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UMBRELLA: Uncertainty-aware Multi-robot Reactive Coordination under Dynamic Temporal Logic Tasks

Qisheng Zhao, Meng Guo, Hengxuan Du, Lars Lindemann, Zhongkui Li

Abstract

Multi-robot systems can be extremely efficient for accomplishing team-wise tasks by acting concurrently and collaboratively. However, most existing methods either assume static task features or simply replan when environmental changes occur. This paper addresses the challenging problem of coordinating multi-robot systems for collaborative tasks involving dynamic and moving targets. We explicitly model the uncertainty in target motion prediction via Conformal Prediction(CP), while respecting the spatial-temporal constraints specified by Linear Temporal Logic (LTL). The proposed framework (UMBRELLA) combines the Monte Carlo Tree Search (MCTS) over partial plans with uncertainty-aware rollouts, and introduces a CP-based metric to guide and accelerate the search. The objective is to minimize the Conditional Value at Risk (CVaR) of the average makespan. For tasks released online, a receding-horizon planning scheme dynamically adjusts the assignments based on updated task specifications and motion predictions. Spatial and temporal constraints among the tasks are always ensured, and only partial synchronization is required for the collaborative tasks during online execution. Extensive large-scale simulations and hardware experiments demonstrate substantial reductions in both the average makespan and its variance by 23% and 71%, compared with static baselines.

UMBRELLA: Uncertainty-aware Multi-robot Reactive Coordination under Dynamic Temporal Logic Tasks

Abstract

Multi-robot systems can be extremely efficient for accomplishing team-wise tasks by acting concurrently and collaboratively. However, most existing methods either assume static task features or simply replan when environmental changes occur. This paper addresses the challenging problem of coordinating multi-robot systems for collaborative tasks involving dynamic and moving targets. We explicitly model the uncertainty in target motion prediction via Conformal Prediction(CP), while respecting the spatial-temporal constraints specified by Linear Temporal Logic (LTL). The proposed framework (UMBRELLA) combines the Monte Carlo Tree Search (MCTS) over partial plans with uncertainty-aware rollouts, and introduces a CP-based metric to guide and accelerate the search. The objective is to minimize the Conditional Value at Risk (CVaR) of the average makespan. For tasks released online, a receding-horizon planning scheme dynamically adjusts the assignments based on updated task specifications and motion predictions. Spatial and temporal constraints among the tasks are always ensured, and only partial synchronization is required for the collaborative tasks during online execution. Extensive large-scale simulations and hardware experiments demonstrate substantial reductions in both the average makespan and its variance by 23% and 71%, compared with static baselines.

Paper Structure

This paper contains 32 sections, 1 theorem, 13 equations, 6 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Our Method
  4. Problem Description
  5. Robots and Targets
  6. Task Specification
  7. Problem Statement
  8. Proposed Solution
  9. Trajectory Estimation of Dynamic Targets
  10. Trajectory Predictor
  11. Conformal Prediction Regions
  12. R-posets for Task Formulas
  13. Uncertainty-Aware Task Assignment
  14. CP-based Monte Carlo Tree Search
  15. Selection and Expansion
  16. ...and 17 more sections

Key Result

Lemma 1

Given an expanded node $\nu^+$, the completion times of key subtasks in $\Omega^{\texttt{s}}_{\nu^+}$ satisfy that where $T_{\omega}$ is the actual completion time of subtask $\omega\in \Omega^{\texttt{s}}_{\nu^+}$; $m$ is the associated target; $\mathcal{I}_{\omega}$ is the set of robots executing $\omega$; $v_{n}$ and $v^{\star}_{m}$ are the velocities of robot $n$ and target $m$.

Figures (6)

  • Figure 1: Top: Task plans with $12$ robots coordinating to track $4$ dynamic targets across $12$ tasks in two scenes (Scene-1: left and middle; Scene-2: right). Middle: ROS simulation with $8$ robots and $3$ dynamic targets executing $10$ tasks. Bottom: Hardware experiments with $4$ robots and $2$ dynamic targets performing $7$ tasks, showing snapshots at different times.
  • Figure 2: Overview of the proposed framework, consisting of four main components: (i) trajectory estimation via LSTM and CP, (ii) task decomposition into an R-poset, (iii) CP-MCTS for uncertainty-aware assignment, and (iv) online execution and receding-horizon adaptation. In the R-poset illustration, precedence and mutual-exclusion relations are marked by black and red arrows, respectively.
  • Figure 3: The average makespan and the number of explored nodes with different random factors $\epsilon$ and expansion strategies (with or without CP-based metric $\zeta$ in (\ref{['eq:metric']})) during initial planning in Scene-1.
  • Figure 4: Left: Gantt chart of Scene-1, where replanning happens when the predicted value $\eta^\star_t$ exceeds a threshold (orange line) and new tasks are triggered (green and blue lines). Right: Gantt chart of Scene-1 where two robots fail at $40s$ and $70s$ (in grey), respectively.
  • Figure 5: ROS simulation results. Top: Robot and target trajectories. Bottom: Gantt chart of the execution timeline with task allocation and replanning.
  • ...and 1 more figures

Theorems & Definitions (6)

  • Example 1
  • Definition 1: R-poset
  • Definition 2: VaR and CVaR
  • Lemma 1
  • proof
  • Remark 1