IEEE Robotics & Automation Magazine - March 2014 - 38

Conclusions and Future Work
This article proposes a generic formation control framework
enabling accurate relative positioning in various multirobots
applications. Based on a path tracking approach, adaptive
and predictive control have been developed to supplement
the standard longitudinal and lateral control laws proposed
for ideal robots satisfying pure rolling without sliding
assumptions, so that guidance accuracy can be preserved
whatever the grip conditions, terrain geometry, misestimated
robot parameters, biased measurements or actuators settling
time. In addition, the proposed approach allows us to
address the control of any formation shape, as well as online
formation shape modification or addition/withdrawal of
robots. The performances have been largely investigated by
means of numerous full-scale experiments carried out in offroad environments. The proposed approach is generic and
open and permits us to address various formation control
applications in order to meet end-users expectations.
To develop the capabilities of this approach further, three
axes may be considered. First, the accuracy of control laws

Reference Trajectory
Leader Trajectory
Follower Trajectory

can still be improved by extending the scope of the predictive
action. Currently, only the variations in the reference path
curvature are anticipated. Higher control accuracy could be
achieved if the upcoming changes in the terrain geometry and
in the contact conditions could also be taken into account.
However, it is difficult to acquire relevant information to be
reported into the predictive algorithm. If each robot, for the
needs of a specific application, is equipped with an elaborate
sensing device supplying it with a local digital elevation map
online (for instance, a stereovision system), then terrain information could be extracted from it. Otherwise, the main terrain features could be inferred from the sideslip angles and
the cornering stiffnesses estimated by each robot. If they are
sent jointly with the localization data to the other robots via
wireless communication, the robots located behind could
then incorporate this information into the predictive algorithm to anticipate the major terrain variations (such as a
transition from grass to asphalt) and the transient longitudinal and lateral errors due to the actuators settling time could
be reduced.
Next, the control law accuracy is not the only performance index to be considered: safety of the robot must also

Lateral Distance (m)

dynamics can be found in [17]. The same control framework has also been successfully implemented to achieve
accurate platooning with small urban electric vehicles
intended for the ultimate short displacements within a multimodal transportation system. An identical level of
accuracy has been demonstrated, although monocular
cameras have been considered, instead of RTK GPS sensors, to ensure a reliable vehicle localization in the urban
environment, see [20].

0
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Leader
Follower
0

20
30
40
50
Curvilinear Abscissa (m)
(a)

20
30
40
50
60
Curvilinear Abscissa (m)
(b)

12
11
Interdistance (m)

B Coordinate (m)

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0
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-20

-10

A Coordinate (m)
Figure 14. The reference path and trajectories achieved.

IEEE ROBOTICS & AUTOMATION MAGAZINE

MARCH 2014

20
Figure 15. The results of the path tracking with variable desired
lateral distance: (a) lateral deviations of the leader (blue) and of the
follower (red) and (b) curvilinear interdistance between the leader
and the follower.

Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - March 2014