# A Unified Approach to Multi-task Legged Navigation: Temporal Logic Meets Reinforcement Learning

arXiv: https://arxiv.org/abs/2407.06931 · HTML: https://mlsanity.com/paper/2407.06931/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL for robot locomotion and manipulation, one of 15 directions in Deep reinforcement learning methods.
- Builds on 7 of its 23 references that are in the map.
- First posted on arXiv 9 Jul 2024.

## Placed in

- Deep reinforcement learning methods / [RL for robot locomotion and manipulation](https://mlsanity.com/deeprl/rl-for-robot-locomotion-and-manipulation/)

## Builds on (most cited first, 7 of 7)

- [Safe Reinforcement Learning via Shielding](https://mlsanity.com/paper/1708.08611/) (2017)
- [Safe Reinforcement Learning in Constrained Markov Decision Processes](https://mlsanity.com/paper/2008.06626/) (2020)
- [Foundations for Restraining Bolts: Reinforcement Learning with LTLf/LDLf restraining specifications](https://mlsanity.com/paper/1807.06333/) (2018)
- [A Tutorial on Sparse Gaussian Processes and Variational Inference](https://mlsanity.com/paper/2012.13962/) (2020)
- [Correct-by-synthesis reinforcement learning with temporal logic constraints](https://mlsanity.com/paper/1503.01793/) (2015)
- [Integrated Task and Motion Planning for Safe Legged Navigation in Partially Observable Environments](https://mlsanity.com/paper/2110.12097/) (2021)
- [Walking-by-Logic: Signal Temporal Logic-Guided Model Predictive Control for Bipedal Locomotion Resilient to External Perturbations](https://mlsanity.com/paper/2309.13172/) (2023)

## Abstract (arXiv)

This study examines the problem of hopping robot navigation planning to achieve simultaneous goal-directed and environment exploration tasks. We consider a scenario in which the robot has mandatory goal-directed tasks defined using Linear Temporal Logic (LTL) specifications as well as optional exploration tasks represented using a reward function. Additionally, there exists uncertainty in the robot dynamics which results in motion perturbation. We first propose an abstraction of 3D hopping robot dynamics which enables high-level planning and a neural-network-based optimization for low-level control. We then introduce a Multi-task Product IMDP (MT-PIMDP) model of the system and tasks. We propose a unified control policy synthesis algorithm which enables both task-directed goal-reaching behaviors as well as task-agnostic exploration to learn perturbations and reward. We provide a formal proof of the trade-off induced by prioritizing either LTL or RL actions. We demonstrate our methods with simulation case studies in a 2D world navigation environment.