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A Quantum Computing Approach for Multi-robot Coverage Path Planning

Poojith U Rao, Florian Speelman, Balwinder Sodhi, Sachin Kinge

TL;DR

The paper addresses multi-robot Coverage Path Planning, an NP-hard problem, by encoding path search on a 2D grid into a Quantum Approximate Optimization Algorithm (QAOA) framework. It introduces a binary decision variable and a multi-term objective that jointly accounts for obstacle avoidance, coverage, and path overlap, and designs a hierarchy of mixers (including Simultaneous Bit Flip and four-node controlled mixers) and a phase separator to confine search to feasible solutions. A proof of explorability shows that Simultaneous Bit Flip operations on four-node sub-grids can transform any feasible path into any other, enabling thorough exploration. Resource estimates detail qubit counts and gate requirements, and experiments compare QAOA, Simulated Annealing, and DFS on small grids, validating the approach for a single robot and illustrating SA performance for larger multi-robot cases. The work lays groundwork for quantum CPP via QAOA and suggests future QUBO formulations and annealer comparisons, potentially informing real-world multi-robot path planning.

Abstract

This paper tackles the multi-vehicle Coverage Path Planning (CPP) problem, crucial for applications like search and rescue or environmental monitoring. Due to its NP-hard nature, finding optimal solutions becomes infeasible with larger problem sizes. This motivates the development of heuristic approaches that enhance efficiency even marginally. We propose a novel approach for exploring paths in a 2D grid, specifically designed for easy integration with the Quantum Alternating Operator Ansatz (QAOA), a powerful quantum heuristic. Our contribution includes: 1) An objective function tailored to solve the multi-vehicle CPP using QAOA. 2) Theoretical proofs guaranteeing the validity of the proposed approach. 3) Efficient construction of QAOA operators for practical implementation. 4) Resource estimation to assess the feasibility of QAOA execution. 5) Performance comparison against established algorithms like the Depth First Search. This work paves the way for leveraging quantum computing in optimizing multi-vehicle path planning, potentially leading to real-world advancements in various applications.

A Quantum Computing Approach for Multi-robot Coverage Path Planning

TL;DR

The paper addresses multi-robot Coverage Path Planning, an NP-hard problem, by encoding path search on a 2D grid into a Quantum Approximate Optimization Algorithm (QAOA) framework. It introduces a binary decision variable and a multi-term objective that jointly accounts for obstacle avoidance, coverage, and path overlap, and designs a hierarchy of mixers (including Simultaneous Bit Flip and four-node controlled mixers) and a phase separator to confine search to feasible solutions. A proof of explorability shows that Simultaneous Bit Flip operations on four-node sub-grids can transform any feasible path into any other, enabling thorough exploration. Resource estimates detail qubit counts and gate requirements, and experiments compare QAOA, Simulated Annealing, and DFS on small grids, validating the approach for a single robot and illustrating SA performance for larger multi-robot cases. The work lays groundwork for quantum CPP via QAOA and suggests future QUBO formulations and annealer comparisons, potentially informing real-world multi-robot path planning.

Abstract

This paper tackles the multi-vehicle Coverage Path Planning (CPP) problem, crucial for applications like search and rescue or environmental monitoring. Due to its NP-hard nature, finding optimal solutions becomes infeasible with larger problem sizes. This motivates the development of heuristic approaches that enhance efficiency even marginally. We propose a novel approach for exploring paths in a 2D grid, specifically designed for easy integration with the Quantum Alternating Operator Ansatz (QAOA), a powerful quantum heuristic. Our contribution includes: 1) An objective function tailored to solve the multi-vehicle CPP using QAOA. 2) Theoretical proofs guaranteeing the validity of the proposed approach. 3) Efficient construction of QAOA operators for practical implementation. 4) Resource estimation to assess the feasibility of QAOA execution. 5) Performance comparison against established algorithms like the Depth First Search. This work paves the way for leveraging quantum computing in optimizing multi-vehicle path planning, potentially leading to real-world advancements in various applications.
Paper Structure (24 sections, 11 equations, 10 figures)

This paper contains 24 sections, 11 equations, 10 figures.

Table of Contents

  1. Introduction
  2. Related work
  3. Coverage Path Planning problem
  4. Problem definition
  5. Decision variable
  6. Objective function
  7. Initial population
  8. Mutation
  9. Four-node graph
  10. Scaling to larger grids
  11. Logic function representing valid/invalid paths inside four node sub-grid
  12. Proof of explorability
  13. QAOA for Coverage Path Planning
  14. Initial state
  15. Mixers
  16. ...and 9 more sections

Figures (10)

  • Figure 1: On the left - Scenarios where SBF operation searches for paths between two points. Top-left is the $S_1$ operation, and bottom-left is the $S_2$ operation. On the right - Scenarios where SBF operation must be avoided
  • Figure 2: Scenario where SBF operation on a four-node sub-grid results in a loop
  • Figure 3: Exploring all feasible paths between two points $a$ and $b$ by applying SBF operation on 4-node sub-grids.
  • Figure 4: Corner in a closed region
  • Figure 5: Simultaneous Bit Flip mixer that flips all the qubits simultaneously and is controlled by a parameter $\beta$.
  • ...and 5 more figures