Safety is critical during human-robot interaction. But -- because people are inherently unpredictable -- it is often difficult for robots to plan safe behaviors. Instead of relying on our ability to anticipate humans, here we identify robot policies that are robust to unexpected human decisions. We achieve this by formulating human-robot interaction as a zero-sum game, where (in the worst case) the human's actions directly conflict with the robot's objective. Solving for the Nash Equilibrium of this game provides robot policies that maximize safety and performance across a wide range of human actions. Existing approaches attempt to find these optimal policies by leveraging Hamilton-Jacobi analysis (which is intractable) or linear-quadratic approximations (which are inexact). By contrast, in this work we propose a computationally efficient and theoretically justified method that converges towards the Nash Equilibrium policy. Our approach (which we call MCLQ) leverages linear-quadratic games to obtain an initial guess at safe robot behavior, and then iteratively refines that guess with a Monte Carlo search. Not only does MCLQ provide real-time safety adjustments, but it also enables the designer to tune how conservative the robot is -- preventing the system from focusing on unrealistic human behaviors. Our simulations and user study suggest that this approach advances safety in terms of both computation time and expected performance. See videos of our experiments here: https://youtu.be/KJuHeiWVuWY.

翻译：人机交互中的安全性至关重要。然而，由于人类行为本质上不可预测，机器人往往难以规划安全的行为。本文不依赖对人类行为的预测能力，而是识别出对人类意外决策具有鲁棒性的机器人策略。为此，我们将人机交互建模为零和博弈，其中（在最坏情况下）人类的行为直接与机器人的目标相冲突。求解该博弈的纳什均衡，可得到能够在一系列人类行为中最大化安全性与性能的机器人策略。现有方法尝试利用哈密顿-雅可比分析（计算复杂）或线性二次近似（精度不足）来寻求这些最优策略。相比之下，本文提出一种计算高效且具有理论依据的方法，可收敛至纳什均衡策略。我们的方法（称为MCLQ）利用线性二次博弈获得初始安全行为估计，再通过蒙特卡洛搜索迭代优化该估计。MCLQ不仅能提供实时安全性调整，还允许设计者调节机器人的保守程度，避免系统过度关注不切实际的人类行为。仿真实验与用户研究表明，该方法在计算时间与期望性能两方面均提升了安全性。实验视频详见：https://youtu.be/KJuHeiWVuWY。