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In this chapter, we report on work aiming at addressing the navigation task for
systems meeting the two above mentioned conditions. Unlike classical visual ser-
voing methods where the state of the system is the configuration and velocity of the
robot, and the input visual perception, the state of our system is a trajectory exe-
cutable by the robot and the input is a flow of sensor images. This chapter is mostly
a compilation of [8] and [14].
To overcome the issue of local minima arising when implementing local control
laws, we initially plan an admissible trajectory from the initial configuration of the
robot to the goal configuration, using classical approaches of the state of the art in
motionplanning[1,11,19,3,20,12,9,13].
Servoing a trajectory instead of a robot state significantly reduces the issue of
local minima at the cost of heavy computational load.
Following a planned trajectory can lead to collisions if:
•
unexpected obstacles in the environment were not in the map used for planning
the motion;
•
the map in inaccurate; or
•
the localization process is inaccurate.
To overcome these issues, [17] proposed a method that enables a robot to deform on
line the path to be followed in order to get away from obstacles detected along the
motion. This approach has been extended to the case of a unicycle-like mobile robot
in [6] and then to the case of a holonomic mobile manipulator in [2]. In both papers,
the geometry of the robot is approximated by a set of balls and no or only one very
simple nonholonomic constraint is treated. None of these methods is applicable to
more complex nonholonomic systems like car-like robots.
To plan and execute motions in dynamic environments, [5] developed the concept
of velocity obstacles, defining the set of forbidden velocities given the velocity of
the obstacles. This concept is used in [10] to perform local goal oriented obstacle
avoidance. This technique is particularly efficient in environments where a lot of
obstacles are moving since the velocity of the obstacles is taken into account in
the avoidance strategy. However, it is based on very simple models of robot and
obstacles: they all are spherical. This simplification forbids applications for multi-
body mobile robots moving in very cluttered environments where the robot needs to
pass very close to the obstacles.
In this chapter, we describe a generic approach of trajectory deformation applica-
ble to any nonholonomic system. We assume that a first collision-free trajectory has
been computed for the robot in the global frame. When the robot follows the trajec-
tory, on-board sensors, for instance laser scanners, detect surrounding obstacles and
map them in the global frame. If an obstacle not present in the map is detected, it
can be in collision with the initial trajectory. If the localization of the robot is inac-
curate, or if the map is inexact, obstacles of the map might be seen in collision with
the initial trajectory by the sensors. The method we describe in this chapter enables
the robot to deform the initial trajectory in order to move it away from obstacles
and make the current trajectory collision-free . The current trajectory thus changes
along time. As a trajectory is a mapping from an interval of real numbers into the
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