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Safety is often the most important requirement in robotics applications.Nonetheless, control techniques that can provide safety guarantees are stillextremely rare for nonlinear systems, such as robot manipulators. A well-knowntool to ensure safety is the Viability kernel, which is the largest set ofstates from which safety can be ensured. Unfortunately, computing such a setfor a nonlinear system is extremely challenging in general. Several numericalalgorithms for approximating it have been proposed in the literature, but theysuffer from the curse of dimensionality. This paper presents a new approach fornumerically approximating the viability kernel of robot manipulators. Ourapproach solves optimal control problems to compute states that are guaranteedto be on the boundary of the set. This allows us to learn directly the setboundary, therefore learning in a smaller dimensional space. Compared to thestate of the art on systems up to dimension 6, our algorithm resulted to bemore than 2 times as accurate for the same computation time, or 6 times as fastto reach the same accuracy.

VBOC: Learning the Viability Boundary of a Robot Manipulator using Optimal Control