Motion synchronization in unmanned aircrafts formation control with communication delays

https://doi.org/10.1016/j.cnsns.2012.08.015Get rights and content

Abstract

This paper proposes a formation control strategy for unmanned aircrafts using a virtual structure. Cross coupled sliding mode controllers are introduced to cope with uncertainties in the attitude measurement systems of the unmanned aircrafts and unmeasurable bounded external disturbances such as wind effects, and also to provide motion synchronization in the multi-agent system. This motion synchronization strategy improves the agents convergence to their desired positions, and this is useful for a multi-agent system with faulty agents.

Moreover, the proposed motion synchronization strategy is not restricted to specific communication topologies, and sufficient conditions are provided to guarantee the multi-agent system stability in the presence of communication delays. Numerical simulations are presented for a team of five unmanned aircrafts to make a pentagon formation and confirm the accepted performance of the proposed control strategy.

Highlights

► Formation control is an important problem in the area of multi-agent systems. ► We have proposed a motion synchronization strategy in formation control. ► The motion synchronization can tolerate the effects of agents faults in formations. ► This approach guarantees the stability of the system under communication delays. ► This approach is robust prone to uncertainties and external disturbances, as well.

Introduction

Maneuvering of unmanned vehicles maintaining a geometric formation has became one of interesting research areas in recent years with wide civilian applications in surveillance, discovering, atmospheric studies, rescue missions, fire monitoring, operations in hazardous environments, and so on. Indeed, a formation can be applied in a group of aerial robots, ground robots, and so on with a cooperative task [1], [2], [3], [4], [5].

Numerous researches are devoted to the leader–follower structure. In this structure, each agent follows leaders to maintain a desired relative position from them, and keep a formation. Although this structure is easy to implement and understand, the formation is sensitive to the leaders behavior, and disturbed or failed leaders affect their followers motion. Moreover, since there are not any loops in this structure, there are no feedbacks from a follower to its leaders. To cope with this issue, the virtual and behavioral structures have been developed. In the virtual structure, agents follow a virtual leader to provide a rigid body formation in the frame of the virtual leader, and a formation trajectory is defined for all the agents as a single rigid body. In the behavioral structure, no definite formation is considered, and it is useful for multi objective missions such as target seeking, obstacle avoidance, and so on [6], [7].

There are two main approaches for multi-agent systems control in the literature, namely: centralized and decentralized approaches each of whom has its own advantages and disadvantages. In the centralized approach, control of each agent is based on a central controller. The ability to override the control in emergency conditions and having global information are the merits of a central controller. However, the possible malfunction of the central controller affects the performance of the whole multi-agent system. Moreover, in long maneuvers, agents may have problems to communicate with the central controller, cohesively. In the decentralized approach, each agent makes decisions based on its local information achieved through its own sensors and from the neighboring agents [8], [9].

One of important problems in cooperative dynamic systems is motion synchronization. Synchronization means simultaneous convergence to desired positions or trajectories [10], or motion with identical speeds [11], [12]. The concept of cross coupling for motion synchronization has been developed extensively in the literature with a wide range of applications for motion control of multi-axis systems [13], [14], [15], cooperative manipulator robots [16], [17], [18], etc.

In recent years, there have been a number of studies on motion synchronization in multi-agent systems formation control using cross coupling. For instance, cross coupled PI controllers were applied to synchronize the errors of positions and velocities of flying wings and aircrafts, respectively in [19], [20]. Synchronized position tracking PI controllers of flying wings were also applied in [6]. Two coupling topologies were employed in [21] for attitude trajectory tracking of 3-DOF helicopters based on feedforward controllers. In [22], a consensus control strategy was proposed to synchronize the acceleration of agents in a formation to reach an arbitrary velocity. By using only visual measurements, attitude tracking synchronization in a leader–follower multi-agent system was applied in [23]. In [24], attitude tracking synchronization of unmanned helicopters in a leader–follower formation was proposed by using neural network adaptive controllers, and adaptive control was applied in [25] for synchronization of position tracking errors in the presence of communication loss.

For motion synchronization, coupling with more agents provides a better motion synchronization. On the other hand, it may not be feasible to couple agents in any topology. A drawback of the above mentioned approaches is that they are restricted to specific topologies that are defined for coupling agents, and the stability analysis of the multi-agents system is guaranteed for these topologies. Moreover, each agent receives the information of other agents with time-delays which may degrade the performance and stability of the multi-agent system. This issue has not been considered in the above mentioned papers.

The current study is devoted to formation control of multiple-unmanned aircraft systems with 3-DOF point mass model using the virtual structure. It is intended to provide a rigid formation of unmanned aircrafts in the frame of a virtual leader and couple their behaviors to synchronize their motion. To summarize, the main contributions of this paper are stated as follows:

  • 1.

    Motion synchronization in a decentralized approach without considering a specific coupling topology is applied.

  • 2.

    To cope with the uncertain attitude measurement systems of the unmanned aircrafts and also wind effects, cross coupled sliding mode controllers are applied. The measured attitudes of the unmanned aircrafts are prone to uncertainties due to errors and uncertainties which intrinsic in sensors and observers. Moreover, wind effects can affect the performance of the unmanned aircrafts in formation flight.

  • 3.

    The multi-agent systems stability is guaranteed in the presence of constant communication delays. In a decentralized multi-agent system, for motion synchronization it is necessary for each agent to receive the position and velocity of other agents, and this information may be received with time-delays. Communication delays can degrade the performance and stability of the multi-agent system; therefore, sufficient conditions are provided on the agents coupling to guarantee the multi-agent system stability in the presence of constant communication delays.

The following notations are considered in the paper: In shows an n×n identity matrix, 0n×m is an n×m matrix with zero entries, denotes the Kronecker products, the Laplace transform of f(t) is shown by f¯(s),det(.) means determinant, and diag(M1,M2,,Mm) shows a block diagonal matrix composed of matrices M1,M2,, and Mm.

The reminder of this paper is organized as follows: In Section 2, the dynamical equations of the unmanned aircrafts are given. The proposed virtual structure formulations are provided in Section 3, the sliding mode based synchronization strategy is presented in Section 4, the simulation results and numerical examples are provided in Section 5, and conclusions are given in Section 6.

Section snippets

Model definition

Consider a multi-agent system with N unmanned aircrafts in R3. The ith unmanned aircraft dynamical equations can be considered by 3-DOF point mass model as follows [8], [26]:p˙xi(t)=Vi(t)cosγi(t)cosψi(t),p˙yi(t)=Vi(t)cosγi(t)sinψi(t),p˙zi(t)=Vi(t)sinγi(t),V˙i(t)=gTi(t)-Di(t)Wi-gsinγi(t),ψ˙i(t)=ayi(t)Vi(t)cosγi(t),γ˙i(t)=-gcosγi(t)Vi(t)+api(t)Vi(t)where pi(t)=[pxi(t)pyi(t)pzi(t)] denotes the Cartesian position of the unmanned aircraft, Vi(t) is the speed, γi(t) and ψi(t) are the flight path and

Virtual structure formulation

The main objective in the virtual structure is to locate the ith unmanned aircraft in a fixed point in the frame of a virtual leader, and this can provide various rigid body formations of unmanned aircrafts in three dimensions. In Fig. 2, the frames of the unmanned aircraft and the virtual leader are depicted by xˆi-yˆi-zˆi axes and xˆv-yˆv-zˆv axes, respectively. To locate the ith unmanned aircraft in a fixed point in the frame of a virtual leader, the following three parameters should be

Synchronized cross coupled sliding mode controllers

A popular technique for robust control of nonlinear systems with uncertainty, model imperfection, and so on is sliding mode control. In this technique, the controller leads a system state to slide on a surface and this sliding guarantees the system stability [27].

In this section, sliding mode controllers are coupled to synchronize the motion of agents in a multi-agent system formation with virtual structure. Therefore, sliding mode control can guarantee the system stability when the agents are

Simulation results

In this section, the accuracy of the proposed approach for motion synchronization in formation flight is shown in two examples.

Example 1

Consider a group of five unmanned aircrafts to provide a pentagon formation which is depicted in Fig. 3. The position, speed, heading angle, and flight path angle of the ith unmanned aircraft where i{1,2,,5} are initialized with the values presented in Table 1.

To achieve a pentagon formation of the unmanned aircrafts which the magnitude of its edges is 23.51m, the

Conclusions

A decentralized formation control strategy using the virtual structure was addressed in this paper. To cope with the problem of uncertain attitude measurements and wind effects, sliding mode controllers were proposed. By coupling the sliding mode controllers, synchronization of the convergence of agents to desired positions was achieved. The proposed approach for cross coupling provides a general communication topology such that each agent can communicate with others, in any topology.

References (34)

  • J. Qiu et al.

    Tracking analysis for general linearly coupled dynamical systems

    Commun Nonlinear Sci Numer Simul

    (2011)
  • I. Blekhman et al.

    On self-synchronization and controlled synchronization

    Syst Control Lett

    (1997)
  • C. Yin et al.

    Design pd controller for masterslave synchronization of chaotic lure systems with sector and slope restricted nonlinearities

    Commun Nonlinear Sci Numer Simul

    (2011)
  • N. Michael et al.

    The grasp multiple micro-UAV test bed

    IEEE Rob Autom Mag

    (2010)
  • S.M. Azizi et al.

    A hierarchical architecture for cooperative actuator fault estimation and accommodation of formation flying satellites in deep space

    IEEE Trans Aerosp Electron Syst

    (2012)
  • D. Schoerling et al.

    Experimental test of a robust formation controller for marine unmanned surface vessels

    Auton Robots

    (2010)
  • P. Massioni et al.

    A decomposition-based approach to linear time-periodic distributed control of satellite formations

    IEEE Trans Control Syst Technol

    (2011)
  • Y. Kuwata et al.

    Cooperative distributed robust trajectory optimization using receding horizon MILP

    IEEE Trans Control Syst Technol

    (2011)
  • Li NH, Liu HH. Formation UAV flight control using virtual structure and motion synchronization. In: Proceedings of the...
  • Rezaee H, Abdollahi F. A synchronization strategy for three dimensional decentralized formation control of unmanned...
  • Kim S, Kim Y. Three dimensional optimum controller for multiple UAV formation flight using behavior-based decentralized...
  • Rezaee H, Abdollahi F. Mobile robots cooperative control and obstacle avoidance using potential field. In: Proceedings...
  • W. Zhoua et al.

    Synchronization control for the competitive complex networks with time delay and stochastic effects

    Commun Nonlinear Sci Numer Simul

    (2012)
  • Cheng MH, Bakhoum EG. Adaptive robust control of tracking and synchronization for multi-axis motion system. In:...
  • Cheng MH, Mitra A, Chen C. Synchronization controller synthesis of multi-axis motion system. In: Proceedings of the...
  • Shao D, Lv W. Research on simulation of multi-axis servo synchronization control strategy. In: Proceedings of the...
  • Chung S, Slotine JE. Cooperative robot control and synchronization of lagrangian systems. In: Proceedings of the 46th...
  • Cited by (0)

    View full text