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.

翻译：安全性通常是机器人应用中最关键的要求。然而，对于非线性系统（如机器人操作臂）而言，能够提供安全保证的控制技术仍极为罕见。确保安全性的著名工具是可行核（viability kernel），即能保证安全性的最大状态集合。遗憾的是，对于非线性系统，计算这一集合通常极具挑战性。文献中已提出多种数值近似算法，但这些方法均受维数灾问题困扰。本文提出一种用于数值近似机器人操作臂可行核的新方法。该方法通过求解最优控制问题，计算可确保位于集合边界上的状态，从而直接学习集合边界，即在更低维空间中进行学习。与面向6维及以下系统的现有技术相比，本算法在相同运算时间内精度提升超2倍，或在达到相同精度时速度提升达6倍。