With the increasing demand for interactive aerial operations, the application of aerial manipulators is becoming more promising. However, there are a few critical problems on how to improve the energetic efficiency and pose control of the aerial manipulator for practical application. In this paper, a novel cable-driven aerial manipulator used for remote water sampling is proposed and then its rigid-flexible coupling dynamics model is constructed which takes joint flexibility into account. To achieve high precision joint position tracking under lumped disturbances, a newly controller, which consists of three parts: linear extended state observer, adaptive super-twisting strategy, and fractional-order nonsingular terminal sliding mode control, is proposed. The linear extended state observer is adopted to approximate unmeasured states and unknown lumped disturbances and achieve model-free control structure. The adaptive super-twisting strategy and fractional-order nonsingular terminal sliding mode control are combined together to achieve good control performance and counteract chattering problem. The Lyapunov method is utilized to prove the overall stability and convergence of the system. Lastly, various visualization simulations and ground experiments are conducted, verifying the effectiveness of our strategy, and all outcomes demonstrate its superiorities over the existing control strategies.

Recently, unmanned aerial vehicles (UAVs), as a special robotic system, have been widely used in various aerial applications including aerial photography [

To effectively solve the above issue, various robust control schemes for aerial manipulators have already been designed and investigated including sliding mode control (SMC) [

To employ these methods easily in complex practical applications, scholars have tried to find methods that do not need precise system information as much as possible. In these methods [

The major contributions of our research are briefly summarized as follows:

A cable-driven aerial manipulator used for remote water sampling has been designed. The adoption of cable-driven technique makes drive motors installed at the base, therefore the energy consumption and the dynamics coupling effect of the system are significantly reduced.

To achieve high precision trajectory tracking in joint space under lumped disturbances, an observer-based robust control strategy is proposed. Combining the LESO as basic framework and utilizing FONTSMC along with AST, the proposed strategy can achieve good control performance while being model-free.

To demonstrate the validity and superiorities of our designed strategy, visualization simulations and ground test experiments are performed compared with existing other control strategies.

The rest of this article is arranged as follows: The structure of our proposed cable-driven aerial manipulator and its rigid-flexible coupled dynamics model are presented in

The cable-driven aerial manipulator we designed is shown in

To minimize the mass of manipulator, we employ cable drive technology (as shown in

When the cable-driven manipulator is in motion, the drive motor transmits the torque to the joint axis through the flexible cable. Obviously, the flexibility of the cable is mainly concentrated at the joint. So, the joint of the cable-driven manipulator can be treated as a flexible one and furtherly simplified to a linear spring for modelling and analyzing [

Combining

Actually, exact dynamics model of cable-driven manipulator is usually difficult to obtain. So, we adopt a diagonal gain matrix

As can be seen in

Rewrite the

Supposing that the disturbance

Finally, the linear extended state observers for system

Taking joint 1 as an example to extrapolate the design process of our control scheme. Joint position tracking error and its first order derivative are defined as

Taking the derivative of

In order to further achieve high performance and strong robustness in the reaching phase, we adopt the AST method as follows:

Finally, combining

Similarly, we can get the control law of joint 2 as follows:

Meanwhile, the system

For simplify, we also use the joint 1 to prove the convergence and stability of our designed strategy. Combining the above control law

Then, two steps are followed to demonstrate the stability.

First, the

Then, the

Because of the first order derivative of LESO error

Combining

Thus, we can conclude from the above analytical process that if

Second, the stability analysis of our controller is performed. The following Lyapunov function is chosen

Differentiating

Combing with

The

For

Considering

Substituting

Considering the inequality

It is obvious that

In fact, system state

Taking

Combining

Considering

Similarly, we can conclude

Lastly, the overall system stability is demonstrated and the tracking errors will converge as

To demonstrate the effectiveness of our designed controller, we molded the cable-driven aerial manipulator in MATLAB/SIMSCAPE and performed two visualization simulations. In the following simulations, the quadrotor is hovering, as shown in

Controllers | Values |
---|---|

Proposed | |

LADRC | |

FNTSMC |

The

As shown in

Overall, the effectiveness and superiority of our method have clearly been proved through the above simulations. The proposed controller can converge quickly and track accurately due to AST and FONTSM schemes. Moreover, benefiting from LESO scheme, the control efforts of designed strategy are continued and nonsingular while without chattering.

For further validating the control performance of our designed controller practically, we performed ground experiments with a platform as shown in

As shown in

Controller | RMSE | MAE | ||
---|---|---|---|---|

Proposed | 0.4719 | 0.4628 | 0.6685 | 0.8779 |

LADRC | 0.8261 | 0.7449 | 1.5066 | 1.5438 |

FNTSMC | 1.1177 | 0.9398 | 2.4565 | 2.1174 |

Finally,

Generally speaking, the experiment outcomes are highly match with the above visualization simulation, verifying the effectiveness and comprehensive control performance of the controller we proposed.

This article presents a novel robust controller for joint-space tracking control of a cable-driven aerial manipulator, which is used to realize remote sampling task at the drain mouth. Because of the adoption of the cable-driven scheme, all drive motors are installed at the manipulator base, which reduces energy consumption and dynamic coupling effect. Then, the proposed controller is developed from LESO and AST-FONTSMC. The AST-FONTSMC guarantees fast convergence and high accuracy while avoiding both singularity and chattering issues. What’s more, the utilization of LESO enhances the control performance of our designed strategy and makes it model-free. Next, the convergence and stability of our controller are proved through Lyapunov method. Lastly, the comparative simulations and experiments results between proposed controller and the other controllers, such as the LADRC and the FNTSMC, prove the superiority of the designed scheme in achieving comprehensive control performance under the lumped disturbances.

In future works, the complex coupling effect between quadrotor and cable-driven manipulator will be further investigated and a hybrid control strategy for the cable-driven aerial manipulator will be designed. Additionally, actual water sampling tests will also be performed outdoors for verifying the effectiveness of designed strategy.

Inertia matrix

Coriolis and centrifugal matrix

Gravitational force vector

Inertia matrix of motors

Damping matrix of motors

Joint stiffness matrix

Joint damping matrix

Angular position vector of links

Angular position vector of motors

Vector of motor torque

Disturbance torque vector

Lumped disturbances

Constant diagonal gain matrix

Observer gain matrix

Estimation of system states

Fractional derivative and integration

Observer bandwidth

Estimation error of LESO