Bipedal humanoid robots must precisely coordinate balance, timing, and contact decisions when locomoting on constrained footholds such as stepping stones, beams, and planks -- even minor errors can lead to catastrophic failure. Classical optimization and control pipelines handle these constraints well but depend on highly accurate mathematical representations of terrain geometry, making them prone to error when perception is noisy or incomplete. Meanwhile, reinforcement learning has shown strong resilience to disturbances and modeling errors, yet end-to-end policies rarely discover the precise foothold placement and step sequencing required for discontinuous terrain. These contrasting limitations motivate approaches that guide learning with physics-based structure rather than relying purely on reward shaping. In this work, we introduce a locomotion framework in which a reduced-order stepping planner supplies dynamically consistent motion targets that steer the RL training process via Control Lyapunov Function (CLF) rewards. This combination of structured footstep planning and data-driven adaptation produces accurate, agile, and hardware-validated stepping-stone locomotion on a humanoid robot, substantially improving reliability compared to conventional model-free reinforcement-learning baselines.

翻译：双足人形机器人在受限立足点（如踏脚石、横梁和木板）上移动时，必须精确协调平衡、时机和接触决策——即使微小误差也可能导致灾难性失败。经典优化与控制流程能良好处理这些约束，但高度依赖对地形几何的精确数学描述，当感知存在噪声或不完整时容易出错。与此同时，强化学习已展现出对干扰和建模误差的强大鲁棒性，但端到端策略很少能发现非连续地形所需的精确立足点放置与步序规划。这些对比性局限促使我们采用基于物理结构引导学习的方法，而非单纯依赖奖励塑形。本研究提出一种步态框架：通过降维步态规划器提供动态一致的运动目标，并借助控制李雅普诺夫函数奖励引导强化学习训练过程。这种结构化步态规划与数据驱动自适应相结合的方法，在人形机器人上实现了精确、敏捷且经硬件验证的踏脚石步态，相比传统无模型强化学习基线显著提升了可靠性。