# Robust-Locomotion-by-Logic: Perturbation-Resilient Bipedal Locomotion via Signal Temporal Logic Guided Model Predictive Control

arXiv: https://arxiv.org/abs/2403.15993 · HTML: https://mlsanity.com/paper/2403.15993/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Mar 2024.

## Built on by (most cited first, 8 of 8)

- [A Survey of Optimization-based Task and Motion Planning: From Classical To Learning Approaches](https://mlsanity.com/paper/2404.02817/) (2024)
- [Gameplay Filters: Robust Zero-Shot Safety through Adversarial Imagination](https://mlsanity.com/paper/2405.00846/) (2024)
- [Zero-Shot Trajectory Planning for Signal Temporal Logic Tasks](https://mlsanity.com/paper/2501.13457/) (2025)
- [Learning Gait-Aware Quadruped Locomotion with Temporal Logic Specifications](https://mlsanity.com/paper/2607.00442/) (2026)
- [GraSP-STL: A Graph-Based Framework for Zero-Shot Signal Temporal Logic Planning via Offline Goal-Conditioned Reinforcement Learning](https://mlsanity.com/paper/2603.29533/) (2026)
- [Shield-Loco: Shielding Locomotion Policies with Predictive Safety Filtering](https://mlsanity.com/paper/2606.07193/) (2026)
- [From LLM-Generated Specifications to Learned Quadruped Locomotion](https://mlsanity.com/paper/2609.07111/) (2026)
- [Video2STL: Grounding VLM-Generated Temporal Specifications for Robot Learning](https://mlsanity.com/paper/2609.37519/) (2026)

## Abstract (arXiv)

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 stability metric for bipedal locomotion and quantify this metric using STL specifications, which guide the generation of recovery trajectories to achieve maximum robustness degree. 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.