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A Robust Neural Control Design for Multi-drone Slung Payload Manipulation with Control Contraction Metrics

Xinyuan Liang, Longhao Qian, Yi Lok Lo, Hugh H. T. Liu

TL;DR

Problem: robust trajectory tracking for a three-drone slung payload under disturbances and actuator saturation. Approach: learn a neural contraction metric (N-CCM) baseline controller with a dual metric W = L(x)^T L(x) + w I and a saturating neural control law; contraction conditions $dP/dt + sym(P(A+GK)) + 2λ P < 0$ are enforced during training, and a separate uncertainty and disturbance estimator (UDE) handles persistent disturbances. Theoretical contribution: the closed-loop system is contracting with AGAS attitude tracking, with disturbance estimation errors bounded and Barbalat's lemma ensuring convergence. Empirical contribution: simulations on a 1.3 kg payload with three drones show effective tracking of complex trajectories under constant and stochastic disturbances, improved performance with UDE, and bounded control under saturation.

Abstract

This paper presents a robust neural control design for a three-drone slung payload transportation system to track a reference path under external disturbances. The control contraction metric (CCM) is used to generate a neural exponentially converging baseline controller while complying with control input saturation constraints. We also incorporate the uncertainty and disturbance estimator (UDE) technique to dynamically compensate for persistent disturbances. The proposed framework yields a modularized design, allowing the controller and estimator to perform their individual tasks and achieve a zero trajectory tracking error if the disturbances meet certain assumptions. The stability and robustness of the complete system, incorporating both the CCM controller and the UDE compensator, are presented. Simulations are conducted to demonstrate the capability of the proposed control design to follow complicated trajectories under external disturbances.

A Robust Neural Control Design for Multi-drone Slung Payload Manipulation with Control Contraction Metrics

TL;DR

Problem: robust trajectory tracking for a three-drone slung payload under disturbances and actuator saturation. Approach: learn a neural contraction metric (N-CCM) baseline controller with a dual metric W = L(x)^T L(x) + w I and a saturating neural control law; contraction conditions are enforced during training, and a separate uncertainty and disturbance estimator (UDE) handles persistent disturbances. Theoretical contribution: the closed-loop system is contracting with AGAS attitude tracking, with disturbance estimation errors bounded and Barbalat's lemma ensuring convergence. Empirical contribution: simulations on a 1.3 kg payload with three drones show effective tracking of complex trajectories under constant and stochastic disturbances, improved performance with UDE, and bounded control under saturation.

Abstract

This paper presents a robust neural control design for a three-drone slung payload transportation system to track a reference path under external disturbances. The control contraction metric (CCM) is used to generate a neural exponentially converging baseline controller while complying with control input saturation constraints. We also incorporate the uncertainty and disturbance estimator (UDE) technique to dynamically compensate for persistent disturbances. The proposed framework yields a modularized design, allowing the controller and estimator to perform their individual tasks and achieve a zero trajectory tracking error if the disturbances meet certain assumptions. The stability and robustness of the complete system, incorporating both the CCM controller and the UDE compensator, are presented. Simulations are conducted to demonstrate the capability of the proposed control design to follow complicated trajectories under external disturbances.

Paper Structure

This paper contains 14 sections, 3 theorems, 36 equations, 3 figures.

Table of Contents

  1. INTRODUCTION
  2. Problem Formulation
  3. Mathematical Preliminaries
  4. System Dynamics
  5. Neural Robust Control with CCM
  6. The Uncertainty and Disturbance Estimator
  7. Effective Disturbances
  8. The Disturbance Estimation Law
  9. The Quadrotor Attitude Control Law
  10. Stability Analysis
  11. Simulation Verification
  12. The Training Environment Setup
  13. Trajectory Tracking Under External Disturbances
  14. CONCLUSIONS

Key Result

Theorem 1

Theorem 2.4 of Ref. tsukamoto2021contraction: If the system in (eq: ctrl_affine) is contracting, then the path integral $V_\mathcal{L}(\underline{\boldsymbol{q}}, \delta \underline{\boldsymbol{q}}, t) = \int^{\underline{\boldsymbol{\eta}}_1}_{\underline{\boldsymbol{\eta}}_0}||\boldsymbol{\Theta}(\un then we have the following relation:

Figures (3)

  • Figure 1: System geometry.
  • Figure 2: The complete closed-loop system.
  • Figure 3: Trajectory tracking MATLAB simulation performance plots, (a): comparison with UDE on and off; (b): payload tracking error and noise estimation error with respect to time when using UDE.

Theorems & Definitions (4)

  • Theorem 1
  • Lemma 1
  • Theorem 2
  • proof