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Graph Neural Planning and Predictive Control for Multi-Robot Communication-Constrained Unlabeled Motion Planning
Manohari Goarin, Yang Zhou, Giuseppe Loianno
Intelligence
Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 90%
Last extracted: 7/8/2026, 5:28:05 PM
Summary
This paper proposes a hierarchical framework combining a Graph ATtention Planner (GATP) and a decentralized Nonlinear Model Predictive Controller (NMPC) for multi-robot unlabeled motion planning. The GATP utilizes a 2-layer Graph Neural Network with attention mechanisms to generate intermediate subgoals through minimal communication, while the NMPC enforces safety and dynamic feasibility under nonlinear constraints. Evaluated in simulation and real-world quadrotor experiments, the framework demonstrates robustness to communication delays up to 200 ms and practical feasibility with decentralized on-board inference.
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Authors → affiliatedwith → New York University
confidence 95% · The authors are with New York University, NY 10012, USA.
Authors → affiliatedwith → University of California, Berkeley
confidence 95% · The author is with the University of California Berkeley, Department of Electrical Engineering and Computer Sciences, Berkeley, CA 94720, USA.
Graph ATtention Planner (GATP) → providessubgoalsto → Nonlinear Model Predictive Controller (NMPC)
confidence 95% · GATP provides intermediate subgoals through multi-robot cooperation, and the NMPC enforces safety under nonlinear dynamics and actuation constraints.
Proposed Framework → evaluatedon → Quadrotors
confidence 90% · We evaluate our framework in both simulation and real-world quadrotor experiments.
Proposed Framework → robustto → Communication Delays
confidence 90% · Thanks to attention mechanisms and minimal communication requirements, we demonstrate improved generalization to larger teams, robustness to communication delays up to 200 ms
Graph ATtention Planner (GATP) → trainedvia → Imitation Learning
confidence 90% · GATP is trained with imitation learning. The centralized expert employs the Hungarian Algorithm to assign the robots to the goals minimizing the total distance traveled.
Graph ATtention Planner (GATP) → uses → Graph Neural Networks (GNNs)
confidence 90% · We design our GNN architecture as a Graph Attention Network (GAT) which improves expressiveness by learning adaptive importance weights for each node’s neighbors.
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Abstract
Abstract:The multi-robot unlabeled motion planning problem of concurrently assigning robots to goals and generating safe trajectories is central in many collaborative tasks. Recent Graph Neural Network methods offer scalable decentralized solutions but rely on simplified dynamics and simulation environments, overlooking key challenges of real-world deployment such as dynamic feasibility and communication constraints. To address these gaps, we propose a hierarchical framework that combines a Graph ATtention Planner (GATP) with a decentralized Nonlinear Model Predictive Controller (NMPC). GATP provides intermediate subgoals through multi-robot cooperation, and the NMPC enforces safety under nonlinear dynamics and actuation constraints. We evaluate our framework in both simulation and real-world quadrotor experiments. Thanks to attention mechanisms and minimal communication requirements, we demonstrate improved generalization to larger teams, robustness to communication delays up to 200 ms and practical feasibility with decentralized on-board inference.
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- Source: https://arxiv.org/abs/2605.19209v1
- Canonical: https://arxiv.org/abs/2605.19209v1
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Graph Neural Planning and Predictive Control for Multi-Robot Communication-Constrained Unlabeled Motion Planning Manohari Goarin1 Yang Zhou1 and Giuseppe Loianno2 1The authors are with New York University, NY 10012, USA. email: mg7363, yz5794@nyu.edu.2The author is with the University of California Berkeley, Department of Electrical Engineering and Computer Sciences, Berkeley, CA 94720, USA. email: loiannog@eecs.berkeley.edu.This work was supported by the DARPA YFA Grant D22AP00156-00, the DEVCOM ARL grant SARA W911NF-24-2-0057, and the NSF CPS Grant CNS-2603416. Abstract The multi-robot unlabeled motion planning problem of concurrently assigning robots to goals and generating safe trajectories is central in many collaborative tasks. Recent Graph Neural Network methods offer scalable decentralized solutions but rely on simplified dynamics and simulation environments, overlooking key challenges of real-world deployment such as dynamic feasibility and communication constraints. To address these gaps, we propose a hierarchical framework that combines a Graph ATtention Planner (GATP) with a decentralized Nonlinear Model Predictive Controller (NMPC). GATP provides intermediate subgoals through multi-robot cooperation, and the NMPC enforces safety under nonlinear dynamics and actuation constraints. We evaluate our framework in both simulation and real-world quadrotor experiments. Thanks to attention mechanisms and minimal communication requirements, we demonstrate improved generalization to larger teams, robustness to communication delays up to 200 ms and practical feasibility with decentralized on-board inference. Video: https://youtu.be/OocpY1PnUfs I Introduction In recent years, multi-robot systems have attracted significant attention due to their ability to speed up task execution compared to single robot solutions, while concurrently offering additional resilience to robot failures. Cooperative multi-robot planning has been extensively studied for exploration, surveillance, search and rescue, or warehouse automation [33, 36]. By coordinating their actions, robots can solve these tasks with increased energy and time efficiency. The unlabeled motion planning problem offers a unifying formulation for many of these applications when the robots are homogeneous and interchangeable. It is a joint assignment and trajectory planning problem, with the objective of cooperatively reaching a set of goals while minimizing the total distance and time to travel and avoiding collisions. While centralized methods can find optimal solutions, the computational burden of large robot teams make them impractical, motivating the development of decentralized methods. Among recent works, learning-based methods and especially Graph Neural Networks (GNNs) have shown strong potential to solve multi-robot collaborative tasks [16, 11, 10, 8, 29, 44, 43, 30, 42] and notable works have applied them to the decentralized unlabeled motion planning problem [13, 21, 12, 38]. GNNs are inherently decentralized through their message-passing architecture and can exploit the structural information of the team topology to learn solutions that are close to optimal while scaling to large robot teams. However, these GNN-based methods rely on simplified dynamics in simulation environments and overlook key challenges for real-world deployment such as communication constraints, trajectory smoothness, and guaranteed safety under actuation limits. Figure 1: Hierarchical Architecture for cooperative and safe unlabeled motion planning: a Graph ATtention Planner (GATP) that exchanges information over the robot communication graph and provides subgoals; a Nonlinear Model Predictive Control (NMPC) that tracks these subgoals with safety and actuation constraints. To address these challenges in unlabeled motion planning, we propose a hierarchical architecture that integrates a GNN for high-level prediction of subgoals with a decentralized Nonlinear Model Predictive Control (NMPC) for trajectory execution toward these subgoals (see Figure 1). This hierarchy leverages the complementary strengths of both components: the GNN captures collaborative behavior through inter-robot communication to guide the robots toward their goals, and the NMPC guarantees safety and smooth motion under nonlinear dynamics and actuation constraints. The planner provides intermediate goals to the robots over a future horizon, and continuously updates them according to the robots’ position changes during NMPC execution. This dynamic-agnostic high-level planning formulation allows low frequency replanning and direct deployment in real-world scenarios. Moreover, our GNN architecture relies on minimal communication, improving robustness to communication delays. We summarize our contributions as follows • We propose a hierarchical framework combining a Graph ATtention Planner (GATP) and an NMPC for multi-robot collaborative and safe unlabeled motion planning with minimal communication. • We perform an ablation study on our GNN architecture and benchmark it against Graph Convolution Networks (GCN) commonly used in prior works. We compare their coverage performance and generalization across various team sizes. • We test our GATP-NMPC in simulation with 1010 quadrotors in two application scenarios, circle formation and zone coverage. We evaluate its coverage time performance under increasing communication delays and show its robustness for delays under 200200 msms. • We implement a ROS 2 decentralized inference algorithm and deploy our framework in real-world experiments with 44 quadrotors. We quantify the inference times and communication delays to demonstrate its practical feasibility. I Related Works Multi-robot motion planning is particularly challenging in the unlabeled setting, where robots are interchangeable and the joint assignment–planning problem is PSPACE-hard [27]. Centralized solutions exist, such as C–CAPT [31] that employs the Hungarian algorithm for assignment [15] and constant-velocity trajectory generation with collision avoidance guarantees under certain conditions. However, they are often impractical in real-world scenarios since they rely on global knowledge of the team’s state, which is typically unavailable due to communication constraints. Moreover, they scale poorly as the number of robots increases. These limitations have motivated the development of decentralized approaches, presented in this section. Model-based unlabeled motion planning. These methods often solve the assignment problem explicitly and combine it with robot and task-dependent trajectory optimization techniques. Switching-based strategies [1, 3, 31, 9, 22] allow robots to iteratively refine their goal selection through local interactions with their neighbors, requiring little communication, but often suffering from slow or suboptimal convergence. Other methods rely on decentralized optimization-based and auction-based algorithms [18, 28, 41, 20]. They can achieve better assignments, but typically require numerous communication rounds before converging to an optimal solution, and degrade in restricted communication settings [7]. In addition, explicit assignment can lead to abrupt changes in direction resulting in inefficient trajectories. Learning-based unlabeled motion planning. Learning-based methods, including reinforcement learning [14, 26, 23, 35, 4] and unsupervised learning [25], have been explored to enhance the scalability and efficiency of unlabeled motion planning. Notably, GNNs gained significant attention due to their intrinsic ability to model and process graph-structured data, composed of nodes and edges, using graph filters [40]. Naturally decentralized, they offer an effective representation for multi-robot systems with robot nodes and communication edges. Through a message-passing framework, robots share information with their neighbors and make predictions locally. They have been applied successfully to various multi-robot applications like path planning [16, 11], coverage [10, 8, 30], flocking [10, 29], collaborative perception [44], target tracking [43], or exploration [30, 42]. By optimizing information sharing between robots, GNNs can learn near-optimal solutions with limited communication [7]. In the context of unlabeled motion planning, GNN-based methods have been proposed to learn end-to-end the concurrent goal assignment and trajectory planning problem [13, 21, 12, 38]. Collision avoidance is typically handled either as a soft constraint within a reinforcement learning framework [21, 12, 38], or by applying a safety filter to the GNN outputs [13]. However, these approaches rely on simplified dynamics in simulation and directly predict velocity commands, which may cause abrupt accelerations and assume dynamic feasibility on real robots. Moreover, incorporating collision avoidance as a penalty term does not guarantee safety, while applying a post hoc safety filter can alter the network outputs and degrade performance. Finally, these GNN-based methods require multi-hop communication and 44 to 55 layers, which impose a heavy communication burden and make the system more vulnerable to delays in real-world settings. Building on these works, this paper proposes a hierarchical GATP–NMPC framework that maintains trajectory optimality and safety guarantees under nonlinear dynamics and actuation limits. In addition, our GNN relies on only 22 layers of communication which is more robust to practical delays, and is directly deployable in real-world. To the best of our knowledge, we are the first to validate our GNN-based unlabeled motion planner in real-world settings with fully decentralized, on-board inference on the robots. Real-world Communication challenges for GNNs. A major challenge when deploying GNNs on multi-robot systems is communication. While most learning-based works assume reliable message exchanges, real-world deployments are subject to communication delays, drops, and asynchronous updates [5]. A handful of studies evaluate their GNNs in physical multi-robot experiments, and typically rely on off-board centralized inference [11, 39]. In contrast, the authors in [2] introduce a decentralized ROS 2 framework to execute inference directly on-board. By testing standard velocity-planning GNN architectures, they notice that communication constraints, typically communication delays, lead to non-negligible performance degradation. In this paper, we analyze the impact of increasing communication delays on our task performance and show that our GNN is robust to bounded delays under ∼200 200 msms. I Problem Formulation In the following, all variables are time-dependent, but we drop the t for better clarity. We denote column vectors with bold notation like x, matrices with capital notation like A, and scalars with unbold notation like d. We consider a team of N identical robots i∈1,…,Ni∈\1,...,N\ and a set of N goals j∈1,…,Nj∈\1,...,N\. Each robot follows nonlinear dynamics: ∀i,˙i=f(i,i),∀ i, x_i=f(x_i,u_i), with x the state of robot i, including its position ip_i and velocity iv_i, and iu_i its control input. The unlabeled motion planning objective is to compute minimum-time and collision-free trajectories from some initial positions to the goal positions as follows: 1. Coverage objective. Robots are interchangeable, not pre‑assigned to goals and need to cover all goals as fast as possible. The task is complete when each goal is within a coverage threshold c of some robot: ∀j,mini‖j−i‖2<c.∀ j, _i \|p_j-p_i \|_2<c. 2. Pairwise safety. For all times t and robot pairs (i,i′)(i,i ), ‖i−i′‖2>dsafe, \|p_i-p_i \|_2>d_safe, with dsafed_safe the safety distance to maintain. In a decentralized setting, robots have limited sensing and communication capabilities. We consider that each robot i can sense its PgP_g closest goals and PrP_r closest robots and estimate their relative positions. We define its observation as i=[i⊤i,1⊤⋯i,Pg⊤i,1⊤⋯i,Pr⊤]⊤,o_i= bmatrixp_i &g_i,1 ·sg_i,P_g &r_i,1 ·sr_i,P_r \\ bmatrix , with i,jg_i,j the relative position of goal j with respect to i, and i,i′r_i,i the relative position of robot i′i with respect to i. =i∣i∈1,…,NO=\o_i i∈\1,...,N\\ is the set of all robots’ observations. ℛiR_i is the set of all PrP_r robots sensed by robot i. Additionally, a robot i can communicate with its M closest neighbors, and we note this neighborhood iN_i. IV Methodology IV-A Hierarchical Planning and Control Overview Our hierarchical framework is depicted in Fig. 1. From an initial set of robot and goal positions, we can model a graph connecting robot nodes with communication edges. Each robot is connected to its M closest neighbors (M=2M=2 on the figure). We define the multi-robot graph as =,G=\O,A\. The adjacency matrix ∈ℝN×NA ^N× N describes the topology of the graph with its coefficients being Aii′=1if i′∈i0otherwiseA_i = cases1&if i _i\\ 0&otherwise cases The framework is decomposed in two main parts: 1. Our GNN-based planner GATP, applied on each robot i. It takes as input the local graph i=i,:iG_i=\o_i,A_:i\ with :iA_:i the i’s column of A, and outputs a subgoal position command sis_i. sis_i is an intermediate goal point for the robot to reach within the prediction horizon TpT_p of the planner. 2. A Nonlinear Model Predictive Controller with a prediction horizon TcT_c. Each robot i’s NMPC tracks a straight linear minimum jerk reference trajectory [19] to the subgoal sis_i while respecting hard safety and dynamic constraints. This module allows smooth and safe motion of the robots toward their subgoals. GATP continuously updates the NMPC reference depending on the evolution of the robots’ positions during execution. IV-B Graph Neural Network for high-level planning We design our GNN architecture as a Graph Attention Network (GAT) [32] which improves expressiveness by learning adaptive importance weights for each node’s neighbors. We add Multi Layer Perceptrons (MLPs) update functions between layers, allowing each node to fuse its initial embedding with aggregated neighbor information. This mechanism preserves the permutation invariance property of the GNN and enhances node differentiation. At a robot node i, the GNN architecture can be decomposed into three steps: the Encoder, the Attention-based Message-passing module, and the Decoder. We note ilh_i^l the embedding of node i at layer l, and ϕ∗ _* MLPs with two linear layers and a LeakyReLuLeakyReLu activation function in between. 1. The Encoder transforms the robots’ observations into embedding vectors of size F i0←ϕenc(~i),h_i^0← _enc( o_i), (1) where ~i o_i is the normalized observation io_i with respect to the environment spatial dimension DwD_w, obtained by dividing ip_i by DwD_w and i,jg_i,j, i,i′r_i,i by 2Dw2D_w. 2. The Attention-based Message-passing module applies L layers (or communication rounds) of 1-hop neighbor information aggregation and embedding update. At each layer l, first, attention coefficients eii′le^l_i are computed between node i and each of its neighbors i′i ∀i′∈i,eii′l=l(lil,li′l).∀ i _i, e^l_i =a^l(W^lh^l_i,W^lh^l_i ). (2) The attention function la^l is a weight vector of size 2F2F followed by a LeakyReLuLeakyReLu. lW^l is a weight matrix of size F×F× F. These attention coefficients are normalized throughout the neighborhood using a softmax function ∀i′∈i,e~ii′l=softmaxi′(eii′l).∀ i _i, e^l_i =softmax_i (e^l_i ). (3) Finally, a weighted sum using the coefficients e~ii′l e^l_i followed by a nonlinear activation function combines the neighbors’ embeddings ¯il=tanh(∑i′∈ie~ii′lli′l). h^l_i=tanh ( _i _i e^l_i W^lh^l_i ). (4) We apply multi-head attention by performing K attention mechanisms in parallel. These heads k are combined using the maxmax function ^il=maxk∈1,…,K¯il,k. h^l_i= _k∈\1,...,K\ h^l,k_i. (5) Once this message-passing is performed, we update node i’s embedding by combining its initial encoded embedding i0h^0_i with the aggregated information ^il h^l_i il+1←ϕupdate(i0∣^il).h^l+1_i← _update(h^0_i h^l_i). (6) This fusion strategy improves expressiveness and node differentiation. 3. The Decoder predicts an output s~i s_i for i from its final embedding iLh^L_i s~i=tanh(ϕdec(iL)),∈[−1,1]n. s_i=tanh( _dec(h^L_i)), ∈[-1,1]^n. (7) The Cartesian dimension n is 22 or 33 depending on whether the environment is 2D or 3D. Then this output is converted into a relative subgoal command by scaling and clamping it to its maximum magnitude, i.e, its maximum desired distance SpS_p from i si=min(1,Sp∣s~i∣2)s~i,s_i= (1, S_p s_i _2 ) s_i, (8) where Sp=vmaxTpS_p=v_maxT_p represents the spatial horizon of the planner, given a desired time horizon TpT_p and a desired maximum speed vmaxv_max of the robots. IV-C Safe Predictive Control for Trajectory Execution We formulate a nonlinear optimization problem over the prediction horizon TcT_c for a robot i in continuous time argmini *arg\,min_u_i ∫t0t0+Tc(‖i−i∗(si)‖Q2+‖i−i∗‖R2)t _t_0^t_0+T_c (\|x_i-x_i^*(s_i)\|_Q^2+\|u_i-u_i^*\|_R^2 )\,dt (9a) s.t.∀t, .t. ∀ t, ˙i=f(i,i), x_i=f(x_i,u_i), (9b) i∈,i∈, _i , 10000\ u_i , (9c) Gii′(i,i′,i)≥0,∀i′∈ℛi, G_i (x_i,x_i ,u_i)≥ 0, 10000\ ∀ i _i, (9d) where Eq. (9a) represents the quadratic objective function minimizing the distance to the min-jerk reference trajectory i∗(si)x_i^*(s_i) guiding the robot toward its subgoal sis_i with a maximum desired speed vmaxv_max, and the reference control inputs i∗u_i^*. Eq. (9b) is the nonlinear dynamics of the robot, Eq. (9c) the state and input constraints, and Eq. (9d) safety constraints maintaining the safety distance dsafed_safe between i and the closest robots it can sense i′∈ℛi\i _i\. In this paper, we choose to formulate Gii′G_i as Control Barrier Function (CBF) constraints which can provide strong safety guarantees under actuation constraints [6]. The NMPC prediction horizon TcT_c is lower or equal than GATP prediction horizon TpT_p. V Experimental Setup V-A GATP Training Setup GATP is trained with imitation learning. The centralized expert employs the Hungarian Algorithm [15] to assign the robots to the goals minimizing the total distance traveled. The optimal subgoals si∗s^*_i are calculated by discretizing straight trajectories toward the assigned goals with a step size SpS_p. During training, the robots follow simple simulation dynamics under a mixed GATP/expert policy ∀i,∀t,i(t+1)=si(t)with a probability βsi∗(t)with a probability 1-β∀ i,∀ t, _i(t+1)= casess_i(t)&with a probability $β$\\ s^*_i(t)&with a probability 1-$β$ cases We adopt a scheduled sampling scheme, gradually increasing β to replace expert subgoals with the GATP predictions. The planning spatial horizon is set at Sp=4S_p=4 m, which defines the maximum magnitude of the predicted subgoals. Since the GNN outputs are normalized, different horizons can still be applied at test time. The choice of SpS_p was empirically tuned to balance convergence speed and stability near the goals: larger horizons lead to oscillations around the targets, while smaller horizons result in slower learning and convergence. We build a dataset of 1000010000 graphs of N=10N=10 agents with random initial and goal positions in an environment of 20×2020× 20 meters, and rollout trajectories of Nt=70N_t=70 timesteps. We train our GNN with centralized inference using the Deep Graph Library [37] to minimize the mean squared error between the normalized predicted subgoals s~i s_i and the normalized expert subgoals s~i∗ s^*_i, summed over trajectories and averaged across robots per batch. The loss is formulated as ℒ=1NB∑i∑twi(t)∣s~i(t)−s~i∗(t)∣22,L= 1NB _i _tw_i(t) s_i(t)- s^*_i(t) ^2_2, with B the batch size. wi(t)w_i(t) is an adaptive weight that increases when the error is small, to refine the predictions’ accuracy and stabilize the planning behavior around the goal locations. It is obtained as wi(t)=1+α1exp(−α2∣s~i(t)−s~i∗(t)∣2),w_i(t)=1+ _1 (- _2 s_i(t)- s^*_i(t) _2 ), where the parameters α1 _1 and α2 _2 are hand-tuned. In the context of restricted communication scenarios in the real world, and to reduce the GNN sensitivity to possible delays during deployment, we limit the message-passing module to 1-hop aggregations, L=2L=2 layers, and M=2M=2 maximum neighbors each robot can communicate with. We restrict the observation of the robots to Pg=5P_g=5 closest goals and Pr=3P_r=3 closest robots, use K=3K=3 heads of attention, and a feature dimension F=64F=64. In the following subsections, the training runs and comparisons were conducted using a batch size of B=200B=200 graphs and 80 epochs on a 12th-generation Intel CPU I9-12900H. We increase the probability β incrementally from 0.50.5 to 1.01.0 every 2020 epochs, and fix the loss parameters α1=5.0 _1=5.0 and α2=4.0 _2=4.0. The learning rate is set at 6e−46e-4 and 1e−41e-4 on the last 2020 epochs. V-B Quadrotor dynamics In our experiments, we demonstrate and deploy our framework with quadrotors. The state and control inputs of a quadrotor i can be described as i=[i⊤i⊤i⊤i⊤]⊤,i=[ui0ui1ui2ui3]⊤,x_i= bmatrixp_i &v_i &q_i & ω_i bmatrix ,u_i= bmatrixu_i0&u_i1&u_i2&u_i3 bmatrix , where i∈ℝ3p_i ^3 and i∈ℝ3v_i ^3 are respectively the position and linear velocity of the quadrotor in the inertial frame, i∈ℝ4q_i ^4 the rotation in quaternions from the quadrotor’s body frame to the inertial frame, i∈ℝ3 ω_i ^3 the angular velocity in the body frame, and uik∈ℝ,k∈[0,…,3]\u_ik ,k∈[0,...,3]\ the motor thrusts of the quadrotor. The dynamic equations are as presented in [24] and can be written in a control-affine form as follows ˙i=f′(i)+g(i)i. x_i=f (x_i)+g(x_i)u_i. The safety constraints in Eq. (9d) from the NMPC formulation are based on Exponential Control Barrier Functions (ECBFs) which can provide forward invariance guarantees of the safe set for the quadrotors’ higher-order dynamics. We refer the readers to [6] for further details. VI Results and Analysis in Simulation and Real-World Figure 2: GATP coverage performance analysis with 1010 robots. Figure 3: GATP generalization analysis to larger teams with a simulation duration of Tf=40T_f=40s. VI-A GATP coverage performance analysis First, we evaluate the planning performance of GATP using point-like robots and show the benefits of attention and our MLP fusion strategy (Eq. (6)) on coverage performance and generalization to larger teams. We define coverage performance as the percentage of goals reached in a given time TfT_f. The spatial horizon is still fixed at Sp=4S_p=4 m. We report in Figs. 3 and 3 the total coverage percentage over 200200 scenarios, for different simulation durations TfT_f from 1010 to 4040 s and different team sizes from N=10N=10 to 5050 robots. We test 3 different GNN architectures for comparison: • GATP-f1, our architecture as presented in section IV-A, with f1f_1 the update function from Eq. (6): f1(i,l)=ϕupdate(i0∣^il)f_1(i,l)= _update(h^0_i h^l_i). • GCN-f1, a Graph Convolutional Network as employed in [13, 21, 12], similar to GATP-f1 but with 22 layers of 1-hop convolutional filters instead of attention layers. • GATP-f2, a variation of GATP-f1 that uses a different update function f2(i,l)=il+ϕupdate(^il)f_2(i,l)=h^l_i+ _update( h^l_i) that combines the aggregated information with the previous node embedding instead of the initial encoded embedding. This function was used in [21]. First, we analyze the coverage performance on 1010 robots with increasing simulation durations (Figure 3). GCN-f1 and GATP-f1 achieve comparable results. With a limited time of Tf=10T_f=10 s, GATP-f1 reaches 86.15%86.15\% of the goals compared to 86.65%86.65\% for GCN-f1, despite relying on only 1-hop neighbor aggregation and 2 communication rounds. In Tf=40T_f=40 s, GATP-f1 reaches 94.55%94.55\% of coverage against 95.00%95.00\% for GCN-f1. These results exhibit the ability of GNNs to learn efficient heuristics through optimized information exchange. Both architectures outperform GATP-f2 which completes at most 81.45%81.45\% in 1010 s and 91.25%91.25\% in 4040 s. The greater performance of GCN-f1 and GATP-f1 can be attributed to the update function f1f_1 that re-injects the initial node embedding after each layer via a learnable MLP. This strategy enhances node differentiation and reduces assignment conflicts. Second, we analyze the generalization of the GNN architectures to larger teams of up to 5050 robots. For lower computation cost and faster training, the GNNs are trained with 1010 robots but are directly transferrable to larger team sizes thanks to the decentralized nature of GNNs. On Figure 3, we analyze the evolution of the coverage percentage as we increase the number of robots for a fixed simulation duration of 4040 s. Overall, the more robots we add, the more the GNNs degrade in performance because of the small number of robots used for training. However, GATP-f1 outperforms both GCN-f1 and GATP-f2. Although GCN-f1 demonstrated similar performance to GATP-f1 with 1010 robots, GATP-f1 and GATP-f2 are more generalizable to larger teams with a smaller decrease in performance. From 1010 to 5050 robots, GATP-f1 experiences a performance drop of 23.5%23.5\%, compared to 24.5%24.5\% for GATP-f2 and 34.5%34.5\% for GCN-f1. We conclude that attention mechanisms improve generalization. By dynamically weighting neighbors’ information, the network can capture more complex interactions and account for the varying importance of different neighbors. VI-B GATP-NMPC performance analysis under increasing communication delays (a) Circle Formation (b) Zone Coverage Figure 4: Simulation with 1010 quadrotors for a circle formation task and a coverage task. The green circle is the desired circle to form, and the green area is the environment zone to cover. The quadrotors are in blue, and their trajectories are yellow. (a) Circle Formation (b) Zone Coverage Figure 5: Performance analysis under increasing communication delays on both tasks. In this section, we test our hierarchical GATP-NMPC in simulation with quadrotors. We run 1010 robot nodes in a ROS 2 environment, each running its own NMPC but with a centralized GATP node, only for this simulation experiment, to avoid overloading our computer with parallel inferences. The planner runs at 22 HzHz and the NMPC at 100100 HzHz. We set the GATP time horizon at Tp=2T_p=2 s and the desired maximum speed of the robots at vmax=2v_max=2 m/sm/s, which is equivalent to a planning spatial horizon of Sp=4S_p=4 mm. The desired safety distance between robots is dsafe=0.5d_safe=0.5 mm. We use acados [34] to solve the NMPC with SQP-RTI and a prediction horizon of Tc=1.5T_c=1.5 ss. We demonstrate the efficacy of our framework in two example tasks: (a) a circle formation task, where robots start from a set of random positions and must form a circle, and (b) a zone coverage task, where robots must uniformly cover a given zone of the environment. Two simulation runs illustrate these tasks in Figure 4. Additional examples for different tasks can be found in the video. The performance metric for these experiments is the coverage time, defined as the total time required for the team to reach all goals, with a coverage threshold of c=0.2c=0.2 m per goal. First, the GATP–NMPC framework successfully guides the quadrotors to their goal locations in both tasks, producing smooth and safe trajectories through the seamless integration of the graph-based planner with the NMPC. The high-level planner leverages local information to minimize the distance traveled by the robots, helping to deconflict the multi-robot system and facilitate NMPC feasibility. In the real world, significant delays may arise from inter-robot communication, which the message-passing module depends on, and can lead to planning updates based on outdated observations. To model this effect, we assume that all robots experience the same communication delay d per communication round (i.e., GNN layer). The total communication delay is then D=LdD=Ld. We test different values of D and analyze its impact on coverage time performance for both tasks. The inference time also contributes to the total delay but is negligible compared to the communication effect in practice. We run each task 1010 times with identical initial and goal positions, and report the mean and standard deviation of the coverage time in Fig. 5. Variations across runs are due to additional uncertainties related to ROS 2 processes and numerical approximations in the NMPC. In both scenarios, we notice some performance degradation for large communication delays D=0.4D=0.4 ss and D=0.6D=0.6 ss. However, the framework is robust to delays under 0.20.2 s, with an average increase of coverage time of 0.440.44 ss (3.83.8%) on the circle formation task, and 0.860.86 ss (5.55.5%) on the zone coverage task. The performance degradation becomes impactful when the delay is comparable to the planning update interval of 0.50.5 ss. At such delays, the outputs are too outdated to remain valid for effective planning. With D=0.6D=0.6 ss, the coverage time increases by 31.8%31.8\% in the circle formation task and by 39.2%39.2\% in the zone coverage task. The effect is more pronounced in the last scenario, where robots must travel longer distances and thus accumulate larger errors over time. In conclusion, our GATP architecture with L=2L=2 layers for high-level, low-frequency planning is robust enough to bounded communication delays of up to 0.20.2 s (i.e., d=0.1d=0.1 ss per layer). Using more layers (e.g., 44–55 as in previous works [13, 21, 12]) could potentially improve planning performance, but would also make the system significantly more sensitive to delays, since with 0.10.1 s per layer the total communication latency would already reach D=0.4D=0.4 to 0.50.5 ss. VI-C System Implementation and Deployment in Real-World We deploy our solution in an indoor 10 m×6 m×4 m$10\,m$×$6\,m$×$4\,m$ testbed with Vicon111https://w.vicon.com/ localization and 44 custom quadrotors based on [17] and equipped with Qualcomm® SnapdragonTM VOXL® 2222https://w.modalai.com/products/voxl-2?variant=39914779836467. We demonstrate the applicability of our GATP–NMPC framework in a formation task, where robots sequentially form different shapes (see Figure 6 and the attached multimedia material). Taking into account our environmental dimensions, we set the desired maximum speed of the robots at vmax=0.5v_max=0.5 m/sm/s, the planner time horizon at Tp=1.5T_p=1.5 ss, and the NMPC horizon Tc=1T_c=1 ss. Each robot senses its Pg=4P_g=4 closest goals and Pr=2P_r=2 closest neighbors. Both the planner and the controller run onboard each quadrotor at 11 HzHz and 160160 HzHz, respectively. 11 HzHz was sufficient for this experimental setup given the small flying area and the robots’ velocity. Algorithm 1 GATP inference ROS 2 node on quadrotor i 1: while t<Tft<T_f do 2: Get observation io_i 3: Run encoder 4: for l=1l=1 to L do 5: Wait for all neighbors’ messages 6: if all messages received then 7: Aggregate messages 8: Update embedding 9: end if 10: end for 11: Run decoder 12: Send subgoal command to NMPC 13: end while We implement a decentralized inference as in Algorithm 1. For each layer, robots wait for all neighbors’ messages before proceeding. GATP replans concurrently with the NMPC until the experiment ends. (a) Without obstacles (b) With obstacles Figure 6: Real-world Experiments. Each circle represents a robot, the arrow line its trajectory, and the dashed line a desired shape. Color red is used for Robot 11, yellow for Robot 22, blue for Robot 33, green for Robot 44, and purple for obstacles. Our framework transfers directly to the real world thanks to its hierarchical design: the NMPC accounts for nonlinear quadrotor dynamics with actuation constraints while GATP uses position‑based observations and commands that are dynamic‑agnostic, facilitating sim-to-real transfer and generalization across platforms. For all tested formation shapes, quadrotors successfully reach the goals safely as shown on Figure 6 and in the video. In this experiment, the coverage time performance is similar in simulation and the real world. We further validate our framework in the presence of obstacles (Figure 6). Two obstacles were placed along the transitions between shapes 2→3 and 3→4. During 2→3, the robots have to deviate significantly from their reference trajectories to avoid the obstacles. GATP re-planned accordingly, providing a new global solution in which the yellow and blue quadrotors swapped positions compared to the obstacle-free case (Figure 6). In contrast, during 3→4, obstacle avoidance did not alter the optimal solution, and GATP maintained the same plan. Finally, we measure the average inference times and communication delays during the experiment (Table I). The total inference time of GATP is only about 11 msms, thanks to its compact architecture and the use of ONNX Runtime333https://onnxruntime.ai/. In contrast, the average communication delay per layer is around 2626 msms, confirming that delays are mainly due to communication rather than computation. We also observe some delay variability between robots, with a total GATP time per robot ranging from 5151 msms to 134134 msms. A 134134 msms of planning time implies that GATP could be run at a maximum frequency of roughly 77 Hz, which is compatible with our low-frequency subgoal planning formulation. Moreover, this maximum total delay falls within the 0.10.1–0.20.2 ss range tested in simulation, where coverage performance was shown to remain mostly unaffected. This justifies the absence of noticeable performance loss between simulation and real-world. Table I: Inference times and Communication delays Metric Time (ms) Average GATP inference time (comm. excluded) 1.03 Average communication delay per layer 26.04 Total GATP time per robot Robot 1 62.88 Robot 2 134.29 Robot 3 106.90 Robot 4 51.23 VII Conclusion In this work, we introduced a novel hierarchical approach that combines a Graph ATtention Planner (GATP) with a decentralized Nonlinear Model Predictive Controller (NMPC) for collaborative and safe unlabeled motion planning under nonlinear dynamics and limited communication. In simulation, we demonstrated improved generalization to larger teams thanks to attention mechanisms, and robustness of our two‑layer design against delays up to 200 ms200\,ms. We deployed decentralized on‑board inference on quadrotors, highlighting practical feasibility and effective sim-to-real transfer. 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