
Elastic Bands: Connecting Path Planning and Control
Sean Quinlan and Oussama Khatib
Robotics Laboratory
Computer Science Department
Stanford University
Abstract
Elastic bands are proposed as the
basis
for a new
framework to close the gap between global path planning
and real-time sensor-based robot control. An elastic
band is a deformable collision-jree path. The initial
shape of the elastic
is
the free path generated by a
planner. Subjected
to
artijkial forces, the elastic band
deforms
in
real time to a short and smooth path that
maintains clearance from the obstacles. The elastic con-
tinues to deform as changes in the environment are
detected by sensors, enabling the robot to accommodate
uncertainties and react to unexpected and moving obsta-
cles. While providing a tight connection between the
robot and its environment, the elastic band preserves the
global nature of the planned path. This paper outlines the
framework and discusses an efficient implementation
based on bubbles.
1.
Introduction
It
is difficult
to
build a robot system that executes
motion tasks autonomously. The problem has generally
been approached from two directions: path planning and
control.
Path planning uses models of the world and robot to
compute a path for the robot
to
reach its goal.
It
has been
shown that the general problem is computationally expen-
sive although much progress has been made in producing
fast planners for practical situations
[l].
The output of a
path planner is
a
continuous path along which the robot
will not collide with the obstacles. However, any model
of the real world will be incomplete and inaccurate, thus
collisions may still occur if he robot moves blindly along
such a path.
Control theory enables a robot to
use
sensing
to
close a
feedback loop and interact with the environment in real
time. One conventional application is for the robot to
track
a
trajectory.
More
recently,
work
has
been
done
on
increasing the level of competence
of
control systems, for
example,
by
including real-time collision avoidance
capabilities
[2].
Such local
or
reactive behaviors operate
in real time but cannot solve the global problem of mov-
ing to
an
arbitrary goal.
To build a complete system we would like
to
combine
these two approaches.
A
path planner provides a global
solution to move the robot to the goal.
A
control system
then moves the robot along the path while handling
dis-
turbance forces, small changes in the environment and
unexpected obstacles.
The conventional solution is first
to
convert the path to
a trajectory by time parameterization, then to uack the
trajectory. Path planners are often designed to find any
feasible path, with little attention
to
its suitability
for
exe-
cution. Even if the time optimal parametrization is used,
the path may have abrupt changes in direction
or
maintain
little clearance from obstacles, requiring the robot to
move slowly.
In
addition, if the controller is
to
imple-
ment some
sort
of real-time obstacle avoidance scheme
then it must be able to deviate
from
the path. Once the
robot
is
off the path, however, the controller has no global
information on how to reach the goal.
2.
A
New
Framework
We propose a new framework to close the gap
between path planning and control. The idea
is
to imple-
ment local sensor based motions by deforming in real
time the path computed
by
the
planner.
We call such a
deforming collision-free path an
elastic band
[3].
We can view this framework as a three level hierarchy,
as
depicted in figure
1.
At each level there
is
a closed
loop
with the environment whose reaction time decreases
from slow (at the planning level) to
very
fast (at the con-
trol
level). The three levels
are:
0
Path planning:
A
world model is used
to
generate glo-
bal solutions
to
specified tasks.
0
Elastic bands: The path from the planner is deformed
in real time to handle local changes in the environment
detected by sensors and
to
smooth the path.
802
1050-4729/93 $3.00
0
1993
IEEE