This paper deals with the problem of multiquadrotor collaborative control by developing and analyzing a new type of fixed-time formation control algorithm. The control strategy proposes a hierarchical control framework, which consists of two layers: a coordinating control layer and a tracking control layer. On the coordinating control layer, according to the fixed-time consistency theory, the virtual position and virtual velocity of each quadrotor are calculated and acquired to form a virtual formation, and the virtual velocity reaches consistency. On the tracking control layer, the real position and the real velocity track the virtual position and the virtual velocity, respectively. Thus, multiquadrotor can achieve the required formation shape and velocity consensus. Finally, the comparative simulations are carried out to illustrate the feasibility and superiority of the proposed fixed-time hierarchical formation control method for multiquadrotor collaborative control.

Multiquadrotor systems have been widely used in various fields in the last decade, for example, agricultural plant protection, expressing, aerial photogrammetry, and emergency relief [

Up to now, researchers have achieved rich research results in the field of cooperative control of multiagents and have put forward many theories of formation control, which include leader-follower methods, virtual structure methods, and behavior-based methods and all of these are widely used in the field of multiquadrotor formation control. By adopting the lead-following formation architecture, the formation control methods which combined state estimation and backstepping method were given in [

Compared with the finite-time control theory, fixed-time consistency has better convergence and robustness. In [

As far as the authors know, due to the strong nonlinear coupling and high dimension of multiquadrotor system, there are relatively few references for formation control of multiple quadrotors. For some complex control systems, new types of control methods are often needed. In [

The main contribution of this paper is to decouple the originally highly complex quadrotors formation control model and simplify it into two-layer structure. The upper layer designs a coordinating control layer based on a fixed-time method to calculate and get virtual state information of each quadrotor. The lower layer is the PID-based tracking control algorithm, which is used to obtain the real state information to track the virtual position and velocity. On the basis of the given architecture, the multiquadrotors will reach the desired formation and velocity consensus; moreover, the convergence efficiency is significantly improved.

The communication topology structure among multiple quadrotors is denoted by using an undirected graph

In order to describe the position, attitude, velocity, and other information of the multiquadrotors in the spatial range, two coordinate systems were established, where one is geographic coordinate system

Due to the fact that the aerodynamic effects cannot be neglected, the position dynamical model for each quadrotor is presented as follows:

From [

In this section, in order to provide theoretical support for subsequent stability proof, we will introduce some lemmas about fixed-time method.

For a double integral system as shown in equation (

(see [

When

This section will introduce the core layered structure, shown in Figure

For the coordinated control level, due to the fact that this layer of collaborative control algorithm is separated from the control of a single quadrotor, it belongs to model-free control. The virtual leader’s state information can be used as input data, and the output data can be used as virtual state information, which are acquired by fixed-time consensus method. Next, we define the leader’s position

For the tracking control level, the technology of PID control method is used. The virtual state information of each quadrotor can be used as input data of the tracking control module, which is composed of an attitude controller and a position controller. Each quadrotor tracks the virtual state which is received from the coordination module. Finally, thrust

The diagram of hierarchical formation control.

For the cooperative control part, its advantage is that it is separated from the control part of a single quadrotor; that is to say, the design of the coordinated controller is not involved in dynamics model. The controller is set as follows:

Although a consensus on the virtual location has been reached, the required formation shape has not yet been accomplished. In order for the quadrotors to reach a desired formation pattern, a reference configuration vector

In this section, in order to make the real position and real velocity converge to the virtual positon and virtual velocity, i.e.,

Using the classic PID control, the position controller

The desired attitudes, roll

Similarly, the attitude controller

According to the results above, the desired torque

The stability proof of the coordinating control algorithm is given.

Suppose that the undirected communication topology

Define

Set a Lyapunov constructor as follows:

For the first term in

Then, in a similar way for the second term, it can be obtained that

Therefore, it can be obtained that

Then, due to [

Therefore, we get

Invoking Lemma

Next, the position consensus is considered, and the related theorem and proof are as follows.

Suppose that the undirected communication topology

Basically, it is the same as the proof of Theorem

Hence, protocol (

Similarly, set a Lyapunov constructor

Then, one finally obtains

Thus, similar to the proof of Theorem

In this section, simulation experiments are used to illustrate the feasibility and superiority of the proposed fixed-time consistency control algorithm. The following content will be divided into two parts for verification of the feasibility and superiority of the control algorithm.

The communication topology of a five-node multiquadrotor system includes four followers and a virtual leader; the four quadrotors form a square as the desired formation shape. The leader points to quadrotor 1, which means that data can be transmitted in a directional manner and the communication method of other quadrotors is presented by the direction of the arrow as presented in Figure

Communication topology and the desired formation shape.

Parameters of control algorithms.

Parameter | Value |
---|---|

3.0 | |

0.6 | |

3.5 | |

0.7 | |

5.00 | |

49.0 | |

6 | |

5 | |

8 | |

500 | |

300 | |

30 |

Due to the control saturation constraints of the real quadrotors and the formation control problem, the quadrotor cannot quickly fly, parameters

In simulations, the leader’s initial state information is set:

The initial acceleration for the leader is

Then, through curve fitting, the leader’s trajectory curve can be approximated by the following function:

Next, one will choose the initial conditions of four quadrotors as follows:

Based on the proposed control architecture, simulation outcomes are shown in Figure

Simulation results. (a) The trajectory of all quadrotors in 3D space. (b) The adjacent distance between every two quadrotors. (c) The virtual velocity of all quadrotors. (d) The real velocity of all quadrotors. (e) The position curves of the leader and the quadrotors. (f) Response of attitude angles of all quadrotors.

In order to verify the superiority of the proposed fixed-time hierarchical control algorithm, that is, the convergence time of the quadrotor system is not affected by its initial state, the comparative simulations were conducted.

The comparative controller is a finite-time consistency control protocol; refer to [

In the simulations, the initial position of the leader quadrotor remains unchanged, which is set

Next, four sets of initial positions are given for the four follower quadrotors; in order to conform to the reality, the position coordinates in the

In addition, the initial state of this simulation takes the position as an example, so the initial velocities of the four quadrotors are set as

Based on the above analysis and data, the simulation results are shown in Figures

The adjacent distance between every two quadrotors under the control algorithm (

The adjacent distance between every two quadrotors under the control algorithm (

The flight trajectory of all quadrotors in the range of (10, 20). (a) Under the control algorithm (

Comparison results with two control algorithms.

Control algorithm ( | 3.39 | 6.49 | 9.85 | >15 |

Control algorithm ( | 2.53 | 2.51 | 2.54 | 2.79 |

Performance improvement (%) | 25.4 | 61.3 | 74.2 | >81 |

A hierarchical formation control structure which can solve the problem of multiquadrotor control has been developed through the previous discussion. First, this new kind of formation control structure is composed of a coordinating control part and a tracking control part. Based on the fixed-time consensus methods and PID methods, respectively, a coordinating control algorithm and a tracking control algorithm are given. Second, we have proved the convergence of the coordinating control algorithm in detail and illustrated the feasibility of the algorithm. Third, the proposed control algorithm has a good reference value in practical applications and can be used in actual flight. Finally, the aforementioned simulation results have elaborated the feasibility and superiority of hierarchical formation control structure.

The simulation data used to support the findings of this study have not been made available because the data also form part of an ongoing study.

The authors declare that they have no conflicts of interest.

This work was supported in part by the New Talent Plan Project of Zhejiang Province (Zhejiang Provincial Science and Technology Innovation Activity Plan for University Students) under Grant 2020R407075 and in part by the Zhejiang Provincial Public Welfare Technology Foundation of China under Grant LGF19F030003.