  To safely navigate unknown environments, robots must accurately perceive
dynamic obstacles. Instead of directly measuring the scene depth with a LiDAR
sensor, we explore the use of a much cheaper and higher resolution sensor:
programmable light curtains. Light curtains are controllable depth sensors that
sense only along a surface that a user selects. We use light curtains to
estimate the safety envelope of a scene: a hypothetical surface that separates
the robot from all obstacles. We show that generating light curtains that sense
random locations (from a particular distribution) can quickly discover the
safety envelope for scenes with unknown objects. Importantly, we produce
theoretical safety guarantees on the probability of detecting an obstacle using
random curtains. We combine random curtains with a machine learning based model
that forecasts and tracks the motion of the safety envelope efficiently. Our
method accurately estimates safety envelopes while providing probabilistic
safety guarantees that can be used to certify the efficacy of a robot
perception system to detect and avoid dynamic obstacles. We evaluate our
approach in a simulated urban driving environment and a real-world environment
with moving pedestrians using a light curtain device and show that we can
estimate safety envelopes efficiently and effectively. Project website:
https://siddancha.github.io/projects/active-safety-envelopes-with-guarantees
