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Passivity-based Decentralized Control for Collaborative Grasping of Under-Actuated Aerial Manipulators

Jinyeong Jeong, Min Jun Kim

TL;DR

The paper addresses stable collaborative grasping using under-actuated aerial manipulators (AMs) without centralized control. It introduces a decentralized passivity-based impedance control framework built on an inertially decoupled AM model achieved via a coordinate transformation, ensuring modular stability through passive interconnections. Key contributions include formal uniform asymptotic stability in free-flight, input-output passivity for a single AM, and convergence guarantees during collaboration, plus extensions to many AMs and practical considerations like force sensing and CoM trajectory design, all validated by simulations with 2 and 10 AMs. The results demonstrate a scalable, robust approach to aerial manipulation that reduces coordination complexity while maintaining stability and effective grasping dynamics.

Abstract

This paper proposes a decentralized passive impedance control scheme for collaborative grasping using under-actuated aerial manipulators (AMs). The AM system is formulated, using a proper coordinate transformation, as an inertially decoupled dynamics with which a passivity-based control design is conducted. Since the interaction for grasping can be interpreted as a feedback interconnection of passive systems, an arbitrary number of AMs can be modularly combined, leading to a decentralized control scheme. Another interesting consequence of the passivity property is that the AMs automatically converge to a certain configuration to accomplish the grasping. Collaborative grasping using 10 AMs is presented in simulation.

Passivity-based Decentralized Control for Collaborative Grasping of Under-Actuated Aerial Manipulators

TL;DR

The paper addresses stable collaborative grasping using under-actuated aerial manipulators (AMs) without centralized control. It introduces a decentralized passivity-based impedance control framework built on an inertially decoupled AM model achieved via a coordinate transformation, ensuring modular stability through passive interconnections. Key contributions include formal uniform asymptotic stability in free-flight, input-output passivity for a single AM, and convergence guarantees during collaboration, plus extensions to many AMs and practical considerations like force sensing and CoM trajectory design, all validated by simulations with 2 and 10 AMs. The results demonstrate a scalable, robust approach to aerial manipulation that reduces coordination complexity while maintaining stability and effective grasping dynamics.

Abstract

This paper proposes a decentralized passive impedance control scheme for collaborative grasping using under-actuated aerial manipulators (AMs). The AM system is formulated, using a proper coordinate transformation, as an inertially decoupled dynamics with which a passivity-based control design is conducted. Since the interaction for grasping can be interpreted as a feedback interconnection of passive systems, an arbitrary number of AMs can be modularly combined, leading to a decentralized control scheme. Another interesting consequence of the passivity property is that the AMs automatically converge to a certain configuration to accomplish the grasping. Collaborative grasping using 10 AMs is presented in simulation.
Paper Structure (21 sections, 3 theorems, 21 equations, 6 figures)

This paper contains 21 sections, 3 theorems, 21 equations, 6 figures.

Table of Contents

  1. Introduction
  2. System Modeling
  3. Dynamic equations of aerial manipulator
  4. Inertially decoupling coordinate transformation
  5. Control Framework
  6. Control strategy
  7. Control design
  8. CoM control
  9. Floating base orientation control
  10. End-effector impedance control
  11. Controller analysis
  12. Controller discussion
  13. Extension to many AMs
  14. Force/Torque sensor measurement
  15. Force closure
  16. ...and 6 more sections

Key Result

Theorem 1

Assume that $\bm{F}_e=\bm{0}$ and $\|m\ddot{\bm{r}}_{c, d}+mg\bm{e}_3\|<B_1$. With the control law (eq:Com_controller), (eq:ori_controller), and (eq:u3), an AM system has a uniformly asymptotically stable equilibrium point $\tilde{\bm{r}}_c=\bm{0}, \tilde{\bm{e}}_R=\bm{0}$, and $\tilde{\bm{y}}=\bm{0

Figures (6)

  • Figure 1: This work aims at accomplishing collaborative grasping using multiple AMs with a decentralized control scheme. The passivity-based impedance control makes AMs converge to certain configurations at which they can balance each other.
  • Figure 2: An under-actuated aerial vehicle equipped with an $n$ DOF non-redundant robotic manipulator.
  • Figure 3: Collaborative grasping using two AMs can be interpreted as a feedback interconnection of passive systems.
  • Figure 4: (a) The new I/O pair $(\dot{\bm{y}}_{new}, \bm{F}_y)$ of the entire system is passive. (b) The new I/O can be interconnected with 'AM 3' by feedback, which preserves passivity. (c) Collaborative grasping with multiple AMs can be achieved by repeating the feedback interconnection.
  • Figure 5: Simulation results for one AM. The green, yellow, and gray areas correspond to approaching, grasping, and hovering, respectively. (a) Collaborative grasping using two AMs with force compensation. (b) Collaborative grasping using two AMs without force compensation.
  • ...and 1 more figures

Theorems & Definitions (6)

  • Theorem 1: Uniform asymptotic stability of free-flight
  • proof
  • Theorem 2: Passivity under interaction
  • proof
  • Theorem 3: Convergence under collaborative grasping
  • proof