# Walking-by-Logic: Signal Temporal Logic-Guided Model Predictive Control for Bipedal Locomotion Resilient to External Perturbations

arXiv: https://arxiv.org/abs/2309.13172 · HTML: https://mlsanity.com/paper/2309.13172/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Sep 2023.

## Built on by (most cited first, 6 of 6)

- [A Survey of Optimization-based Task and Motion Planning: From Classical To Learning Approaches](https://mlsanity.com/paper/2404.02817/) (2024)
- [Enhancing Model-Based Step Adaptation for Push Recovery through Reinforcement Learning of Step Timing and Region](https://mlsanity.com/paper/2411.01000/) (2024)
- [Learning Gait-Aware Quadruped Locomotion with Temporal Logic Specifications](https://mlsanity.com/paper/2607.00442/) (2026)
- [A Unified Approach to Multi-task Legged Navigation: Temporal Logic Meets Reinforcement Learning](https://mlsanity.com/paper/2407.06931/) (2024)
- [Autotuning Bipedal Locomotion MPC with GRFM-Net for Efficient Sim-to-Real Transfer](https://mlsanity.com/paper/2409.15710/) (2024)
- [From LLM-Generated Specifications to Learned Quadruped Locomotion](https://mlsanity.com/paper/2609.07111/) (2026)

## Abstract (arXiv)

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.