Scalable Multi-Robot Path Planning via Quadratic Unconstrained Binary Optimization

TL;DR

This paper investigates Quadratic Unconstrained Binary Optimization (QUBO) as a structurally scalable alternative for simultaneous multi-robot path planning and establishes a practical and reproducible baseline for future quantum and quantum-inspired multi-robot coordinations.

Abstract

Multi-Agent Path Finding (MAPF) remains a fundamental challenge in robotics, where classical centralized approaches exhibit exponential growth in joint-state complexity as the number of agents increases. This paper investigates Quadratic Unconstrained Binary Optimization (QUBO) as a structurally scalable alternative for simultaneous multi-robot path planning. This approach is a robotics-oriented QUBO formulation incorporating BFS-based logical pre-processing (achieving over 95% variable reduction), adaptive penalty design for collision and constraint enforcement, and a time-windowed decomposition strategy that enables execution within current hardware limitations. An experimental evaluation in grid environments with up to four robots demonstrated near-optimal solutions in dense scenarios and favorable scaling behavior compared to sequential classical planning. These results establish a practical and reproducible baseline for future quantum and quantum-inspired multi-robot coordinations.

Figures (9)

• Figure 1: Sparse matrix visualization of a single-robot QUBO formulation on a 5×5 grid. Dark regions indicate non-zero entries representing penalty interactions.
• Figure 2: Sparse matrix for two-robot scenario showing increased sparsity. Note the separation corresponding to each robot's variable space.
• Figure 3: Example QAOA circuit for a small pathfinding problem with 2 qubits (after pre-processing). The circuit alternates between cost and mixer Hamiltonians for p=2 layers.
• Figure 4: A* (left) and QUBO solved with simulated QAOA (right) on a 5x5 grid
• Figure 5: QUBO and Classical get to the same optimal answer. Dijkstra is faster