global model is usually to o expensive to b e done repeatedly.
Local or reactive approaches, on the other hand, use only a small fraction of the world
model, to generate rob ot control. This comes at the obvious disadvantage that they
cannot pro duce optimal solutions. Lo cal approaches are easily trapp ed in lo cal minima
(such as U-shap ed obstacle congurations). However, the key advantage of local tech-
niques over global ones lies in their low computational complexity, which is particularly
important when the world mo del is updated frequently based on sensor information. For
example, potential eld methods, as prop osed by [7], determine the steering direction by
(hypothetically) assuming that obstacles assert negative forces on the robot, and that the
target lo cation asserts a positive force. These metho ds are extremely fast, and they typi-
cally consider only the small subset of obstacles close to the robot. Borenstein and Koren
[8] identied that such methods often fail to nd tra jectories between closely spaced ob-
stacles; they also can pro duce oscillatory behavior in narrow corridors. In [2], the
vector
eld histogram
approach is prop osed, which extends the previously developed
virtual force
eld histogram
[1]. This approach uses an occupancy grid representation for mo deling the
robot's environment, which is generated and updated continuously using ultrasonic prox-
imity sensors. Occupancy information is transformed into a histogram description of the
free space around the robot, which is used to compute the motion direction and velocity
for the rob ot. In [12] a metho d similar to ours has been prop osed which, according to
Simmons, has b een developed later but indep endently. As noted above, lo cal metho ds
are typically very fast, and they quickly adapt to unforeseen changes in the environment.
1m
robot
target
right wall I right wall II
left wall
Figure 2. Example situation
Most of these lo cal approaches generate motion commands for the rob ot in two sep-
arate stages [1, 2, 7]. In the rst stage a desired motion direction is determined. In
the second stage the steering commands yielding a motion into the desired direction are
generated. Strictly sp eaking, such an approach is only justiable if innite forces can be
asserted on the rob ot. However, for rob ots with limited accelerations it is necessary to
take into account the impulse of the robot.
For example consider the situation given in Figure 2 and suppose that the rob ot is
in a fast straight motion in the corridor while the target p oint is in the small opening to
its right. Obviously, the optimal target direction implies a turn to the right. Without
4
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