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GPU-Accelerated Quantum Annealing-Inspired UAV Path Planning for Smart Agriculture
Maho Hirahara, Aohan Li
TL;DR
Large agricultural UAV path-planning problems face practical constraints and combinatorial growth as farmland expands. The paper formulates planning as QUBO and solves it with a GPU-parallelized Ising solver on Fixstars Amplify. Simulations report superior paths and stable computation compared with GA and SA, including optimal paths in under 320 milliseconds for tested grids.
Problem
Agricultural UAV planning is limited by battery life, payload capacity, coverage difficulty, and combinatorial search growth in expanding grid-based farmland.
Method
The paper maps constrained UAV path planning into QUBO and solves it through parallel annealing with a GPU-parallelized Ising solver on Fixstars Amplify.
Results
The proposed method consistently identifies superior flight paths with stable computation versus GA and SA, returning optimal paths in under 320 milliseconds on tested 3×3 to 6×6 grids.
Takeaways & Limitations
The method supports real-time and scalable agricultural spraying by exploiting GPU parallel processing for large-scale path search.
Abstract
from arXiv · showhide
Traditional path planning methods are often constrained by local optima, limited scalability, and slow convergence, which significantly restrict their effectiveness in solving large-scale problems. To address these limitations, this paper shifts the problem-solving paradigm from algorithmic refinement to parallelization of computational architecture. We propose a novel optimization framework utilizing a Graphics Processing Unit (GPU)-parallelized Ising solver. Our method mimics the operational principles of quantum annealing on GPU hardware, enabling rapid search for the minimum-energy state of Ising models. Unlike physical quantum devices, which are often constrained by the number of qubits, our approach leverages the Fixstars Amplify (FA) platform to perform parallel annealing on highly parallelized GPUs. This enables the simultaneous evaluation of thousands of potential path candidates and vast state transitions. By leveraging large-scale parallel processing, the core strength of this framework lies in minimizing computation time even as the problem scale increases. Furthermore, to solve the path planning problem using the FA platform, we formulate the problem as a Quadratic Unconstrained Binary Optimization (QUBO) model. This formulation converts the objectives of flight constraints and operational time minimization into an energy state, enabling problem processing via the Ising-based architecture. Simulation results demonstrate that our proposed method consistently identifies superior flight paths while maintaining stable computational performance compared with the genetic algorithm and simulated annealing method. These findings highlight its potential as a robust, scalable real- time solution for next-generation large-scale smart agriculture.
I. INTRODUCTION
The paper addresses agricultural UAV path-planning constraints by using GPU-parallelized Ising computation to solve a QUBO formulation with scalable parallel search. Simulations report better flight-path quality and stable computation than GA and SA as problem size increases.
- Agricultural UAV planning remains constrained by limited battery life, low payload capacity, and difficulty covering large areas.
- Grid-based cooperative planning becomes NP-hard as expanding farmland increases grid cells and causes combinatorial search-space growth.
- The proposed framework uses Fixstars Amplify to map QUBO path-planning models onto a GPU-parallelized Ising solver that evaluates many candidate paths and state transitions simultaneously.
- The QUBO formulation combines total flight-time minimization with constraints requiring each grid to be visited once and the UAV to occupy one grid at each time step.
- Simulation results show superior performance to Genetic Algorithm and Simulated Annealing in balancing mission completion time with coverage constraints.
II. SYSTEM MODEL
The system models an agricultural field as an M × N grid and represents UAV movement with travel-time costs and binary cell-at-time decisions. One-hot constraints enforce valid coverage and occupancy while minimizing total flight time.
- The agricultural field is discretized into M × N rectangular grid cells, each representing a basic task-area unit.
- The model uses n = M × N locations and time steps, with travel costs stored in an n×n matrix T.
- Binary variable x_t,i equals 1 when the UAV occupies cell i at time step t and 0 otherwise.
- The objective minimizes total UAV flight time while ensuring that all target cells are covered.
- Constraints require exactly one occupied cell per time step, exactly one visit per grid cell, and binary decision variables.
III. PROPOSED METHOD
The proposed method transforms UAV path planning into a QUBO and solves it through high-speed parallel GPU processing, using quantum annealing as its theoretical foundation.
- The method converts the UAV path-planning problem into QUBO form and solves it with high-speed parallel GPU processing.
A. Quantum annealing
Quantum annealing searches for minimum-energy states of Ising models to solve combinatorial optimization problems. The paper maps UAV objectives and constraints onto this Ising structure and minimizes its Hamiltonian.
- Quantum annealing controls a spin system to search for the minimum-energy state of an Ising model.
- Ising variables σ_k take values +1 or −1, with k indexing flattened multidimensional decision variables.
- The Hamiltonian represents energy through external-field terms h_kσ_k and pairwise interaction terms J_klσ_kσ_l.
- The UAV path-planning objective and constraints are mapped onto the Ising structure, and the resulting Hamiltonian is minimized.
B. QUBO Formulation for UAV Path Planning
The UAV path-planning objective is formulated as a QUBO Hamiltonian that minimizes flight time while covering all target cells and enforcing mission constraints.
- The objective seeks a grid-visit sequence that minimizes total UAV flight time while ensuring all target cells are covered.
- The flight-time objective and path constraints are converted into energy-function terms for QUBO optimization.
- The final Hamiltonian combines the distance term with visit and time constraints using weighting parameters A and λp.
- The mission contains n time steps, with n = M × N equal to the total number of grid cells to be covered.
C. GPU-Accelerated QA Solver
The GPU-accelerated QA solver provides an interface for converting abstract optimization problems into executable QUBO inputs and uses Fixstars’ Amplify Annealing Engine for parallel optimization.
- The solver automatically translates abstract optimization problems into machine-executable formats through GPU-oriented preprocessing.
- Fixstars’ Amplify Annealing Engine solves QUBO-formulated combinatorial optimization problems through the Fixstars Amplify SDK.
D. UAV Path Planning Using GPU-Accelerated QA Solver
The path-planning pipeline constructs binary trajectory variables and constraint terms, submits the QUBO to Amplify AE, and reconstructs the optimal feasible flight path from the returned solution.
- The pipeline computes a travel-time matrix from grid coordinates and defines x_t,i to indicate the UAV’s cell occupancy at each time step.
- Visit and time requirements are combined into Hconstraints before the distance term is added to form the QUBO Hamiltonian.
- The completed QUBO is imported into Amplify AE, which runs with a specified solver time limit L.
- The solver returns the optimal spin combination x*_t,i, which is used to reconstruct the time-series trajectory P and minimum mission cost.
- The resulting trajectory is reconstructed as the final feasible flight path.
IV. PERFORMANCE EVALUATION
The evaluation compares the proposed GPU-accelerated annealing process with baseline methods using total flight time and computation time.
- The simulation compares the proposed method with baseline methods using total flight time and computation time.
A. GPU-Accelerated Annealing Process
The proposed method uses Fixstars Amplify’s GPU-based Annealing Engine to solve QUBO formulations through massive parallel annealing, and benchmarks it against GA and SA.
- A. GPU-Accelerated Annealing Process: Fixstars Amplify combines a unified SDK with a high-performance GPU-based Annealing Engine for complex combinatorial optimization.The engine uses GPU parallelism rather than hardware quantum annealing.
- A. GPU-Accelerated Annealing Process: Parallel annealing simulates thousands of independent state replicas simultaneously, enabling high-density exploration of the solution space.
- A. GPU-Accelerated Annealing Process: The proposed method is benchmarked against two widely used metaheuristics: Genetic Algorithm and Simulated Annealing.
C. Simulation Parameters
The simulations model agricultural fields as grids and vary grid dimensions from 3 × 3 to 6 × 6 to assess how increasing node density affects computational efficiency and path quality.
- C. Simulation Parameters: The agricultural field is modeled as an M × N grid with unit width wgrid = 5.0 m and UAV travel speed of 5.0 m/s.The objective and constraint weights A and λp were both set to 1.
- C. Simulation Parameters: The Amplify Annealing Engine computation time limit L was set to 100 ms to support real-time feasibility in dynamic agricultural environments.
- C. Simulation Parameters: Simulations used grid sizes ranging from 3 × 3 to 6 × 6 to evaluate the effect of increasing node density on computational efficiency.
- C. Simulation Parameters: The proposed method achieved the lowest total flight time, while the difference from GA and SA became clearer as grids expanded to 4×5, 5×6, and 6 × 6.
2) Calculation Time Stability:
Calculation time remains stable for the proposed GPU-based method as grid size increases, whereas conventional metaheuristics become slower, particularly on larger grids.
- 2) Calculation Time Stability:: SA and GA show significant execution-time increases with node count, while Fixstars Amplify remains stable across the tested grid sizes.GA required the most computational time for all grid sizes.
- 2) Calculation Time Stability:: SA is fastest on small configurations, but its execution time rises sharply when the grid exceeds 4 × 4.The increase is attributed to exponential growth in the search space.
- 2) Calculation Time Stability:: On the largest 6 × 6 grid, Fixstars Amplify consistently returns solutions in a fraction of the time required by conventional metaheuristic methods.
- 2) Calculation Time Stability:: Across grid dimensions from 3×3 to 6×6, the proposed method consistently identified optimal paths in less than 320 milliseconds.The conclusion links this efficiency to real-time UAV operations requiring immediate path updates.
- 2) Calculation Time Stability:: The current study uses a simplified flight-time-based Hamilton; future work will incorporate battery capacity and pesticide application amount.Larger M × N grids are also planned for computation and evaluation.