Quadratic-programming-based control of multi-robot systems for cooperative object transport

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, position-tracking controllers for the robots are designed. 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, by viewing 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, nonlinear small-gain techniques are applied to analyze the closed-loop system stability. The effectiveness of the proposed design is demonstrated through numerical simulations. © 2026 European Control Association.