IAES Inter national J our nal of Robotics and A utomation (IJRA) V ol. 15, No. 3, September 2026, pp. 589 ∼ 596 ISSN: 2722-2586, DOI: 10.11591/ijra.v15i3.pp589-596 ❒ 589 Cost-awar e global fr ontier matching f or R OS 2 multi-r obot exploration Chu V an Cuong, T ran T uan Anh A V iS Lab, Posts and T elecommunications Institute of T echnology , Hanoi, V ietnam Article Inf o Article history: Recei v ed May 2, 2026 Re vised Jul 23, 2026 Accepted Aug 6, 2026 K eyw ords: Cost-a w are allocation Frontier allocation Global matching Multi-robot e xploration P ath o v erlap R OS 2 ABSTRA CT Multi-robot frontier e xplor ation supports w arehouse mapping and inspection robotics, b ut geometric assignment can produce o v erlapping motion and inef- cient tar get pairing. This paper presents a R OS 2 frontier -allocation layer that combines a weighted frontier cost with global one-to-one matching. The study isolates global matching from sequential assignment while k eeping the cost for - mulation and R OS 2 e x ecution stack x ed. Three policies are e v aluated on tw o indoor maps, four team sizes, and three seeds. Across 72 completed main-polic y runs, global matching gi v es the l o west mean completion time, tra v elled distance, path o v erlap, and assignment conict. Relati v e to sequential cost-based assign- ment, it reduces compl etion time by 24.3%, tra v elled distance by 14.2%, and path o v erlap by 65.8%, with lo wer nal co v erage under the same stopping rule. The results support a coordination-ef cienc y benet in the tested R OS 2 sim- ulations; broader claims require lar ger , heterogeneous, dynamic, and ph ysical deplo yments. This is an open access article under the CC BY -SA license . Corresponding A uthor: Anh T ran T uan Posts and T elecommunications Institute of T echnology Hanoi, V ietnam Email: anhtt@ptit.edu.vn 1. INTR ODUCTION Autonomous e xploration lets mobile robots b uild maps before na vig ation, inspection, or aut omation tasks. In industrial robotics, it supports AMR/A GV w arehouse mapping, production-oor inspection, and digital-twin preparation. Frontier -based e xploration selects goals at the boundary between kno wn free space and unkno wn space [ 1 ] , and multi-robot e xtensions use shared information to coordinate complementary re- gions [2], [3]. The central problem is assigning useful frontiers without redundant team motion. A nearby tar get may still be poor if another robot is mo ving to w ard the same cluster or if the path o v erlaps in a corridor . Prior w ork sho ws that cost, information g ain, o v erlap reduction, task-allocation mechanisms, and frontier -detection ef cienc y all af fect team beha vior [4]-[10]. Recent w ork has broadened the allocation design space in se v eral directions. V oronoi and parti tion- based methods distrib ute robots across dif ferent spatial re gions, sometimes combined with reinforcement learn- ing to reduce duplicate e xploration [11]-[14]. Learning-based and h ybrid planning approaches modify frontier selection or path generation to impro v e e xploration beha vior in structured en vironments [15]-[17]. Other stud- ies emphasize trajectory planning, auction-style task al location, and deadlock beha vior in multi-robot systems [18]-[21]. Benchmark-dri v en system e v aluation, utility-v alue allocation, and multi-resolution frontier scoring J ournal homepage: http://ijr a.iaescor e .com Evaluation Warning : The document was created with Spire.PDF for Python.
590 ❒ ISSN: 2722-2586 further sho w the need to assess e xploration by more than nal co v erage alone [22]-[25]. These studies pro vide important components, b ut man y comparisons change the frontier score, assign- ment mechanism, and e x ecution stack together . This paper therefore studies a narro wer g ap: whether global one-to-one mat ching impro v es team coordination when the frontier score, frontier source, and R OS 2 stack are x ed. The linear assignment solv er is standard; the contrib ution is the e v aluated allocation layer . The main contrib utions are: − A R OS 2 e xploration pipeline in which the allocation layer combines distance, acti v e-tar get repulsion, robot-specic skip memory , information g ain, and spatial dispersion before Na v2 goal e x ecution. − A controlled comparison of geometric proximity assignment (GP A), sequential cost-based assignment (RSA), and cost-a w are global matching (RGM), with distance-only , distance–g ain, partition-based, auction- style, and no-dispersion references. − A simulation e v aluation o v er tw o indoor maps, four team sizes, and three seeds, using completion time, nal co v erage, tra v elled distance, co v erage ef cienc y , assignment conict, and path o v erlap. The e vidence is limited to the tested indoor simulations; deplo yment-scale claims require lar ger , dynamic, heterogeneous, and ph ysical tests. 2. THE PR OPOSED METHOD 2.1. System ar chitectur e The R OS 2 pipeline inputs per -robot pos es, local SLAM maps, a mer ged occupanc y grid, candidate frontiers, and acti v e tar gets. It outputs at most one na vig ation goal per a v ailabl e robot. Figure 1 summarizes the data o w . LiD AR and odometry update local SLAM maps, local maps are mer ged, frontier clusters are e xtracted, a robot-frontier cost matrix is b uilt, and selected goals are sent to Na v2. Na v2 feedback updates acti v e-tar get and skip-memory states before the ne xt allocation c ycle. SLAM, map mer ging, and l ocal na vig a- tion are standard components; the paper focuses on scoring and matching. Figure 1. R OS 2 e xploration pipeline with cost-a w are allocation 2.2. Cost-awar e fr ontier scor e Let R = { r 1 , . . . , r m } be the set of a v ailable robots and F = { f 1 , . . . , f n } be the set of candidate frontiers. F or robot r i and frontier f j , the allocator uses the follo wing combined cost: C ij = w d ˆ d ij − w a A j − w s S ij + w g G j − w p P ij (1) where lo wer v alues are preferred. The terms encode distance, acti v e-tar get cro wding, robot-specic skip mem- ory , frontier -cluster g ain, and spatial dispersion. IAES Int J Rob & Autom, V ol. 15, No. 3, September 2026: 589–596 Evaluation Warning : The document was created with Spire.PDF for Python.
IAES Int J Rob & Autom ISSN: 2722-2586 ❒ 591 Each frontier candidate is represented by a cluster centroid c j on the mer ged occupanc y grid. Dis- tances are measured in the shared map frame. The implementation uses the follo wing c ycle-le v el normaliza- tion: norm( z ) = z − z min z max − z min + ε , (2) where z min and z max are computed o v er v alues a v ailable in the current allocation c ycle. The constant ε = 0 . 1 a v oids di vision by zero and is k ept x ed across all maps, team sizes, and compared policies. The terms are instantiated as ˆ d ij = d ij max k ,l d k l + ε (3) A j = norm   X a ∈ T act I ( ∥ c j − c a ∥ 2 < ρ a ) ∥ c j − c a ∥ 2 + ε ! (4) S ij = I ( f j ∈ H skip i ) (5) G j = | Q j | max k | Q k | + ε (6) P ij = norm X k ̸ = i 1 ∥ c j − p k ∥ 2 + ε (7) where d ij is the Euclidean distance from robot pose p i to centroid c j , T act is the set of acti v e tar gets, H skip i is a per -robot skip memory , and Q j is the set of grid cells in frontier cluster f j . The same parameter set is used for all maps, team sizes, and methods, as summarized in T able 1. Acti v e-tar get and skip-memory parameters are x ed; sensiti vity analysis is left for future w ork. T able 1. Allocation parameters P arameter V alue Role ε 0.1 A v oids di vision by zero in normalization ρ a 3.0 m Acti v e-tar get repulsion radius. w d , w a , w s , w g , w p w d = 0 . 4 , w a = 0 . 2 , w s = 0 . 1 , w g = 0 . 2 , w p = 0 . 3 Same cost weighting across all non-ablation cost policies. Frontier representation cluster centroid One candidate tar get per frontier cluster Allocation mode batch dispatch A ne w assignment is issued when a v ailable robots can recei v e goals RGM solv er Hung arian linear sum assignment One-to-one global matching o v er the current cost matrix 2.3. Assignment policies and complexity Three main assignment congurations are e v aluated. GP A is the geometric reference polic y and as - signs frontiers using nearest-distance preference. RSA applies the combined cost in (1) sequentially , assigning robots one by one according to the currently lo west a v ailable cost. RGM uses the same cost matrix as RSA b ut solv es all a v ailable robot-frontier pairs jointly as a one-to-one assignment. F or RGM, the binary v ariable x ij equals one when robot r i is assigned to frontier f j in the current allocation round: min x ij m X i =1 n X j =1 C ij x ij , (8) s.t. n X j =1 x ij ≤ 1 , ∀ i, (9) Cost-awar e global fr ontier matc hing ... (Chu V an Cuong) Evaluation Warning : The document was created with Spire.PDF for Python.
592 ❒ ISSN: 2722-2586 m X i =1 x ij ≤ 1 , ∀ j , (10) x ij ∈ { 0 , 1 } . (11) The rst constraint allo ws each a v ail able robot to recei v e at most one frontier , and the second pre v ents duplicate assignment of the same frontier in one round. Cost-matrix construct ion requires O ( mn ) e v alua- tions. The Hung arian solv er operates on the rectangular matrix after padding when needed, and the dominant assignment step scales cubically in the lar ger matrix dimension. 3. METHOD 3.1. Simulation setup and pr otocol Experiments are conducted in a R OS 2 simulation en vironment using the same SLAM, map-mer ging, frontier -detection, and Na v2 na vig ation stack for all compared policies. The allocator is the only component changed. The benchmark contains tw o indoor maps: Map 1 is a cluttered open-space layout of approximately 12 m × 10 m , and Map 2 is a structured layout of approximate ly 15 m × 10 m with partial partitions. The conguration can be seen in T able 2. T able 2. Simulation and measurement conguration Item Conguration used in all compared policies Platform R OS 2 Humble, Gazebo, homogeneous T urtleBot3 Bur ger robots, 0.26 m/s nominal max- imum speed, simulated 2D LDS-01 LiD AR with 360 ◦ vie w and 0.12–3.5 m range. Mapping/frontiers SLAM T oolbox 2D LiD AR SLAM; mer ged occupanc y grid at 0.05 m/cell; frontier cells ha v e a free 4-neighbor , clusters use 8-neighbor BFS, S min = 0 . 5 m, and centroid tar gets. Protocol/metrics Shared Na v2 settings for all policies; st ops at 0.90 co v erage, no reachable frontier with all robots idle, timeout, or f atal f ailure; d c = 1 . 5 m and 0.05 m o v erlap grid. The main comparison e v aluates GP A, RSA, and RGM with 3, 4, 5, and 6 robots and seeds 0, 2, and 4, yielding 24 completed runs per polic y . P aired comparisons use the same map, seed, and robot count. Across seeds, map geometry , robot model, sensor range, softw are stack, and parameters remain x ed; the seed changes only small start-pose perturbations and tie-breaking among equal or near -equal frontier priorities. Extended analysis uses the same protocol for GGM, DGM, PN A, A U A, and RGM-noD. T w o no-dispersion no-data runs are e xcluded, with no outlier remo v al. All policies use the same LiD AR SLAM, map mer ging, frontier clustering, and Na v2 conguration. A run is completed when no feasible frontier remains and all robots return to idle. Run-le v el metrics are completion time, nal co v erage, total distance, co v erage ef cienc y , ass ignment conict, and path o v erlap. Assignment conict is the fraction of assignment rounds in which an y pair of goals is closer than d c = 1 . 5 m or belongs to the same frontier cluster κ t i = κ t k . P ath o v erlap rasterizes TF/odometry trajectories onto a 0.05 m grid and computes |{ q : n ( q ) ≥ 2 }| / |{ q : n ( q ) ≥ 1 }| , where n ( q ) is the number of robots visiting cell q . Lo wer conict and o v erlap indicate less t ar get cro wding and less repeated tra v ersal. W e report mean ± standard de viation and paired W ilcoxon tests o v er matched map, seed, and robot-count settings. 4. RESUL TS AND DISCUSSION 4.1. Main policy comparison T able 3 summarizes the main comparison. RGM gi v es the lo west mean completion time, tra v elled distance, assignment conict, and path o v erlap among the three main policies, while achie ving the highest co v erage ef cienc y . Its trade-of f is lo wer nal co v erage than GP A under the same stopping rule, so the claim is coordination ef cienc y rather than co v erage dominance. T able 3. Main polic y comparison Polic y Description T ime (s) Co v . Dist. (m) Ef f. Conict Ov erlap GP A Geometric proximity assignment 240.40 ± 51.56 0.940 ± 0.011 80.3 4 ± 9.24 1.345 ± 0.159 0.340 ± 0.162 0.024 ± 0.018 RSA Sequential cost-based assignment 232.45 ± 47.50 0.912 ± 0.005 81 .24 ± 10.39 1.336 ± 0.152 0.302 ± 0.127 0.027 ± 0.020 RGM Proposed cost-a w are global matching 176.05 ± 34.75 0.896 ± 0.021 69.6 9 ± 7.47 1.549 ± 0.114 0.250 ± 0.157 0.009 ± 0.012 IAES Int J Rob & Autom, V ol. 15, No. 3, September 2026: 589–596 Evaluation Warning : The document was created with Spire.PDF for Python.
IAES Int J Rob & Autom ISSN: 2722-2586 ❒ 593 Compared with RSA, RGM reduces mean completion time from 232.45 s to 176.05 s (24.3%), total distance by 14.2%, and path o v erlap by 65.8%. Compared with GP A, it reduces completion time by 26.8%, distance by 13.3%, and path o v erlap by 62.2%. Co v erage ef cienc y increases to 1.549 m 2 /m. The W ilcoxon tests in T able 4 support the ef cienc y claim. RSA slightly increases o v erlap relat i v e to GP A (0.027 vs. 0.024), whereas RGM lo wers it to 0.009, indicating that the sequential greedy mechanism, not the composite cost itself, causes this de gradation. RGM signicantly reduces time and distance relati v e to GP A, RSA, GGM, A U A, and PN A; o v erlap reduction is signicant ag ainst GP A, RSA, and A U A. T able 4. W ilcoxon paired tests Comparison T ime ∆ (%, p ) Distance ∆ (%, p ) Ov erlap ∆ (%, p ) RGM vs GP A -64.358 (26.8%, < 0 . 001 ) -10.650 (13.3%, < 0 . 001 ) -0.015 (62.2%, 0.003) RGM vs RSA -56.408 (24.3%, < 0 . 001 ) -11.552 (14.2%, < 0 . 001 ) -0.018 (65.8%, 0.001) RGM vs GGM -64.013 (26.7%, < 0 . 001 ) -6.218 (8.2%, 0.003) -0.003 (21.8%, 0.363) RGM vs A U A -60.388 (25.5%, < 0 . 001 ) -7.404 (9.6%, < 0 . 001 ) -0.012 (56.6%, 0.010) RGM vs PN A -65.287 (27.1%, < 0 . 001 ) -2.604 (3.6%, 0.360) -0.004 (31.1%, 0.355) Figure 2 sho ws that RGM is f aster , tra v els less, and reduces repeated tra v ersal. RSA can commi t early robots to locally attracti v e tar gets and le a v e later robots with poor team-le v el choices; RGM e v aluates assignments jointly . The lo wer nal co v erage under RGM is therefore interpreted as an ef cienc y trade-of f under the current stopping rule. Figure 3 illustrates the trajectory-visualization format for GP A, RSA, and RGM runs. Quantitati v e o v erlap claims remain based on T ables 3–4 and Figure 2. Map 1 Map 2 0 50 100 150 200 250 300 Completion T ime (s) Map 1 Map 2 0 20 40 60 80 100 T otal Distance (m) Map 1 Map 2 0.00 0.01 0.02 0.03 0.04 0.05 0.06 P ath Overlap R atio GP A RS A RGM Figure 2. Main quantitati v e comparison for GP A, RSA, and RGM Figure 3. T rajectory visualization used for qualitati v e inspection of the three main policies Cost-awar e global fr ontier matc hing ... (Chu V an Cuong) Evaluation Warning : The document was created with Spire.PDF for Python.
594 ❒ ISSN: 2722-2586 4.2. Extended baselines and ablation T able 5 compares RGM with solv er -isolation and e xternal-style references. GGM isolates d i stance- only global m atching, DGM adds information g ain, PN A approximates partition/V oronoi-style nearest-frontier assignment, A U A approximates utility auction allocation, and RGM-noD remo v es dispersion. These same- stack baselines are not full reimplementations of all auction or V oronoi methods [5], [7], [8], [11]-[14]. RGM is f aster than all listed v ariants and has t he lo west mean distance e xcept for the non-signicant dif ference relati v e to PN A. T able 5. Extended baselines and no-dispersion ablation Polic y Description Runs T ime (s) Dist. (m) Conict Ov erlap RGM Proposed cost-a w are global matching 24 176.05 ± 34.75 69.69 ± 7.47 0.250 ± 0.157 0.009 ± 0.012 GGM Distance-only global matching 24 240.06 ± 76.96 75.91 ± 7.91 0.370 ± 0.177 0.012 ± 0.012 DGM Distance–g ain global matching 24 253.31 ± 101.93 75.43 ± 12.01 0.258 ± 0.154 0.014 ± 0.016 PN A P artition-based nearest-frontier assignment 24 241.33 ± 58.94 72.29 ± 7.59 0.252 ± 0.167 0.013 ± 0.014 A U A Auction-style utility assignment 24 236.43 ± 92.35 77.09 ± 10.24 0.320 ± 0.173 0.021 ± 0.016 RGM-noD RGM without spatial dispersion term 22 222.04 ± 48.78 77.81 ± 9.82 0.297 ± 0.146 0.011 ± 0.009 Ag ainst PN A, RGM has nearly the same conict rate (0.250 vs. 0.252) and a non-signicant distance dif ference, b ut reduces completion time by 27.1% ( p < 0 . 001 ). Ag ainst A U A, RGM reduces completion time by 25.5%, distance by 9.6%, path o v erlap by 56.6%, and mean conict from 0.320 to 0.250. These comparisons support the narro wer claim that the tested global matching layer is more time-ef cient than the implemented partition- and auction-style basel ines under the same simulator , frontier source, and Na v2 stack. Relati v e to GGM, RGM reduces time by 26.7% and distance by 8.2%, so the g ain is not from matching alone. RGM-noD further suggests that dispersion helps reduce time, distance, and conict, although acti v e-tar get and skip-memory sensiti vity is not e v aluated. 4.3. Industrial implications and limitations The allocation layer is rele v ant to w arehouse mapping, smart-f actory commissioning, sensor -dri v en inspection, and digital-twin mapping, where repeated tra v ersal increases time and ener gy use. The e xperiments remain simulation-only , with tw o indoor maps and homogeneous teams of up to six robots; dynamic obsta- cles, sensor noise, communication delay , heterogeneous platforms, and ph ysical eets remain future v alidation tar gets. A natural ne xt step is learning-based frontier selection upstream of the x ed global matching layer . 5. CONCLUSION This paper presented a R OS 2 frontier -allocation layer that combines weighted cost scoring with global one-to-one matching. Across 72 main-polic y runs, RGM achie v ed the lo west mean compl etion time, distance, path o v erlap, and assignment conict among GP A, RSA, and RGM, while impro ving co v erage ef cienc y . Rel- ati v e to RSA, it reduced completion time by 24.3%, distance by 14.2%, and path o v erlap by 65.8%, with lo wer nal co v erage under the same stopping rule. Future w ork will study lar ger maps, dynamic obstacles, sensor noise, heterogeneous eets, communication delays, learning-based frontier selection, and ph ysical deplo yment. A CKNO WLEDGMENTS The authors thank A V iS Lab for its research en vironment and support. FUNDING INFORMA TION Authors state no funding in v olv ed. A UTHOR CONTRIB UTIONS ST A TEMENT This journal uses the Contrib utor Roles T axonomy (CRediT) to recognize indi vidual author contrib u- tions, reduce authorship disputes, and f acilitate collaboration. IAES Int J Rob & Autom, V ol. 15, No. 3, September 2026: 589–596 Evaluation Warning : The document was created with Spire.PDF for Python.
IAES Int J Rob & Autom ISSN: 2722-2586 ❒ 595 Name of A uthor C M So V a F o I R D O E V i Su P Fu Chu V an Cuong ✓ ✓ ✓ ✓ ✓ ✓ T ran T uan Anh ✓ ✓ ✓ ✓ C : C onceptualization I : I n v estig ation V i : V i sualization M : M ethodology R : R esources Su : Su pervision So : So ftw are D : D ata Curation P : P roject Administration V a : V a lidation O : Writing - O riginal Draft Fu : Fu nding Acquisition F o : F o rmal Analysis E : Writing - Re vie w & E diting CONFLICT OF INTEREST ST A TEMENT Authors state no conict of interest. INFORMED CONSENT Not applicable because the study uses simulation e xperiments and does not in v olv e human parti ci- pants. ETHICAL APPR O V AL This study uses simulation e xperiments and does not in v olv e human participants or animals. D A T A A V AILABILITY Deri v ed metrics and conguration details are a v ailable from the corresponding author upon reasonabl e request. REFERENCES [1] B. Y amauchi, “ A frontier -based approach for autonomous e xploration, ” in Pr oceedings of the IEEE International Symposium on Computational Intellig ence in Robotics and A utomation , 1997, pp. 146–151, doi: 10.1109/CIRA.1997.613851. [2] B. Y amauchi, “Frontier -based e xploration using multiple robots, ” in Pr oceedings of the Second International Confer ence on A u- tonomous Ag ents , 1998, pp. 47–53, doi: 10.1145/280765.280773. [3] B. Y amauchi, “Decentralized coordination for multirobot e xploration, ” Robotics and A utonomous Systems , v ol. 29, no. 2–3, pp. 111–118, 1999, doi: 10.1016/S0921-8890(99)00046-9. [4] R. Simmons, D. Apfelbaum, W . Bur g ard, D. F ox, M. Moors, S. Thrun, and H. Y ounes, “Coordination for multi-robot e xploration and mapping, ” in Pr oceedings of the Se venteenth National Confer ence on Articial Intellig ence (AAAI-00) , 2000, pp. 852–858. [5] R. Zlot, A. Stentz, M. B. Dias, and S. Thayer , “Multi-robot e xploration controlled by a mark et economy , ” in Pr oceedings of the IEEE International Confer ence on Robotics and A utomation , 2002, pp. 3016–3023, doi: 10.1109/R OBO T .2002.1013690. [6] W . Bur g ard, M. Moors, C. Stachniss, and F . E. Schneider , “Coordinated multi-robot e xploration, ” IEEE T r ansactions on Robotics , v ol. 21, no. 3, pp. 376–386, 2005, doi: 10.1109/TR O.2004.839232. [7] B. P . Gerk e y and M. J. Matari ´ c, “Sold!: Auction methods for m ultirobot coordination, ” IEEE T r ansactions on Robotics and A u- tomation , v ol. 18, no. 5, pp. 758–768, 2002, doi: 10.1109/TRA.2002.803462. [8] B. P . Gerk e y and M. J. Matari ´ c, “ A formal analysis and taxonomy of task allocation in multi-robot systems, ” The International J ournal of Robotics Resear c h , v ol. 23, no. 9, pp. 939–954, 2004, doi: 10.1177/0278364904045564. [9] M. Juli ´ a, A. Gil, and O. Reinoso, “ A comparison of path planning strate gies for autonomous e xploration and mapping of unkno wn en vironments, ” A utonomous Robots , v ol. 33, no. 4, pp. 427–444, 2012, doi: 10.1007/s10514-012-9298-8. [10] M. K eidar and G. A. Kaminka, “Ef cient frontier detection for robot e xploration, ” The International J ournal of Robotics Resear c h , v ol. 33, no. 2, pp. 215–236, 2014, doi: 10.1177/0278364913494911. [11] J. Hu, H. Niu, J. Carrasco, B. Lennox, and F . Arvin, “V oronoi-based multi-robot autonomous e xploration in unkno wn en viron- ments via deep reinforcement learning, ” IEEE T r ansactions on V ehicular T ec hnolo gy , v ol. 69, no. 12, pp. 14413–14423, 2020, doi: 10.1109/TVT .2020.3034800. [12] Q. Bi, X. Zhang, J. W en, Z. P an, S. Zhang, R. W ang, and J. Y uan, “CURE: A hierarc hical frame w ork for multi-robot autonomous e xploration inspi red by centroids of unkno wn re gions, ” IEEE T r ansactions on A utomation Science and Engineering , v ol. 21, no. 3, pp. 3773–3786, 2024, doi: 10.1109/T ASE.2023.3285300. [13] H. Zhao, Y . Guo, Y . Liu, and J. Jin, “Mul tirobot unkno wn en vironment e xploration and obstacle a v oidance based on a V oronoi diagram and reinforcement learning, ” Expert Systems with Applications , v ol. 264, 2025, Art. no. 125900, doi: 10.1016/j.esw a.2024.125900. [14] Y . Lei, J. Hou, P . Ma, and M. Ma, “V oronoi-GR U-based multi-robot collaborati v e e xploration in unkno wn en vironments, ” Applied Sciences , v ol. 15, no. 6, 2025, Art. no. 3313, doi: 10.3390/app15063313. Cost-awar e global fr ontier matc hing ... (Chu V an Cuong) Evaluation Warning : The document was created with Spire.PDF for Python.
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