Quadratic-Programming-based Control of Multi-Robot Systems for Cooperative Object Transport

TL;DR

This paper presents a quadratic programming-based control method for multi-robot systems to cooperatively transport objects, ensuring stability and optimal force distribution through a novel control framework.

Contribution

It introduces a QP-based control scheme for cooperative object transport that guarantees unique solutions and stability, with a comprehensive stability analysis and simulation validation.

Findings

The QP controller effectively generates desired contact forces.

The control scheme guarantees Lipschitz continuity and stability.

Numerical simulations demonstrate successful cooperative transport.

Abstract

This paper investigates the control problem of steering a group of spherical mobile robots to cooperatively transport a spherical object. By controlling the movements of the robots to exert appropriate contact (pushing) forces, it is desired that the object follows a velocity command. To solve the problem, we first treat the robots' positions as virtual control inputs of the object, and propose a velocity-tracking controller based on quadratic programming (QP), enabling the robots to cooperatively generate desired contact forces while minimizing the sum of the contact-force magnitudes. Then, we design position-tracking controllers for the robots. By appropriately designing the objective function and the constraints for the QP, it is guaranteed that the QP admits a unique solution and the QP-based velocity-tracking controller is Lipschitz continuous. Finally, we consider the closed-loop system as an interconnection of two subsystems, corresponding to the velocity-tracking error of the object and the position-tracking error of the robots, and employ nonlinear small-gain techniques for stability analysis. The effectiveness of the proposed design is demonstrated through numerical simulations.