Algorithms for safe robot navigation

Abstract

As drones and autonomous cars become more widespread it is becoming increasingly important that robots can operate safely under realistic conditions. The noisy information fed into real systems means that robots must use estimates of the environment to plan navigation. Efficiently guaranteeing that the resulting motion plans are safe under these circumstances has proved difficult. We build a mathematical framework for analyzing the quality of estimated geometry, rigorously developing the notion of shadows. We then examine how to use these tools guarantee that a trajectory or policy is safe with only imperfect observations of the environment. We present efficient algorithms that can prove that trajectories or policies are safe with much tighter bounds than in previous work. Notably, the complexity of the environment does not affect our method's ability to evaluate if a trajectory or policy is safe. We also examine the implications of various mathematical formalisms of safety and arrive at a mathematical notion of safety of a long-term execution, even when conditioned on observational information.