Double-Integrator Multirobot Control With Uncoupled Dynamics for Transport of Deformable Objects

We present a formation controller for a team of mobile robots, modelled with double-integrator dynamics, to manipulate deformable objects grasped around their contour. The manipulation task is defined as reaching a target configuration consisting of a desired shape, scale, position and orientation of the formation in 2D, while preserving the integrity of the object. We provide a set of controllers designed to allow the uncoupled control of the variables that define the task. The formal analysis of the controllers is covered in depth in terms of uncoupling, stability and convergence to the equilibrium state. Besides, we include control barrier functions to enforce safety constraints relevant to the task, i.e., collision and excessive stretching avoidance. The performance of the method is illustrated in simulations and in real experiments.