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

Si Wu, Zhengyan Qin, Tengfei Liu, Zhong-Ping Jiang

TL;DR

The paper tackles cooperative transport of a spherical object by multiple spherical robots using a quadratic-programming (QP) based velocity-tracking approach. By treating robot positions as virtual inputs, it solves a convex QP to allocate contact forces that drive the object’s velocity to follow a commanded $v_c$, while minimizing total contact-force magnitude and ensuring a unique, Lipschitz solution. A local position-tracking controller for the robots is designed to realize the QP’s virtual inputs, and nonlinear small-gain theory analyzes the closed-loop stability as an interconnection of the object's velocity error and robots’ position errors. Numerical simulations validate feasible QP solutions and stable tracking under different gain settings. The work advances theory on distributed, QP-based coordination for constrained multi-robot transport and points to future extensions for more realistic dynamics and safety constraints.

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.

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

TL;DR

The paper tackles cooperative transport of a spherical object by multiple spherical robots using a quadratic-programming (QP) based velocity-tracking approach. By treating robot positions as virtual inputs, it solves a convex QP to allocate contact forces that drive the object’s velocity to follow a commanded , while minimizing total contact-force magnitude and ensuring a unique, Lipschitz solution. A local position-tracking controller for the robots is designed to realize the QP’s virtual inputs, and nonlinear small-gain theory analyzes the closed-loop stability as an interconnection of the object's velocity error and robots’ position errors. Numerical simulations validate feasible QP solutions and stable tracking under different gain settings. The work advances theory on distributed, QP-based coordination for constrained multi-robot transport and points to future extensions for more realistic dynamics and safety constraints.

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.

Paper Structure

This paper contains 14 sections, 1 theorem, 37 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. A Cooperative Object Transport System
  4. Control Objective and Assumptions
  5. Controller Design and Main Result
  6. Velocity-Tracking Control of the Object
  7. Position-Tracking Control of the Mobile Robots
  8. Main Result
  9. Proof
  10. Velocity-Tracking Control of the Object
  11. Position-Tracking Control of the Mobile Robots
  12. Stability Property of the Closed-Loop System
  13. Numerical Simulation
  14. Conclusions

Key Result

Theorem 1

Consider the cooperative object transport system modeled by eq_plantmodel_integrator, eq_objectmodel_doubleintegrator and eq_def_acceleration, and the controller composed of eq_velocityloop_virtualcontroller, eq_velocityloop_QP and eq_positioncontroller. Choose $l_1,\ldots,l_N$ such that Under Assumption assumption_command, with $\bar{v}_c^d$ and $\bar{v}_c^{dd}$ arbitrarily small, by appropriate

Figures (7)

  • Figure 1: Contact forces between the robots and the object.
  • Figure 2: Proposed control system structure of the cooperative object transport system.
  • Figure 3: The position trajectories of the robots and the object under Parameter Set 1.
  • Figure 4: The curves of $\max_i |p_i(t)-p^*_i(t)|$ and $|v_o(t)-v_c(t)|$.
  • Figure 5: The object velocity and the velocity-command signal.
  • ...and 2 more figures

Theorems & Definitions (4)

  • Remark 1
  • Remark 2
  • Theorem 1
  • Remark 3