robots, called catoms able to stick to each other and able to move around each other.

A large set of these catoms constructs therefore a huge modular self-reconfigurable robot. However, the shape of these modules remains a difficult problem as there are numerous constraints to respect to allow connection, motion and make this modular robot filling any complex volume.

We present the geometry of a quasi-spherical module which answers to all the constraints to build programmable matter.

### Our work at a glance

The idea consists in placing 12 squares (Fig. 1.a) at contacts points of cells in a Face-Centered Cubic Lattice.

Then we connect these squares by 8 hexagons (blue) and 6 octagons (green) in order to obtain a regular polyedron (named truncated cuboctahedron). But this shape is not well adapted for rotating.

Finally we replace hexagons and octagons planes by curved surfaces in order to obtain continuous surfaces as shown in the Figure 1.c.

Connectors are made by a square of size c=(2r)/(3+sqrt(2))~~0.45r.

### Papers and conference slides:

For more details about these geometry and how to use it in a programmable matter context, you can access to two publications:

- Designing a quasi-spherical module for a huge modular robot to create programmable matter
- Slides of DARS conference: "Design of quasi-spherical modules for building programmable matter"

### Bibtex

@article{PB18,

title = {Designing a quasi-spherical module for a huge modular robot to create programmable matter},

author = {Piranda, Benoit and Bourgeois, Julien},

year = {2018},

pages = {A venir},

volume = {A venir},

doi = {https://doi.org/10.1007/s10514-018-9710-0},

journal = {Autonomous Robots}

}

@inproceedings{PB16,

domainehal = {INFO:INFO_MC, INFO:INFO_NI, INFO:INFO_MO},

equipe = {omni},

author = {Piranda, Benoit and Bourgeois, Julien},

title = {Design of quasi-spherical modules for building programmable matter},

booktitle = {DARS 2016, 13th IEEE International Symposium on Distributed Autonomous Robotic Systems},

pages = {--},

address = {London, UK},

month = {oct},

year = {2016},

}

### Videos

The first video presents three interesting points of our work:

- First, a 3D catom can be constructed from a planar unfold.
- 3D catoms are placed in a regular Face-Centered Cubic lattice.
- Rotations allows 3D catoms to move from one grid position to another.

The second video shows different possible motions of a catom around another.