# A shape control and object manipulation technique based on function approximation for robotic surfaces

## TL;DR

This paper introduces a new control method for robotic surfaces that maintains constant refresh times regardless of the number of actuators, enabling efficient shape control and object manipulation.

## Contribution

A novel control method with constant refresh time and a modeling strategy for robot-object interaction forces are introduced.

## Key findings

- The proposed method achieves system size-independent refresh times through distributed control.
- Experiments show good agreement between theoretical predictions and shape approximation results.
- The feedback controller effectively validates the model for object transportation tasks.

## Abstract

Robotic surfaces consisting of many actuators can change shape to perform tasks, such as object transportation and sorting. Increasing the number of actuators can enhance the robot’s capacity, but controlling a large number of actuators is a challenging problem that includes issues such as the increased system-wide refresh time. We propose a novel control method that has constant refresh times, no matter how many actuators are in the robot. Having a distributed nature, the method first approximates target shapes, then broadcasts the approximation coefficients to the actuators and relies on itself to compute the inputs. To confirm the system size-independent scaling, we build a robot surface and measure the refresh time as a function of the number of actuators. We also perform experiments to approximate target shapes, and a good agreement between the experiments and theoretical predictions is achieved. Our method is more efficient because it requires fewer control messages to coordinate robot surfaces with the same accuracy. We also present a modeling strategy for the complex robot–object interaction force based on our control method and derive a feedback controller for object transportation tasks. This feedback controller is further tested by object transportation experiments, and the results demonstrate the validity of the model and the controller.