  This paper addresses the problem of safety-critical control of autonomous
robots, considering the ubiquitous uncertainties arising from unmodeled
dynamics and noisy sensors. To take into account these uncertainties,
probabilistic state estimators are often deployed to obtain a belief over
possible states. Namely, Particle Filters (PFs) can handle arbitrary
non-Gaussian distributions in the robot's state. In this work, we define the
belief state and belief dynamics for continuous-discrete PFs and construct safe
sets in the underlying belief space. We design a controller that provably keeps
the robot's belief state within this safe set. As a result, we ensure that the
risk of the unknown robot's state violating a safety specification, such as
avoiding a dangerous area, is bounded. We provide an open-source implementation
as a ROS2 package and evaluate the solution in simulations and hardware
experiments involving high-dimensional belief spaces.
