A tunnel of workspace is computed using overlapping
spheres called bubbles. Geometric criteria based on
the representation of the robot allow to determine if
the tunnel is large enough for the robot to pass.
Note how initially the bubbles have to explore a local
minimum of the work space. Once the local minimum is
filled with bubbles, the goal-directed exploration of the
workspace very quickly connects to the initial
configuration of the robot. The varying size of the
bubbles is indicative of the local difficulty of the
workspace. In tight areas many small bubbles are
needed, the connectivity of open areas can be captured
quickly with few bubbles.
(750KB)
By connecting the centers of the spheres in the order
of their creation, a tree of paths to the goal is
computed. The exploration terminates, once the initial
configuration of the robot is reached. By imposing a
potential function inside the spheres along the paths,
a local minima-free navigation function can be
defined. This navigation function is used to steer the
robot to the goal.
(1MB)
The motion of a free-flying snake-like robot with 11
degrees of freedom is planned in real time. The red
obstacle changes its location during the motion and
each time a new path is generated in response. Note
that the navigation function defined by the spheres
has not been smoothed. As a consequence the robot does
not move on the shortest path, but attempts to follow
the navigation function as closely as possible. Such
an optimization would be easily performed using
well-understood methods.
(1.3MB)
The motion of a mobile manipulator with 9 degrees of
freedom is planned in real time. The red obstacle
changes its location during the motion and each time a
new path is generated in response. Note that the
navigation function defined by the spheres has not
been smoothed. As a consequence the robot does not
move on the shortest path, but attempts to follow the
navigation function as closely as possible. Such an
optimization would be easily performed using
well-understood methods.
