Using R-functions to Control the Shape of Soft Robots

In this paper, we introduce a new approach for soft robot shape formation and morphing using approximate distance fields. The method uses concepts from constructive solid geometry, R-functions, to construct an approximate distance function to the boundary of a domain in $\Re^d$. The gradients of the R-functions can then be used to generate control algorithms for shape formation tasks for soft robots. By construction, R-functions are smooth and convex everywhere, possess precise differential properties, and easily extend from $\Re^2$ to $\Re^3$ if needed. Furthermore, R-function theory provides a straightforward method to creating composite distance functions for any desired shape by combining subsets of distance functions. The process is highly efficient since the shape description is an analytical expression, and in this sense, it is better than competing control algorithms such as those based on potential fields. Although the method could also apply to swarm robots, in this paper it is applied to soft robots to demonstrate shape formation and morphing in 2-D (simulation and experimentation) and 3-D (simulation).

A self-organizing robotic aggregate using solid and liquid-like collective states

Designing robotic systems that can change their physical form factor as well as their compliance to adapt to environmental constraints remains a major conceptual and technical challenge. To address this, we introduce the Granulobot, a modular system that blurs the distinction between soft, modular, and swarm robotics. The system consists of gear-like units that each contain a single actuator such that units can self-assemble into larger, granular aggregates using magnetic coupling. These aggregates can reconfigure dynamically and also split up into subsystems that might later recombine. Aggregates can self-organize into collective states with solid- and liquid-like properties, thus displaying widely differing compliances. These states can be perturbed locally via actuators or externally via mechanical feedback from the environment to produce adaptive shape shifting in a decentralized manner. This in turn can generate locomotion strategies adapted to different conditions. Aggregates can move over obstacles without using external sensors or coordinate to maintain a steady gait over different surfaces without electronic communication among units. The modular design highlights a physical, morphological form of control that advances the development of resilient robotic systems with the ability to morph and adapt to different functions and conditions.