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Scalable Multi-Robot Task Allocation and Coordination under Signal Temporal Logic Specifications

Wenliang Liu, Nathalie Majcherczyk, Federico Pecora

TL;DR

The paper tackles scalable multi-robot task allocation under Signal Temporal Logic specifications by decoupling planning from coordination: it first generates multiple reference paths per robot via single-robot planners, then encodes coordination as RP-STL over path progress and solves a MILP to assign paths and time-stamped targets. A local controller tracks the MILP-derived targets, ensuring the RP-STL is satisfied under practical tracking assumptions. The authors prove formal satisfaction of RP-STL, demonstrate significant runtime improvements over state-of-the-art methods, and show scalability to dozens of robots across diverse scenarios, including interference, counting, and task-allocations in warehouse-like settings. This approach offers a practical, provably correct framework for complex, long-horizon multi-robot coordination with expressive temporal logic requirements.

Abstract

Motion planning with simple objectives, such as collision-avoidance and goal-reaching, can be solved efficiently using modern planners. However, the complexity of the allowed tasks for these planners is limited. On the other hand, signal temporal logic (STL) can specify complex requirements, but STL-based motion planning and control algorithms often face scalability issues, especially in large multi-robot systems with complex dynamics. In this paper, we propose an algorithm that leverages the best of the two worlds. We first use a single-robot motion planner to efficiently generate a set of alternative reference paths for each robot. Then coordination requirements are specified using STL, which is defined over the assignment of paths and robots' progress along those paths. We use a Mixed Integer Linear Program (MILP) to compute task assignments and robot progress targets over time such that the STL specification is satisfied. Finally, a local controller is used to track the target progress. Simulations demonstrate that our method can handle tasks with complex constraints and scales to large multi-robot teams and intricate task allocation scenarios.

Scalable Multi-Robot Task Allocation and Coordination under Signal Temporal Logic Specifications

TL;DR

The paper tackles scalable multi-robot task allocation under Signal Temporal Logic specifications by decoupling planning from coordination: it first generates multiple reference paths per robot via single-robot planners, then encodes coordination as RP-STL over path progress and solves a MILP to assign paths and time-stamped targets. A local controller tracks the MILP-derived targets, ensuring the RP-STL is satisfied under practical tracking assumptions. The authors prove formal satisfaction of RP-STL, demonstrate significant runtime improvements over state-of-the-art methods, and show scalability to dozens of robots across diverse scenarios, including interference, counting, and task-allocations in warehouse-like settings. This approach offers a practical, provably correct framework for complex, long-horizon multi-robot coordination with expressive temporal logic requirements.

Abstract

Motion planning with simple objectives, such as collision-avoidance and goal-reaching, can be solved efficiently using modern planners. However, the complexity of the allowed tasks for these planners is limited. On the other hand, signal temporal logic (STL) can specify complex requirements, but STL-based motion planning and control algorithms often face scalability issues, especially in large multi-robot systems with complex dynamics. In this paper, we propose an algorithm that leverages the best of the two worlds. We first use a single-robot motion planner to efficiently generate a set of alternative reference paths for each robot. Then coordination requirements are specified using STL, which is defined over the assignment of paths and robots' progress along those paths. We use a Mixed Integer Linear Program (MILP) to compute task assignments and robot progress targets over time such that the STL specification is satisfied. Finally, a local controller is used to track the target progress. Simulations demonstrate that our method can handle tasks with complex constraints and scales to large multi-robot teams and intricate task allocation scenarios.

Paper Structure

This paper contains 23 sections, 2 theorems, 12 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. System Model
  4. Reference Path STL
  5. Interference Constraints
  6. The Task Allocation and Coordination Problem
  7. MILP-Based Solution
  8. Constructing the LCCF
  9. Selection vector encoding
  10. RP-STL encoding
  11. Sum of travel time encoding
  12. Eliminating Disjunctions and Counting Operators
  13. Overall MILP Approach
  14. Local Controllers
  15. Experimental Evaluation
  16. ...and 8 more sections

Key Result

Theorem 1

Under Assumption as:in-ball, given an RP-STL specification $\varphi$ and a sequence of TSJPs from solving eq:optimization, the joint temporal profile $\bm\sigma$ executed by the local controller that tracks these TSJPs always satisfies $\varphi$, i.e., $[\mathbf z, \bm\sigma]\models\varphi$.

Figures (3)

  • Figure 1: Left: The critical section between two robots $r_i$ and $r_{i'}$. Right: $3$ robots crossing a bridge (gray) on a river (blue).
  • Figure 2: Experiment results. Black and white circles are waypoints for the selected and unselected paths. Solid lines are the paths between the first two TSJPs. In (d), (e), the red and green circles are the full and empty carts, respectively. Videos of the experiments can be found at https://www.amazon.science/scalable-multi-robot-task-allocation-and-coordination-under-signal-temporal-logic-specifications.
  • Figure 3: Runtime for different number of robots.

Theorems & Definitions (7)

  • Remark 1
  • Remark 2
  • Example 1
  • Theorem 1
  • proof
  • Theorem 2
  • proof