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To Explore or Not to Explore: Regret-Based LTL Planning in Partially-Known Environments

Jianing Zhao, Keyi Zhu, Mingyang Feng, Xiang Yin

TL;DR

The paper addresses optimal path planning for robots under co-safe LTL specifications in partially-known environments. It introduces a partially-known weighted transition system (PK-WTS) to represent multiple possible worlds and adopts regret as the planning objective, defined as the gap between actual performance and the best hindsight strategy. A knowledge-based game arena is constructed to model agent-environment interaction, and a regret-minimizing synthesis algorithm is developed via a min-max formulation with a novel weight function, yielding polynomial-time solvability. The approach is validated through simulations and a firefighting-robot case study, showing improved trade-offs between exploration cost and task satisfaction compared with worst-case and best-case strategies, demonstrating practical relevance for exploration-rich robotic tasks.

Abstract

In this paper, we investigate the optimal robot path planning problem for high-level specifications described by co-safe linear temporal logic (LTL) formulae. We consider the scenario where the map geometry of the workspace is partially-known. Specifically, we assume that there are some unknown regions, for which the robot does not know their successor regions a priori unless it reaches these regions physically. In contrast to the standard game-based approach that optimizes the worst-case cost, in the paper, we propose to use regret as a new metric for planning in such a partially-known environment. The regret of a plan under a fixed but unknown environment is the difference between the actual cost incurred and the best-response cost the robot could have achieved if it realizes the actual environment with hindsight. We provide an effective algorithm for finding an optimal plan that satisfies the LTL specification while minimizing its regret. A case study on firefighting robots is provided to illustrate the proposed framework. We argue that the new metric is more suitable for the scenario of partially-known environment since it captures the trade-off between the actual cost spent and the potential benefit one may obtain for exploring an unknown region.

To Explore or Not to Explore: Regret-Based LTL Planning in Partially-Known Environments

TL;DR

The paper addresses optimal path planning for robots under co-safe LTL specifications in partially-known environments. It introduces a partially-known weighted transition system (PK-WTS) to represent multiple possible worlds and adopts regret as the planning objective, defined as the gap between actual performance and the best hindsight strategy. A knowledge-based game arena is constructed to model agent-environment interaction, and a regret-minimizing synthesis algorithm is developed via a min-max formulation with a novel weight function, yielding polynomial-time solvability. The approach is validated through simulations and a firefighting-robot case study, showing improved trade-offs between exploration cost and task satisfaction compared with worst-case and best-case strategies, demonstrating practical relevance for exploration-rich robotic tasks.

Abstract

In this paper, we investigate the optimal robot path planning problem for high-level specifications described by co-safe linear temporal logic (LTL) formulae. We consider the scenario where the map geometry of the workspace is partially-known. Specifically, we assume that there are some unknown regions, for which the robot does not know their successor regions a priori unless it reaches these regions physically. In contrast to the standard game-based approach that optimizes the worst-case cost, in the paper, we propose to use regret as a new metric for planning in such a partially-known environment. The regret of a plan under a fixed but unknown environment is the difference between the actual cost incurred and the best-response cost the robot could have achieved if it realizes the actual environment with hindsight. We provide an effective algorithm for finding an optimal plan that satisfies the LTL specification while minimizing its regret. A case study on firefighting robots is provided to illustrate the proposed framework. We argue that the new metric is more suitable for the scenario of partially-known environment since it captures the trade-off between the actual cost spent and the potential benefit one may obtain for exploring an unknown region.
Paper Structure (28 sections, 6 theorems, 62 equations, 4 figures, 2 tables, 1 algorithm)

This paper contains 28 sections, 6 theorems, 62 equations, 4 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. LTL Planning in Fully-Known Environments
  3. Weighted Transition Systems
  4. Linear Temporal Logic Specifications
  5. Path Planning for scLTL Specifications
  6. Planning in Partially-Known Environments
  7. Partially-Known Weighted Transition Systems
  8. History and Knowledge Updates
  9. Strategy and Regret
  10. Problem Formulation
  11. Knowledge-Based Game Arena
  12. Knowledge-Based Game Arena
  13. Strategies and Plays in the Game Arena
  14. Game-Based Synthesis Algorithms
  15. Regret-Minimizing Strategy Synthesis
  16. ...and 13 more sections

Key Result

Proposition 1

Given the PK-WTS $\mathbb{T}$, scLTL task $\phi$, and the knowledge-based game arena $G$, for any strategy $\xi\in\textsf{Stra}_\phi(\mathbb{T})$, there exists a unique corresponding agent-player strategy $\sigma_a\in\mathfrak{S}_a$ such that

Figures (4)

  • Figure 1: A motivating example, where a robot needs to reach region $5$ from regin $0$ with partially-known environment information.
  • Figure 2: Numerical Simulation Results on Randomly Generated Environments
  • Figure 3: Experiment Setting
  • Figure 4: Experiment Results

Theorems & Definitions (13)

  • Definition 1: Partially-Known WTS
  • Definition 2: Regret
  • Definition 3: Knowledge-Based Game Arena
  • Remark 1
  • Proposition 1
  • Definition 4: Best Response
  • Remark 2
  • Lemma 1
  • Lemma 2
  • Proposition 2
  • ...and 3 more