  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.
