Legged robots face significant challenges in navigating complex environments, as they require precise real-time decisions for foothold selection and contact planning. While existing research has explored methods to select footholds based on terrain geometry or kinematics, a critical gap remains: few existing methods efficiently validate the existence of a non-collision swing trajectory. This paper addresses this gap by introducing KCFRC, a novel approach for efficient foothold reachability analysis. We first formally define the foothold reachability problem and establish a sufficient condition for foothold reachability. Based on this condition, we develop the KCFRC algorithm, which enables robots to validate foothold reachability in real time. Our experimental results demonstrate that KCFRC achieves remarkable time efficiency, completing foothold reachability checks for a single leg across 900 potential footholds in an average of 2 ms. Furthermore, we show that KCFRC can accelerate trajectory optimization and is particularly beneficial for contact planning in confined spaces, enhancing the adaptability and robustness of legged robots in challenging environments.

翻译：腿式机器人在复杂环境中导航面临重大挑战，因其需要为落脚点选择和接触规划做出精确的实时决策。尽管现有研究已探索了基于地形几何或运动学选择落脚点的方法，但仍存在一个关键空白：现有方法很少能高效验证无碰撞摆动轨迹的存在性。本文通过引入KCFRC这一用于高效落脚点可达性分析的新方法，以填补这一空白。我们首先正式定义了落脚点可达性问题，并建立了落脚点可达性的一个充分条件。基于此条件，我们开发了KCFRC算法，使机器人能够实时验证落脚点的可达性。我们的实验结果表明，KCFRC实现了显著的时间效率，平均仅需2毫秒即可完成单条腿在900个潜在落脚点上的可达性检查。此外，我们证明KCFRC能够加速轨迹优化，并且对受限空间中的接触规划特别有益，从而增强了腿式机器人在挑战性环境中的适应性和鲁棒性。