Reliable Computing 4: 55–61, 1998.
1998 Kluwer Academic Publishers. Printed in the Netherlands.
Interval Methods in Robot Navigation
DAVID MORALES and TRAN CAO SON
Department of Computer Science, University of Texas at El Paso, El Paso, Texas 79968, USA,
D. M. is currently with Nortel (Northern Telecom), Richardson, Texas, USA,
(Received: 24 November 1996; accepted: 29 April 1997)
Abstract. Interval methods helped a robot designed by the University of Texas at El Paso (UTEP)
team win a prestigious third place world-wide in the robot competition held during the American
Association of Artiﬁcial Intelligence conference in Portland, Oregon, August 6–7, 1996.
1. Uncertainty in Robot Navigation: Interval Methods Are Needed
Robots have to deal with two types of uncertainty:
ﬁrst, their sensors are not absolutely accurate; as a result, they measure, e.g.,
distances to obstacles only approximately;
second, their actuators are not absolutely precise; as a result, e.g., a command
to turn 90 degrees can actually leads to an 85 or 95 degree turn.
Traditionally, statistical methods have been used to deal with these two types of
uncertainty; see, e.g.,  and references therein. There are, however, two major
problems related to these methods:
First, statistical methods are very computationally intensive. For every pixel,
at any moment of time, we need to compute and store the probability that the
corresponding point contains an obstacle. In a mobile robot, it is desirable to
have computational methods that are as simple as possible.
Second, even more importantly, these methods require that we know the proba-
bilities of errors for different sensors and actuators, and we usually do not know
the exact values of these probabilities. Instead, we only know the intervals of
possible error values.
We can try to guesstimate the probabilities, but:
if we wrongly guess the probabilities of sensor errors, we may erroneously hit
if we wrongly guess the probabilities of actuator errors, and use these wrong
probabilities in some ﬁltering-type correction, we may worsen the position error
instead of compensating for it.