Contact-rich robotic systems, such as legged robots and manipulators, are often represented as hybrid systems. However, the stability analysis and region-of-attraction computation for these systems are often challenging because of the discontinuous state changes upon contact (also referred to as state resets). In this work, we cast the computation of region-ofattraction as a Hamilton-Jacobi (HJ) reachability problem. This enables us to leverage HJ reachability tools that are compatible with general nonlinear system dynamics, and can formally deal with state and input constraints as well as bounded disturbances. Our main contribution is the generalization of HJ reachability framework to account for the discontinuous state changes originating from state resets, which has remained a challenge until now. We apply our approach for computing region-of-attractions for several underactuated walking robots and demonstrate that the proposed approach can (a) recover a bigger region-of-attraction than state-of-the-art approaches, (b) handle state resets, nonlinear dynamics, external disturbances, and input constraints, and (c) also provides a stabilizing controller for the system that can leverage the state resets for enhancing system stability.

翻译：然而,这些系统的稳定分析和区域吸引计算往往具有挑战性,因为接触时状态变化不连续(也称为州Resets)。在这项工作中,我们将区域吸引计算方法作为汉密尔顿-贾科比(HJ)可达性问题。这使我们能够利用与一般非线性系统动态兼容的HJ可达性工具,并能够正式处理州和输入限制以及受约束的干扰。我们的主要贡献是,HJ可及性框架的普及化,以说明因州里务而出现的不连续状态变化,迄今为止,这种变化一直是一个挑战。我们运用我们的方法计算几个未充分作用的行走机器人的区域吸引力,并表明拟议办法可以:(a) 恢复比目前最先进的方法更大规模的区域吸引性工具,(b) 处理州里务、非线性动态、外部干扰和输入限制。我们的主要贡献是,HJ可达性框架的普及性框架,以说明由州里务Reset公司引发的不连续状态变化。