Multirobot control with deformation modes for transport of deformable objects

In this article, we present a novel formation control approach for transporting deformable objects with a team of robots. The goal of the proposed system is to reach a target configuration consisting of a desired shape, scale, position and orientation, while allowing linear and quadratic deformations of the robotic formation during the transport. The use of this range of deformation modes enables preserving the integrity of the object while making the transport system highly flexible. Our approach applies a linear combination of terms to regulate the different variables that represent the control goal toward their desired values. We propose controllers both in 2D and 3D workspaces, and provide formal analysis of the exponential convergence of the shape variables and the absence of conflicts between the used control terms. In addition, we illustrate that the presented approach accommodates the use of robots with diverse dynamic models. We validate the proposed controllers via numerical simulations in different settings and experiments with physical unicycle-type robots.