  Designing safety-critical control for robotic manipulators is challenging,
especially in a cluttered environment. First, the actual trajectory of a
manipulator might deviate from the planned one due to the complex collision
environments and non-trivial dynamics, leading to collision; Second, the
feasible space for the manipulator is hard to obtain since the explicit
distance functions between collision meshes are unknown. By analyzing the
relationship between the safe set and the controlled invariant set, this paper
proposes a data-driven control barrier function (CBF) construction method,
which extracts CBF from distance samples. Specifically, the CBF guarantees the
controlled invariant property for considering the system dynamics. The
data-driven method samples the distance function and determines the safe set.
Then, the CBF is synthesized based on the safe set by a scenario-based sum of
square (SOS) program. Unlike most existing linearization based approaches, our
method reserves the volume of the feasible space for planning without
approximation, which helps find a solution in a cluttered environment. The
control law is obtained by solving a CBF-based quadratic program in real time,
which works as a safe filter for the desired planning-based controller.
Moreover, our method guarantees safety with the proven probabilistic result.
Our method is validated on a 7-DOF manipulator in both real and virtual
cluttered environments. The experiments show that the manipulator is able to
execute tasks where the clearance between obstacles is in millimeters.
