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

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

This paper presents a methodology to address the complex problem of multi-task legged robot navigation, specifically focusing on simultaneous goal-directed tasks and environment exploration in the presence of system uncertainties. The authors combine Linear Temporal Logic (LTL)-based task specifications with Reinforcement Learning (RL) to create a comprehensive framework that ensures the robot can meet mandatory tasks while optimizing optional exploration tasks.

Core Contributions

The methodology proposed in this paper can be summarized by the following contributions:

1. Probabilistic Planning: This is the inaugural approach combining probabilistic planning to meet LTL-specified goal-reaching tasks while simultaneously maximizing RL-based exploration rewards.
2. IMDP Abstraction for Hopping Dynamics: The authors develop a novel Interval Markov Decision Process (IMDP) abstraction of the dynamics of a 3D hopping robot, which facilitates high-level navigation planning and maintains kinodynamic feasibility.
3. Unified Control Policy Synthesis: The proposed algorithm provides formal trade-offs between prioritizing LTL and RL actions, backed by rigorous theoretical proofs.

Methodology Overview

IMDP Abstraction

The authors abstract the 3D hopping robot dynamics into an IMDP framework. This IMDP abstraction partitions the state space into hyper-rectangular regions with high-level actions treated as transitions between these regions. This simplification ensures that high-level planning is computationally feasible while maintaining a connection to the low-level dynamics through a neural network-based controller.

Learning-based Low-level Controller

To ensure the robot can reach the designated states, the authors employ a neural network that learns the mapping from control inputs (leg angles) to high-level state transitions (hop displacement). This network is trained offline and optimized at runtime to ensure smooth integration of high-level plans with low-level controls.

MT-PIMDP and Synthesis

A Multi-task Product IMDP (MT-PIMDP) framework is constructed by combining the IMDP abstraction with DRA-based LTL specifications and a reward function. The control policy synthesis algorithms leverage Q-learning to ensure not only task satisfaction but also reward optimization. The algorithm incorporates state-ordering to handle the probabilistic nature of the IMDP transitions.

Exploration and Goal-reaching Policies

Two main policies are proposed: an environment-exploration policy combining LTL and RL actions with a defined probability and a goal-reaching policy that adopts an $\epsilon$-decaying strategy to balance reward optimization with LTL satisfaction. These policies switch between high-level goals based on optimality criteria and the learned model of system uncertainties.

Case Studies and Results

The experimental validation of the approach is conducted using a simulation of a 3D hopping robot navigating a structured environment. The environment includes goal regions, hazards, and reward regions with varying values. Key findings from the case studies highlight:

• The proposed algorithm successfully balances LTL and RL tasks, optimizing rewards while ensuring mandatory task satisfaction.
• The exploration policy effectively learns system uncertainties and reward functions, demonstrated through multiple runs where the robot improves its trajectory as it refines its model of the environment.
• The trade-off between LTL task satisfaction speed and reward optimization can be controlled using tuning parameters, validated through varied experiments.

Implications and Future Work

Theoretical Implications: The results underscore the feasibility of integrating LTL and RL within a unified probabilistic framework. This has broad implications for the design of robotic systems that require both high reliability (guarantees of task completion) and adaptability in dynamic, uncertain environments.

Practical Applications: Practically, this approach can be extended to other robotic systems beyond hopping robots, such as bipedal or wheeled robots, particularly those operating in complex environments with inherent uncertainties. The methodology could lead to advancements in autonomous robotic operations in sectors such as search and rescue, maintenance, and exploration.

Future Developments: The paper suggests future work to implement the approach on a real-world bipedal robot, such as Digit. Such implementations would involve addressing additional real-world complexities like sensor noise, unmodeled dynamics, and more varied environmental uncertainties.

Overall, this paper provides a robust framework for tackling multi-task navigation challenges in legged robotics, systematically combining formal methods with adaptive learning techniques. It offers a significant step toward the reliable and versatile deployment of autonomous robots in real-world scenarios.