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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.

This study investigates formal-method-based trajectory optimization (TO) for bipedal locomotion, focusing on scenarios where the robot encounters external perturbations at unforeseen times. Our key research question centers around the assurance of task specification correctness and the maximization of specification robustness for a bipedal robot in the presence of external perturbations. Our contribution includes the design of an optimization-based task and motion planning framework that generates optimal control sequences with formal guarantees of external perturbation recovery. As a core component of the framework, a model predictive controller (MPC) encodes signal temporal logic (STL)-based task specifications as a cost function. In particular, we investigate challenging scenarios where the robot is subjected to lateral perturbations that increase the risk of failure due to leg self-collision. To address this, we synthesize agile and safe crossed-leg maneuvers to enhance locomotion stability. This work marks the first study to incorporate formal guarantees offered by STL into a TO for perturbation recovery of bipedal locomotion. We demonstrate the efficacy of the framework via perturbation experiments in simulations.

This study proposes a novel planning framework based on a model predictive control formulation that incorporates signal temporal logic (STL) specifications for task completion guarantees and robustness quantification. This marks the first-ever study to apply STL-guided trajectory optimization for bipedal locomotion push recovery, where the robot experiences unexpected disturbances. Existing recovery strategies often struggle with complex task logic reasoning and locomotion robustness evaluation, making them susceptible to failures caused by inappropriate recovery strategies or insufficient robustness. To address this issue, the STL-guided framework generates optimal and safe recovery trajectories that simultaneously satisfy the task specification and maximize the locomotion robustness. Our framework outperforms a state-of-the-art locomotion controller in a high-fidelity dynamic simulation, especially in scenarios involving crossed-leg maneuvers. Furthermore, it demonstrates versatility in tasks such as locomotion on stepping stones, where the robot must select from a set of disjointed footholds to maneuver successfully.