  Generating safe motion plans in real-time is a key requirement for deploying
robot manipulators to assist humans in collaborative settings. In particular,
robots must satisfy strict safety requirements to avoid self-damage or harming
nearby humans. Satisfying these requirements is particularly challenging if the
robot must also operate in real-time to adjust to changes in its
environment.This paper addresses these challenges by proposing
Reachability-based Signed Distance Functions (RDFs) as a neural implicit
representation for robot safety. RDF, which can be constructed using supervised
learning in a tractable fashion, accurately predicts the distance between the
swept volume of a robot arm and an obstacle. RDF's inference and gradient
computations are fast and scale linearly with the dimension of the system;
these features enable its use within a novel real-time trajectory planning
framework as a continuous-time collision-avoidance constraint. The planning
method using RDF is compared to a variety of state-of-the-art techniques and is
demonstrated to successfully solve challenging motion planning tasks for
high-dimensional systems faster and more reliably than all tested methods.
