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)