In this paper, we propose a formation control system for deforming and transporting simultaneously a de-formable object with a team of robots, modeled with double-integrator dynamics. The goal is to reach a target configuration, defined as a combination of shape, scale, orientation and position of the formation. We augment this controller with a set of control barrier functions (CBFs). The CBFs allow us to satisfy fundamental constraints for the success of the task: avoidance of agent-to-agent, agent-to-obstacle and object-to-obstacle collisions, and of excessive stretching. We test the performance of our proposal in different simulation scenarios.

Autonomous manipulation of deformable objects is a research topic of increasing interest due to the variety of current processes and applications that include this type of tasks. It is a complex problem that involves aspects such as modeling, control, perception, planning, grasping, estimation, etc. A single robot may be unable to perform the manipulation when the deformable object is too big, too heavy or difficult to grasp. Then, using multiple robots working together naturally arises as a solution to perform coordinately the manipulation task. In this paper, we contribute a survey of relevant state-of-the-art approaches concerning manipulation of deformable objects by multiple robots, which includes a specific classification with different criteria and a subsequent analysis of the leading methods, the main challenges and the future research directions.