Hierarchical Motion Planning under Probabilistic Temporal Tasks and Safe-Return Constraints

TL;DR

This paper introduces a hierarchical planning method for robotic missions that ensures safe return to safe states with high probability while satisfying complex temporal tasks, improving computational efficiency over baseline methods.

Contribution

It presents a novel hierarchical planning algorithm combining symbolic abstraction and constrained optimization for safe, probabilistic, and complex temporal task planning in robotic systems.

Findings

Hierarchical algorithm outperforms baseline in efficiency and scalability.

The method guarantees high-probability safe return and task satisfaction.

Validated through simulations and hardware experiments in search-and-rescue and planetary exploration.

Abstract

Safety is crucial for robotic missions within an uncertain environment. Common safety requirements such as collision avoidance are only state-dependent, which can be restrictive for complex missions. In this work, we address a more general formulation as safe-return constraints, which require the existence of a return-policy to drive the system back to a set of safe states with high probability. The robot motion is modeled as a Markov Decision Process (MDP) with probabilistic labels, which can be highly non-ergodic. The robotic task is specified as Linear Temporal Logic (LTL) formulas over these labels, such as surveillance and transportation. We first provide theoretical guarantees on the re-formulation of such safe-return constraints, and a baseline solution based on computing two complete product automata. Furthermore, to tackle the computational complexity, we propose a hierarchical planning algorithm that combines the feature-based symbolic and temporal abstraction with constrained optimization. It synthesizes simultaneously two dependent motion policies: the outbound policy minimizes the overall cost of satisfying the task with a high probability, while the return policy ensures the safe-return constraints. The problem formulation is versatile regarding the robot model, task specifications and safety constraints. The proposed hierarchical algorithm is more efficient and can solve much larger problems than the baseline solution, with only a slight loss of optimality. Numerical validations include simulations and hardware experiments of a search-and-rescue mission and a planetary exploration mission over various system sizes.