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Safe Consensus of Cooperative Manipulation with Hierarchical Event-Triggered Control Barrier Functions

Simiao Zhuang, Bingkun Huang, Zewen Yang

TL;DR

A distributed control framework that achieves consensus coordination with safety guarantees via hierarchical event-triggered control barrier functions (CBFs) is presented, which is integrated with a risk-aware leader selection and smooth switching strategy to reduce online computation.

Abstract

Cooperative transport and manipulation of heavy or bulky payloads by multiple manipulators requires coordinated formation tracking, while simultaneously enforcing strict safety constraints in varying environments with limited communication and real-time computation budgets. This paper presents a distributed control framework that achieves consensus coordination with safety guarantees via hierarchical event-triggered control barrier functions (CBFs). We first develop a consensus-based protocol that relies solely on local neighbor information to enforce both translational and rotational consistency in task space. Building on this coordination layer, we propose a three-level hierarchical event-triggered safety architecture with CBFs, which is integrated with a risk-aware leader selection and smooth switching strategy to reduce online computation. The proposed approach is validated through real-world hardware experiments using two Franka manipulators operating with static obstacles, as well as comprehensive simulations demonstrating scalable multi-arm cooperation with dynamic obstacles. Results demonstrate higher precision cooperation under strict safety constraints, achieving substantially reduced computational cost and communication frequency compared to baseline methods.

Safe Consensus of Cooperative Manipulation with Hierarchical Event-Triggered Control Barrier Functions

TL;DR

A distributed control framework that achieves consensus coordination with safety guarantees via hierarchical event-triggered control barrier functions (CBFs) is presented, which is integrated with a risk-aware leader selection and smooth switching strategy to reduce online computation.

Abstract

Cooperative transport and manipulation of heavy or bulky payloads by multiple manipulators requires coordinated formation tracking, while simultaneously enforcing strict safety constraints in varying environments with limited communication and real-time computation budgets. This paper presents a distributed control framework that achieves consensus coordination with safety guarantees via hierarchical event-triggered control barrier functions (CBFs). We first develop a consensus-based protocol that relies solely on local neighbor information to enforce both translational and rotational consistency in task space. Building on this coordination layer, we propose a three-level hierarchical event-triggered safety architecture with CBFs, which is integrated with a risk-aware leader selection and smooth switching strategy to reduce online computation. The proposed approach is validated through real-world hardware experiments using two Franka manipulators operating with static obstacles, as well as comprehensive simulations demonstrating scalable multi-arm cooperation with dynamic obstacles. Results demonstrate higher precision cooperation under strict safety constraints, achieving substantially reduced computational cost and communication frequency compared to baseline methods.
Paper Structure (27 sections, 1 theorem, 38 equations, 4 figures, 1 table)

This paper contains 27 sections, 1 theorem, 38 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Graph Theory
  4. System Modeling and Problem Formulation
  5. Manipulator Dynamics and Task-Space Formulation
  6. Hierarchical Control Design
  7. Coordination Objective
  8. Control Barrier Functions
  9. Methodology
  10. Distributed Consensus Tracking Protocol
  11. Acceleration Mapping via Damped Least Squares
  12. Hierarchical Event-Triggered Safety Architecture
  13. Event-Triggered Environmental Safety
  14. Event-Triggered Inter-Agent Interaction Safety
  15. Intrinsic Local Safety
  16. ...and 12 more sections

Key Result

Lemma 1

Under asm:compact_form, for any $\boldsymbol{o}\in\mathcal{O}$, any $j\in\mathcal{V}$, and any $k\in\{1,\dots,K_j\}$, Consequently, $d_\ell^{\mathrm{body}}(t)\ge \bar{R}_{\mathrm{form}}$ implies $\phi_{j,k}\ge 0$ for all $(j,k,\boldsymbol{o})$.

Figures (4)

  • Figure 1: Overview of the proposed framework. The $h_{min}$ function encodes the minimum distance between the robot and the environmental obstacles.
  • Figure 2: Comparison of formation position error and orientation error across methods and leader active duration of HET-CBF (shaded regions).
  • Figure 3: Monte Carlo evaluation comparing formation position error, orientation error, computational time, and task completion time across methods.
  • Figure 4: Visualization of $h_{\min}(t)$ and leader active duration in four-arm scenario.

Theorems & Definitions (2)

  • Lemma 1: Leader-to-Formation Safety Transfer
  • proof