  Safety is often the most important requirement in robotics applications.
Nonetheless, control techniques that can provide safety guarantees are still
extremely rare for nonlinear systems, such as robot manipulators. A well-known
tool to ensure safety is the Viability kernel, which is the largest set of
states from which safety can be ensured. Unfortunately, computing such a set
for a nonlinear system is extremely challenging in general. Several numerical
algorithms for approximating it have been proposed in the literature, but they
suffer from the curse of dimensionality. This paper presents a new approach for
numerically approximating the viability kernel of robot manipulators. Our
approach solves optimal control problems to compute states that are guaranteed
to be on the boundary of the set. This allows us to learn directly the set
boundary, therefore learning in a smaller dimensional space. Compared to the
state of the art on systems up to dimension 6, our algorithm resulted to be
more than 2 times as accurate for the same computation time, or 6 times as fast
to reach the same accuracy.
