Dynamic Tensegrity Based Cooperative Control of Uninhabited Vehicles - Intelligent Computing for Sustainable Energy and Environment - page 488

rotation on the plane can also be achieved by varying the formation's orientation angles.
The controller is designed to ensure: (a) the vehicles in formation can respond under the
limited communication length, (b) the movement of controlled vehicles are predictable
over a wide range of different formations, and (c) the flexible control can be applied to
all the vehicles in the formation changing.

3 Problem Formulation and Definition

Coordination architecture and communications topology are key factors in the im-
plementation of formation control. Here, a centralized control architecture is applied,
where all the vehicles in the formation are controlled relative to a central virtual leader.
The advantage of a virtual leader is that it eliminates the possibility of leader break-
down.

y 2 y 1

Node
Bar
String

f 12

s 1

x 1

ș BS1

UV 1

b 2

UV 2

ș BS2 ȕ 2

b 1

ȕ 1

s 4 f 41

s 2 f 23

O O

ș BS4

ș BS 3

x 4

s 3 f 34

UV 4

UV 3

Fig. 1. Vehicles communication topology referred to a cross-tensegrity structure

The topology of the formation is modelled by a virtual cross-tensegrity structure, as
shown in Figure 1, where the nodes are defined as vehicles and edges are represented by
strings/elastic springs ( s ) and bars ( b ). In this figure, the virtual leader is represented by
the cross point of the bars, O . The edges correspond to communication topology and the
tendon control force between the vehicles. The direction of communication between the
vehicles and the tendon forces are represented as uni-directional as shown in Figure 1.
f ij represents the tendon control force that is exerted on i th vehicle according to the j th
vehicle. A tendon force controller has been designed in [LN12] by assuming a spring
with elastic characteristics which experiences the properties of both spring and string.
The same controller will be employed here for controlling and maintaining the shape of
a group of vehicles.
In addition to the controller and communication topology, a formation definition is
needed to define the location and orientation of the vehicle's formation in the plane. The
position vector of i th vehicle is defined as P i =[ P ix , P iy , P iz ] where the relative distance
between any two vehicles ( i th and j th ) in a group of N vehicles formation is given as:

− r ij = r ji = P j − P i =[ P jx , P jy , P jz ] − [ P ix , P iy , P iz ]

(1)

Where i , j = 1 ,....., N , i = j . Hence, the complete motion definition can be described in

a three dimensional Euclidean space that consists of relative distance ( r ji ) and attitude
( ψ i , θ i , φ i ) of all the vehicles in the formation, where φ i , θ i , ψ i , are the roll, pitch and

yaw angles respectively.