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In [LN12], a formation control strategy was proposed which was used to drive the
dynamic group of vehicles into a specified formation with control forces that are rep-
resented by admissible tendon forces in tensegrity structures. The formation controller
that was proposed in [LN12] has been improved with an advanced formation changing
performance and cascaded with the previous tendon controller that has the function of
maintaining the formation's geometry under the disturbance condition. Here, attention
is paid to the development of virtual tensegrity-based formation control algorithms for
vehicle's motion systems.
A virtual tensegrity structure is used to describe the entire formation as a single
rigid/solid tensegrity configuration that is invariant under translation and rotation of the
structure. The desired motion is assigned to move the virtual tensegrity structure as a
whole in a plane. In this dynamic tensegrity-based formation control, the position of
each vehicle in the group can be controlled by varying the length of the virtual bars.
Note that this change in bars' length is not possible in the use of tensegrity concept in
architecture and mechanical structures. The ratio of bars' lengths is used to control the
admissible tendon forces (control forces) that are applied on the vehicles in the forma-
tion. The overall formation control system here is formed by three main considerations:
vehicles formation geometry that is modelled by a virtual tensegrity configuration, com-
munications topology that is represented by strings and bars of the tensegrity structure,
and the interaction control algorithm.
In the remainder of this paper, Section 2 outlines the benefit of tensegrity's prop-
erties. Formation's problem formulation is defined in Section 3 whilst formation con-
troller design will be explained in Section 4. Simulation results are shown in Section
5 to demonstrate the formation achieving, formation maintaining and dynamic switch-
ing between different shapes formation while manoeuvring on the plane. Concluding
remarks are made in Section 6.
2
Tensegrity Structures
Fuller [Ful62] first used the word tensegrity as a contraction of tensional integrity and
the first tensegrity structure was built by the artist Kenneth Snelson [Sne65]. In biol-
ogy, animal skeletal system for smooth locomotion has proved that the tensegrity is a
fundamental building architecture of life [EP5]. In architectural engineering, geomet-
ric arrangement in these structures can sustain tension and compression, hence make
the buildings responsive to natural environmental disturbances such as earthquakes and
winds [SO09].
The stability and rigidity of tensegrity structures have been proven by energy
function in mathematics [Con82]. This has motivated the development of tensegrity
framework in the design and analysis of static and dynamic systems to achieve shape
formation control and other engineering functions. The absence of physical connec-
tions between rigid members in the structure allows more flexibility over a wide range
of different shapes using the predictable tendon force response. This great impact of
flexible and deployable control in tensegrity can be used as a solution for the problem
of geometry changing in formation control.
The formation controller in this paper is designed to perform formation changing
based on the ratio for the length of the virtual bars. The requirement for geometric
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