This study introduces a robust planning framework that utilizes a model predictive control (MPC) approach, enhanced by incorporating signal temporal logic (STL) specifications. This marks the first-ever study to apply STL-guided trajectory optimization for bipedal locomotion, specifically designed to handle both translational and orientational perturbations. Existing recovery strategies often struggle with reasoning complex task logic and evaluating locomotion robustness systematically, making them susceptible to failures caused by inappropriate recovery strategies or lack of robustness. To address these issues, we design an analytical robustness metric for bipedal locomotion and quantify this metric using STL specifications, which guide the generation of recovery trajectories to achieve maximum locomotion robustness. To enable safe and computational-efficient crossed-leg maneuver, we design data-driven self-leg-collision constraints that are $1000$ times faster than the traditional inverse-kinematics-based approach. Our framework outperforms a state-of-the-art locomotion controller, a standard MPC without STL, and a linear-temporal-logic-based planner in a high-fidelity dynamic simulation, especially in scenarios involving crossed-leg maneuvers. Additionally, the Cassie bipedal robot achieves robust performance under horizontal and orientational perturbations such as those observed in ship motions. These environments are validated in simulations and deployed on hardware. Furthermore, our proposed method demonstrates versatility on stepping stones and terrain-agnostic features on inclined terrains.

翻译：本研究提出一种鲁棒规划框架，利用模型预测控制方法并融入信号时序逻辑规范。这是首次将信号时序逻辑引导的轨迹优化应用于双足运动，特别针对平移和旋转扰动进行设计。现有恢复策略常难以推理复杂任务逻辑并系统评估运动鲁棒性，导致因恢复策略不当或鲁棒性不足而失效。为解决这些问题，我们为双足运动设计了分析性鲁棒性度量，并通过信号时序逻辑规范量化该度量，从而引导恢复轨迹生成以实现最大运动鲁棒性。为实现安全且计算高效的交叉步态操作，我们设计了数据驱动的自腿碰撞约束，其速度比传统基于逆运动学的方法快1000倍。在高保真动态仿真中，本框架优于最先进的运动控制器、不含信号时序逻辑的标准模型预测控制以及基于线性时序逻辑的规划器，尤其在涉及交叉步态的场景中表现突出。此外，Cassie双足机器人在水平和旋转扰动（如船舶运动中的观测现象）下实现了鲁棒性能。这些环境在仿真中验证并部署于硬件。进一步地，所提方法在踏脚石场景中展现了通用性，并在倾斜地形上具备与地形无关的特性。