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.
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