Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Aerial Transportation Control of Suspended Payloads with Multiple Agents

Fatima Oliva-Palomo, Diego Mercado-Ravell, Pedro Castillo

TL;DR

This paper addresses the control problem of aerial cable suspended load transportation, using multiple Unmanned Aerial Vehicles (UAVs), and proposes a hierarchical control scheme based on the attractive ellipsoid method.

Abstract

In this paper we address the control problem of aerial cable suspended load transportation, using multiple Unmanned Aerial Vehicles (UAVs). First, the dynamical model of the coupled system is obtained using the Newton-Euler formalism, for "n" UAVs transporting a load, where the cables are supposed to be rigid and mass-less. The control problem is stated as a trajectory tracking directly on the load. To do so, a hierarchical control scheme is proposed based on the attractive ellipsoid method, where a virtual controller is calculated for tracking the position of the load, with this, the desired position for each vehicle along with their desired cable tensions are estimated, and used to compute the virtual controller for the position of each vehicle. This results in an underdetermined system, where an infinite number of drones' configurations comply with the desired load position, thus additional constrains can be imposed to obtain an unique solution. Furthermore, this information is used to compute the attitude reference for the vehicles, which are feed to a quaternion based attitude control. The stability analysis, using an energy-like function, demonstrated the practical stability of the system, it is that all the error signals are attracted and contained in an invariant set. Hence, the proposed scheme assures that, given well posed initial conditions, the closed-loop system guarantees the trajectory tracking of the desired position on the load with bounded errors. The proposed control strategy was evaluated in numerical simulations for three agents following a smooth desired trajectory on the load, showing good performance.

Aerial Transportation Control of Suspended Payloads with Multiple Agents

TL;DR

This paper addresses the control problem of aerial cable suspended load transportation, using multiple Unmanned Aerial Vehicles (UAVs), and proposes a hierarchical control scheme based on the attractive ellipsoid method.

Abstract

In this paper we address the control problem of aerial cable suspended load transportation, using multiple Unmanned Aerial Vehicles (UAVs). First, the dynamical model of the coupled system is obtained using the Newton-Euler formalism, for "n" UAVs transporting a load, where the cables are supposed to be rigid and mass-less. The control problem is stated as a trajectory tracking directly on the load. To do so, a hierarchical control scheme is proposed based on the attractive ellipsoid method, where a virtual controller is calculated for tracking the position of the load, with this, the desired position for each vehicle along with their desired cable tensions are estimated, and used to compute the virtual controller for the position of each vehicle. This results in an underdetermined system, where an infinite number of drones' configurations comply with the desired load position, thus additional constrains can be imposed to obtain an unique solution. Furthermore, this information is used to compute the attitude reference for the vehicles, which are feed to a quaternion based attitude control. The stability analysis, using an energy-like function, demonstrated the practical stability of the system, it is that all the error signals are attracted and contained in an invariant set. Hence, the proposed scheme assures that, given well posed initial conditions, the closed-loop system guarantees the trajectory tracking of the desired position on the load with bounded errors. The proposed control strategy was evaluated in numerical simulations for three agents following a smooth desired trajectory on the load, showing good performance.
Paper Structure (17 sections, 1 theorem, 44 equations, 8 figures, 1 table)

This paper contains 17 sections, 1 theorem, 44 equations, 8 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Works
  3. Contributions
  4. Problem Statement
  5. Dynamic model
  6. Control problem
  7. Control Strategy
  8. Attractive Ellipsoid Method
  9. Attitude Controller
  10. Position Controller
  11. Load Control and Error Dynamics
  12. Closed-loop Error Dynamics
  13. Assumptions
  14. Stability Analysis
  15. Numerical Simulations
  16. ...and 2 more sections

Key Result

Theorem 1

For the system model:pos and model:load with the restriction model:restriction and the virtual controls control:uL and control:ui, under assumptions $1-3$, and considering some matrices $\tilde{A}$ and $\tilde{B}$, if there exists a symmetric positive definite matrix $P \in \mathbb{R}^{9(n+1) \times where then, there exists an attractive stability region around the origin of the vector state $\ch

Figures (8)

  • Figure 1: Aerial transportation system with multiple UAVs. The cables are assumed rigid and mass-less, while the payload is considered as a punctual mass carried by $n$ aerial vehicles.
  • Figure 2: Blocks diagram of the closed-loop system. A hierarchical control scheme is proposed, where the load control uses the resultant tensions as a virtual control input, then the target tensions are distributed to the agents and a position controller computes the desired thrust force vector in order to guarantee that each agent moves to its desired position. Finally, an attitude controller extracts the desired orientation of each drone and computes the required input torque.
  • Figure 3: Load position $x_L$ (top) and load transportation error $x_e=x_L-x_{Ld}$ (bottom).
  • Figure 4: UAV's positions $x_i$.
  • Figure 5: UAVs' attitude quaternion $\bar{q}_i$.
  • ...and 3 more figures

Theorems & Definitions (4)

  • Remark 1
  • Definition 1
  • Theorem 1
  • proof