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EPJ Quantum Technology

Quantum optimization for multi-target Active Debris Removal missions

Michele Gagliardi, Mattia Boggio, Deborah Volpe, Carlo Novara

Published Sep 29, 2025• 3 citations
Publisher

Abstract

Abstract The rapid accumulation of space debris in Low Earth Orbit (LEO) poses a significant challenge to the sustainability of space operations. While preventive measures limit new debris generation, they are insufficient to mitigate the growing population of defunct satellites, rocket stages, and collision fragments. Active Debris Removal (ADR) has emerged as a viable solution, which requires solving NP-hard combinatorial optimization problemsimilar to the Traveling Salesman Problem (TSP) to maximize mission efficiency by minimizing fuel and mission duration. This work explores the application of Quantum Annealing (QA) and Hybrid Quantum Annealing (HQA) for optimizing multi-target ADR missions. Specifically, it introduces a Quadratic Unconstrained Binary Optimization (QUBO) model for ADR, exploiting quantum computing to enhance solution efficiency. A novel quadratization method is developed to reduce computational complexity, enabling large-scale mission planning. Additionally, a novel constraint-handling strategy is proposed, integrating mission constraints into post-processing to enhance quantum solver efficiency. The proposed approach is validated using real-world satellite debris datasets and benchmarked against classical metaheuristic optimizers, including Simulated Annealing (SA), Tabu Search (TS), and Genetic Algorithms (GA). The obtained results demonstrate the advantages of quantum optimization for ADR mission planning, providing a scalable and computationally efficient solution.

DOI
10.1140/epjqt/s40507-025-00409-3

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Abstract The rapid accumulation of space debris in Low Earth Orbit (LEO) poses a significant challenge to the sustainability of space operations. While preventive measures limit new debris generation, they are insufficient to mitigate the growing population of defunct satellites, rocket stages, and collision fragments. Active Debris Removal (ADR) has emerged as a viable solution, which requires solving NP-hard combinatorial optimization problemsimilar to the Traveling Salesman Problem (TSP) to maximize mission efficiency by minimizing fuel and mission duration. This work explores the application of Quantum Annealing (QA) and Hybrid Quantum Annealing (HQA) for optimizing multi-target ADR missions. Specifically, it introduces a Quadratic Unconstrained Binary Optimization (QUBO) model for ADR, exploiting quantum computing to enhance solution efficiency. A novel quadratization method is developed to reduce computational complexity, enabling large-scale mission planning. Additionally, a novel constraint-handling strategy is proposed, integrating mission constraints into post-processing to enhance quantum solver efficiency. The proposed approach is validated using real-world satellite debris datasets and benchmarked against classical metaheuristic optimizers, including Simulated Annealing (SA), Tabu Search (TS), and Genetic Algorithms (GA). The obtained results demonstrate the advantages of quantum optimization for ADR mission planning, providing a scalable and computationally efficient solution.
A strategy for the analysis of active debris removal missions targeting multiple objects from a set of objects in near-circular orbit with similar inclination is presented. Algebraic techniques successfully reduce the orbital mechanics regarding specific inter-debris transfer and disposal methods to simple computations, which can be used as the coefficients of a quadratic unconstrained binary optimisation (QUBO) problem formulation which minimises the total propellant used in the mission whilst allowing for servicing time and meeting the mission deadline. The QUBO is validated by solving artificial small problems (from 2 to 11 debris) using classical computational methods and the weaknesses in using these methods are examined prior to solution using quantum annealing hardware. The quantum processing unit (QPU) and quantum-classical hybrid solvers provided by D-Wave are then used to solve the same small problems, with attention paid to evident strengths and weaknesses of each approach. Hybrid solvers are found to be significantly more effective at solving larger problems. Finally, the hybrid method is used to solve a large problem using a real dataset. From a set of 79 debris objects resulting from the destruction of the Kosmos-1408 satellite, an active debris removal mission starting on 30 September 2023 targeting 5 debris objects for disposal within a year with 20 days servicing time per object is successfully planned. This plan calculates the total propellant cost of transfer and disposal to be 0.87km/s and would be complete well within the deadline at 241 days from the start date. This problem uses 6,478 binary variables in total and is solved using around 25s of QPU access time.
The continued growth of orbital debris threatens the safety and sustainability of near-Earth space, making Active Debris Removal (ADR) an important mitigation strategy. Selecting kkk targets from NNN candidates yields a combinatorial search space of size (Nk)\binom{N}{k}(kN​), making joint target selection and mission sequencing computationally demanding. We present a topology-aware quantum-classical framework integrating orbital mechanics, weighted orbital-transfer graphs, Gaussian Boson Sampling (GBS), and multi-objective evolutionary optimization. Seven target-prioritization strategies represent physical consequence, orbital persistence, conjunction risk, network centrality, community structure, inferred source families, and random selection. GBS generates candidate target subsets from the weighted graph, which are then evaluated using PyGMO-based evolutionary optimization to identify servicing sequences that jointly minimize total velocity increment (ΔvΔvΔv) and mission duration, accounting for modeled timing, propulsion, and mass feasibility. We evaluate the framework across three benchmark environments, SOCRATES Minefield, Collision Cloud, and Random, with candidate-pool sizes N∈{15,18,22,25}N\in\{15,18,22,25\}N∈{15,18,22,25} and target cardinalities k∈{3,5}k\in\{3,5\}k∈{3,5}. The experiments characterize how benchmark topology, prioritization strategy, and problem scale relate to sampling behavior and downstream mission performance. By separating candidate-subset generation from detailed trajectory optimization, the framework offers a topology-aware approach to focusing computational effort on a limited set of candidate ADR missions.
Abstract The scheduling complexity of Agile Earth Observation Satellites (AEOSs) increases significantly as Earth Observation missions progress. This makes traditional optimization techniques less effective, restricting their application to small-scale and open-loop scheduling problems. In this paper, we investigate the potential of quantum solvers to address the closed-loop scheduling problem for a formation of AEOSs, overcoming the limitations of classical optimization techniques. To this end, we formulate the scheduling problem as a novel Quadratic Unconstrained Binary Optimization (QUBO) problem, i.e., a formulation specifically designed for quantum solvers. Moreover, penalty functions are introduced to minimize mission energy consumption and reduce deviations between the original and rescheduled solutions. The formulated QUBO problem is implemented on a D-Wave quantum annealer for a daily and large-scale scheduling scenario. The obtained results demonstrate significant improvements in computational efficiency and solution quality compared to traditional methods like Simulated Annealing and Tabu Search, highlighting the potential of quantum solvers in optimizing complex scheduling tasks for AEOS formations.
The increasing number of Low Earth Orbit (LEO) satellites, driven by lower manufacturing and launch costs, is proving invaluable for Earth observation missions and low-latency internet connectivity. However, as the number of satellites increases, the number of communication links to maintain also rises, making the management of this vast network increasingly challenging and highlighting the need for clustering satellites into efficient groups as a promising solution. This paper formulates the clustering of LEO satellites as a coalition structure generation (CSG) problem and leverages quantum annealing to solve it. We represent the satellite network as a graph and obtain the optimal partitions using a hybrid quantum-classical algorithm called GCS-Q. The algorithm follows a top-down approach by iteratively splitting the graph at each step using a quadratic unconstrained binary optimization (QUBO) formulation. To evaluate our approach, we utilize real-world three-line element set (TLE/3LE) data for Starlink satellites from Celestrak. Our experiments, conducted using the D-Wave Advantage annealer and the state-of-the-art solver Gurobi, demonstrate that the quantum annealer significantly outperforms classical methods in terms of runtime while maintaining the solution quality. The performance achieved with quantum annealers surpasses the capabilities of classical computers, highlighting the transformative potential of quantum computing in optimizing the management of large-scale satellite networks.
Satellite mission planning for Earth observation satellites is a combinatorial optimization problem that consists of selecting the optimal subset of imaging requests, subject to constraints, to be fulfilled during an orbit pass of a satellite. The ever-growing amount of satellites in orbit underscores the need to operate them efficiently, which requires solving many instances of the problem in short periods of time. However, current classical algorithms often fail to find the global optimum or take too long to execute. Here, we approach the problem from a quantum computing point of view, which offers a promising alternative that could lead to significant improvements in solution quality or execution speed in the future. To this end, we study a planning problem with a variety of intricate constraints and discuss methods to encode them for quantum computers. Additionally, we experimentally assess the performance of quantum annealing and the quantum approximate optimization algorithm on a realistic and diverse dataset. Our results identify key aspects like graph connectivity and constraint structure that influence the performance of the methods. We explore the limits of today’s quantum algorithms and hardware, providing bounds on the problems that can be currently solved successfully and showing how the solution degrades as the complexity grows. This work aims to serve as a baseline for further research in the field and establish realistic expectations on current quantum optimization capabilities.
Earth observation satellites (EOS) play a crucial role in collecting data for applications like weather forecasting and disaster management. Optimizing EOS missions to capture high-priority targets within constraints such as storage, energy, and weather is challenging for traditional computing methods. Quantum computing shows promise in enhancing efficiency by exploring vast solution spaces for optimal schedules, even with complex constraints. This paper demonstrates the potential of a quantum algorithm to improve real-time EOS mission planning, maximizing high-priority target acquisition under resource limitations. Compared to classical algorithms like simulated annealing and Gurobi optimizer, the proposed quantum algorithm outperformed in selecting high-priority targets by 23.46%, executed faster than Gurobi by 39.09%, and successfully satisfied all constraints for all data.