Guaranteeing Safety in the Presence of Moving Obstacles
Abstract
Path planning is a fundamental problem in robotics research. Whether the
robot is a manipulator arm in a factory floor, an unmanned all-terrain vehicle,
a flying drone, or a household assistant serving coffee, the motions
of the robot must be planned and executed in such a way that the robot can
accomplish its goals. Motion planning must take into account
the robot's inherent abilities to move and maneuver, its speed, and
all of the various constraints imposed upon these abilities by the
environment in which the robot is situated. Many real-world application domains
are dynamic, in the sense that the plan-relevant parameters in the
environment evolve over time. In such cases, motion planning must also
take into account the time that it takes to plan. A perfect plan is useless
if it cannot be produced in time to execute it in a changing world.
This technical report focuses upon the problem of avoiding moving obstacles in
a 2-dimensional environment. Specifically, it addresses the problem of
guaranteeing that a robot will never be hit by an obstacle in the
environment. It establishes conditions for guaranteeing that a
safety-preserving path will always exist in the
most commonly studied problem in moving obstacle avoidance, known as the
Asteroids Avoidance Problem. These results are then extended
to less restricted, more realistic variants of the problem, including the
important case where the locations and trajectories are only made known to the
planning algorithm at runtime.
Once these conditions are established, they are used to develop
an incremental algorithm that can solve
the restricted Asteroids problem in low-order polynomial time.
This algorithm takes its own observed worst-case running time into
account, completes in a fraction of a second, and has been used to
control Dodger, a simulated robot that avoids moving obstacles in
hard real time. In over ten machine-weeks of testing, involving well over a
million obstacles generated in a variety of ways, Dodger has not been hit
by a single obstacle. (Also cross-referenced as UMIACS-TR 99-06)