Virtual-Tube-Based Cooperative Transport Control for Multi-UAV Systems in Constrained Environments

Technical Summary: Virtual-Tube-Based Cooperative Transport Control for Multi-UAV Systems in Constrained Environments

Problem Statement
The paper addresses the challenge of cooperative aerial transportation of cable-suspended loads by multiple Unmanned Aerial Vehicles (UAVs) in constrained, obstacle-rich environments. While single UAVs are limited by payload capacity, multi-UAV systems offer a solution for heavy loads. However, existing approaches face significant limitations:

• Formation-based control lacks mechanisms for distributing cable tension, often requiring manual reconfiguration in narrow passages.
• Planning-based control offers high accuracy but suffers from high computational complexity, making it intractable for large-scale systems.
• Admittance control can lead to load distribution imbalances, where a leader operates near its limit while followers experience slack cables, jeopardizing stability.
  Furthermore, most existing research is limited to controlled indoor environments with lightweight loads, failing to address the disturbances and uncertainties of outdoor applications where loads often exceed the capacity of a single UAV.

Methodology
The authors propose a novel distributed control framework that integrates Virtual Tube theory with Dissipative Systems theory. The control architecture consists of a high-level controller and a low-level controller:

1. Intermediate Virtual System: The physical UAV-cable-load system is mapped to an intermediate system comprising a "virtual tray," "virtual nodes" (corresponding to UAVs and the load), and "virtual springs." This abstraction allows the control of the physical system through the dynamics of the virtual nodes.
2. Virtual Tube Passing Control: A pre-planned virtual tube defines a safe corridor from a start terminal to an end terminal, ensuring obstacle avoidance. The controller generates velocity commands to guide the virtual nodes through this tube.
3. Cooperative Transport Control (Dissipative Integration): Unlike standard virtual tube approaches where repulsive potential fields cause formations to disperse, this method incorporates dissipative systems theory. It designs a controller that ensures the virtual nodes (and thus the physical UAVs) maintain a reasonable force distribution. The virtual springs are designed to restore the system to a desired equilibrium state (initial spring lengths), allowing the formation to compress in narrow sections and expand in wider sections while maintaining tension balance.
4. Stability and Convergence: The paper proves the stability of the proposed controller for first-order systems (velocity control mode) using Lyapunov-like functions. It demonstrates that the system converges to an equilibrium point where cable tensions are balanced, and the swarm traverses the virtual tube without colliding with boundaries or obstacles.
5. Implementation: The desired velocities of the virtual nodes are mapped to the physical UAVs. A low-level controller utilizes a Compensatory Function Observer (CFO) to estimate cable forces (disturbances) and employs feedforward and feedback control to regulate the UAV propulsive forces.

Key Contributions
The paper outlines three primary contributions:

1. Novel Control Design: The integration of dissipative systems theory into virtual tube control for constrained environments. Specifically, the authors extend dissipative system theory (typically applicable to second-order systems) to first-order velocity control modes to design a cooperative transport controller.
2. Theoretical Analysis: A formal proof of the stability of the proposed controller for first-order systems. The authors identify a specific equilibrium point significant for cooperative transport and analyze the convergence of the system within the constrained virtual tube.
3. Validation: Extensive numerical simulations involving up to ten UAVs transporting a heavy load (18 kg) through a complex environment with narrow passages. Additionally, outdoor flight experiments with three UAVs and a 3.06 kg load were conducted to validate practical feasibility.

Results

• Simulation: In a 50m × 20m × 20m environment with 11 obstacles, ten UAVs successfully transported an 18 kg load. The system demonstrated the ability to dynamically adjust formation (flattening in narrow sections, restoring in wide sections) while maintaining safe distances from obstacles (>0.68 m) and other UAVs (>0.5 m). Cable tensions were distributed reasonably, staying within the 20 N limit per UAV.
• Comparison: The proposed method was compared against a traditional virtual tube controller (without dissipative integration). The traditional method resulted in unstable, elongated formations, severe load oscillations, and uneven tension distribution (some UAVs bearing up to 100 N, others slack), failing to complete the task under the same load constraints.
• Experiments: Outdoor experiments confirmed the algorithm's ability to navigate geometrically complex environments autonomously. The UAVs maintained a quasi-equilateral triangular formation that compressed and restored as needed, with smooth velocity profiles and physically consistent force allocation.

Significance and Claims
The paper claims that the proposed framework offers a computationally efficient, scalable, and robust solution for multi-UAV cooperative transport. By combining virtual tube theory with dissipative systems, the method overcomes the formation dispersion issues of traditional virtual tube approaches and the computational bottlenecks of planning-based methods. The authors emphasize that the system achieves low computational overhead, adapts dynamically to obstacle layouts, and ensures high stability and robustness, making it suitable for large-scale swarms and real-world outdoor conditions. The work aligns with the emerging research direction of autonomous, dependable, and affordable control.

The authors note that the current implementation relies on a pre-planned virtual tube. Future work is identified as focusing on autonomous virtual tube generation during flight using multisensor fusion (LiDAR/RGB-D cameras) to handle dynamically complex environments.