International Journal of Aerospace Engineering

Volume 2018, Article ID 2857674, 22 pages

https://doi.org/10.1155/2018/2857674

## Energy-Optimized Consensus Formation Control for the Time-Delayed Bilateral Teleoperation System of UAVs

^{1}School of Instrument Science and Engineering, Southeast University, Nanjing 210018, China^{2}School of Automation, Nanjing Institute of Technology, Nanjing 211100, China

Correspondence should be addressed to Guang-ming Song; nc.ude.ues@gnosekim

Received 11 October 2017; Revised 24 March 2018; Accepted 3 April 2018; Published 22 May 2018

Academic Editor: Kenneth M. Sobel

Copyright © 2018 Hui-yu Sun et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper proposes an energy-optimized consensus formation scheme for the time-delayed bilateral teleoperation system of multiple unmanned aerial vehicles (UAVs) in the obstructed environment. To deal with the asymmetric time-varying delays in aerial teleoperation, the local damping is independently distributed on both sides to enforce consensus formation and force tracking of the master haptic device and the slave UAVs. The stability of the time-delayed aerial teleoperation system is analyzed by the Lyapunov function. In addition, a flux-conserved force field is incorporated into the aerial teleoperation system to guarantee a collision-free consensus formation in the obstructed environment. Moreover, to reduce the communication complexity and energy dissipation of the formation, a top-down strategy of 3D optimal persistent graph is first proposed to optimize the formation topology. Under the optimized topology with environmental constraints, communication complexity and energy dissipation can be minimized while the rigid formation can be maintained and transformed persistently in the obstructed environment. Finally, the human-in-the-loop simulations are performed to validate the effectiveness of the proposed scheme.

#### 1. Introduction

Groups of unmanned aerial vehicles (UAVs) rather than a single UAV have proven to be very effective in solving complex tasks like surveillance, exploration, and search and rescue [1, 2]. Nevertheless, when the task is extremely complex and high-level decisions are required online, complete autonomy of the agents is far from being reached and the human intervention is still necessary. Therefore, the bilateral teleoperation of a semiautonomous group seems a very promising solution [3]. In this way, the operator can manipulate a group of UAVs by the master device and receive the feedback force on the status of the slave group.

The research of the bilateral teleoperation system has been studied for several decades [4, 5]. One critical problem is the time delays that existed in communication. Due to the long distance, limited bandwidth, and packet loss, the time delays are unavoidable and they will degrade the system performance or even cause instability [6]. Without proper control strategy, small time delay (e.g., tens of milliseconds) can destabilize the bilateral teleoperation system [7], thus leading to high risk to the human operator and the environment. A large number of researchers have proposed methods to make a trade-off between stability and transparency as reported in literature [8, 9]. For the constant or time-varying delays, the single-master-single-slave configuration of the teleoperation system has been studied for several decades. Anderson and Spong [7] firstly proposed the scattering theory to passify the system with constant time delays. Niemeyer and Slotine [10] developed the concept of the wave variables introduced from the scattering theory. Both notions have been virtually the only way to enforce passivity of the delayed bilateral teleoperation system.

However, the scattering method brings about the position drifting problem that will degrade the stability of the system [11]. Therefore, Nuño et al. [12, 13] put forward the damping intervention method to overcome the position drifting problem. The large damping injections can be independently distributed on both sides. They not only guarantee the passivity of the teleoperation system but deal with the position drifting problem in the scattering system. Compared with the single slave configuration, there are fewer literatures about the single-master-multi-UAV configuration due to its complexities of model and coupling. Franchi et al. [14] proposed the large damping injections that were distributed on the master and each slave UAV to ensure the passivity of the teleoperation system, and the stability conditions of the multi-UAV configuration were given, but the time delays were not considered. Rodríguez-Seda et al. [15] addressed the task of remotely controlling a formation of *n*-degree-of-freedom (DOF) slave agents coupled bilaterally through constant time-delayed communication channels to a single *n*-DOF master robot. The proportional-derivative controller was designed to enforce formation control, master-to-slave position coverage, and static force reflection. However, the time delays were constant. Also, the master-slave robots were isomorphic and had the same kinematics and dynamics. Only the position convergence could be achieved under the proposed controller. The mismatches of master-slave kinematics and dynamics were not considered. Chawda and O’Malley [16] studied the time-varying delays in the multislave system while the consensus formation and the interaction with the environment were not considered. Slawiñski and Mut [17] put emphasis on the consensus problem for the teleoperation system over communication networks with time-varying delays by adding local damping at both sites, but the master and slave robots have the same dynamical models. It is not suitable for UAVs with underactuated dynamics and unbounded workspace. The local damping action on the master was not discussed. To our best knowledge, the consensus formation control for the multi-UAV bilateral teleoperation system in the obstructed environment while considering the asymmetric time-varying delays has as yet little researches.

For the cooperative control of the multi-UAV bilateral teleoperation system, another critical problem is the consensus formation control in the obstructed environment. In the obstructed environment, the researches about collision avoidance have been active for many years. Usually, the collision avoidance approaches can be classified into behavior-based [18, 19] and potential field approaches [20, 21]. In the aerial teleoperation system, a flux-conserved force field that is inspired by the electronic field is incorporated to avoid the obstacles and escape the local minima. As pointed by Olfati-Saber et al. [22], besides collision avoidance, the connectivity maintenance is the fundamental rule for the coordination of multiagent systems in practice. In the multiagent system, moving in formation is a cooperative task and requires collaboration of every agent in the formation. The fundamental of the consensus formation control is that the relative position and velocity of neighbor vehicles are all in agreement. In these literatures, the relative-position-based approach is applied to coordinate the neighbor vehicles, in which each vehicle is required to communicate with its neighbors [23–25]. However, some interactions between the UAVs are not necessary and they will make the communication much more complex. If consensus can be reached with less neighbor information, the communication links and energy dissipation of the slave formation can be decreased. Jakovetic et al. [26] designed the weights in consensus algorithms for spatially correlated random topologies to decrease the topology complexity of graphs while maintaining their shapes. Yan et al. [27] firstly used the min-weighted rigid graph to describe the topology relation of slave robots in the teleoperation system. Correspondingly, the communication complexity and energy consumption in slave sire can be decreased. Lin et al. [28] concentrated on the fundamental coordination problem that requires a network of agents to achieve a specific but arbitrary formation shape. The complex Laplacian was introduced to address the problems of which formation shapes specified by interagent relative positions can be formed and how they can be achieved with distributed control ensuring global stability. However, these emphases were only placed on formation in 2D space or static formation in 3D space.

Inspired by these issues, an energy-optimized consensus formation scheme for the asymmetric time-varying bilateral teleoperation system is studied based on UAV dynamics. The main contributions of this paper mainly lie in the following: (1) coordination control. A passive consensus formation controller is proposed to keep the system be closed-loop stable with the asymmetric time-varying delays while enforcing formation control, master-to-slave velocity convergence, and force reflection; (2) topology optimization. A top-down strategy of 3D optimal persistent graph is first used to describe the topology relationships of slave robots in the obstructed environment. Under the optimized topology with environmental constraints, the communication complexity and energy dissipation can be minimized while the rigid formation can be maintained and transformed persistently in the obstructed environment; and (3) collision avoidance control. Inspired by electromagnetics, each obstacle is regarded as the electronic objects. A new flux-conserved force field is proposed to keep the consensus formation away from the obstacles and escape the local minima.

The rest of the paper is organized as follows. Section 2 introduces a brief summary of the relevant results on graph theory, rigid graph, and system dynamics. Section 3 proposes the time-delayed bilateral aerial teleoperation system with consensus formation in the obstructed environment. Section 4 proposes a top-down strategy of 3D optimal persistent graph to minimize the communication complexity and energy dissipation of the formation. The human-in-the-loop simulation results and discussions that evaluate the effectiveness of the proposed framework are performed in Section 5. Finally, the conclusions and future work are given in Section 6.

#### 2. Preliminaries

##### 2.1. Graph Theory

Each UAV in the formation can be regarded as a vertex, and the topology of the slave UAVs is conveniently described as an undirected graph. Some basic concepts of graph theory are introduced in [29].

Let *G* = (**V**, *E*, **A**) be a weighted graph, where **V** = {1, 2, …, *n*} is the set of vertexes, is the set of edges, and **A** = [*a _{ij}*] is the weighted adjacency matrix. The adjacency elements associated with the edges are positive, that is, . Moreover, the elements

*a*= 0 for all . The set of neighbors of vertex is denoted by . The Laplacian of graph

_{ii}*G*is denoted by

**L**= [

*l*] with , where

_{ij}*w*> 0 if

_{ij}**j**∈

*N*.

_{i}**I**

*is an identity matrix of size*

_{n}*n*, 1

*is a column vector of size*

_{n}*n*with all elements equal to one. The

**L**

_{∞}norm is . The

**L**

_{2}norm is .

##### 2.2. Rigid Graph

As shown in [30], let *q*_{i}(*t*) be the trajectory of vertex in the formation. A graph is said to be rigid if and only if the distances between every pair ||*q*_{i}(*t*) − *q*_{j}(*t*)|| are constant for all . Or else, it is called flexible.

For a graph , the rigidity matrix **M** is defined as
where each row corresponds to an edge and the columns corresponds to the coordinates of the vertexes.

Lemma 1 [30, 31]. *Let M be the rigidity matrix of a framework of n vertexes in R ^{c}. A framework G = (V, E, A) with n (n ≥ 2) vertexes in R ^{c} is infinitesimally rigid if and only if rank (M) = c n − c(c + 1)/2.*

Lemma 2 [30, 31]. *An infinitesimally rigid framework G = (V, E, A) with n (n ≥ 2) vertexes in R ^{c} is minimally rigid if and only of it has c n − c(c + 1)/2 edges.*

Lemma 3 [30, 31]. *If every edge of the framework G = (V, E, A) is weighted by its length, a min-weighted rigid graph is the minimally rigid that has the minimally weighted sum in all infinitesimally rigid graphs.*

Lemma 4 [30, 31]. *If the framework G = (V, E, A) is the optimal persistent graph if and only if the out-degrees of any vertex in the min-weighted rigid graph are no more than 2.*

*Remark 1. *The optimal persistent graph mainly has two important features. First, it is a directed rigid graph with the smallest communication complexity and the links. Then the weighted sum in all minimally rigid graphs is also the smallest. Based on these features, the optimal persistent graph can be adopted to optimize the communication of the slave UAVs. Examples of the flexible graph, rigid graph, min-weighted graph, and optimal persistent graph in 2D space are shown in Figure 1.