Multi-robot systems are increasingly deployed as heterogeneous fleets with diverse kinematic and actuation capabilities. While graph control barrier function (GCBF) methods provide a scalable framework for decentralized safe control, existing approaches typically assume homogeneous robot dynamics. Methods that directly encode robot classes can distinguish known types, but do not represent state-dependent motion capabilities or naturally transfer to unseen robot models. To address this challenge, we propose the Capability-Conditioned Heterogeneous Graph Control Barrier Function (CC-HGCBF), defined in a shared second-order reference-point operational space. This formulation provides a common geometric representation of safety across heterogeneous robots while retaining their model-specific dynamics and admissible control constraints. To enable zero-shot transfer, we introduce the Radial Capability Field (RCF), a compact, fixed-dimensional representation of each robot's state-dependent finite-horizon reachable velocity set. Conditioning the shared graph barrier and decentralized policy on the RCF enables them to adapt to changes in robot state, kinematic constraints, and control limits without relying on predefined robot identities. We jointly train the barrier and policy using proactive safety labeling and neural CBF-QP supervision, and evaluate them on mixed teams containing both seen and unseen robot models. Experiments demonstrate scalable safe coordination and zero-shot transfer to robot models and capability variations withheld during training. Physical-robot experiments further demonstrate zero-shot deployment to unseen kinematic models without retraining.
Figures & tables
Figure 1: Qualitative trajectory comparison of zero-shot policy transfer to an unseen robot model in a 3.8m×3.8m workspace, where five robots navigate from randomly sampled starts to goals while avoiding three static obstacles (yellow boxes). A forward-only (FO) robot (purple), with motion capabilities different from those seen during training, is introduced only at evaluation. (a) Our capability-conditioned policy maintains safe trajectories with the unseen FO robot, while (b) baselines relying on discrete robot identities result in robot–robot or robot–obstacle collisions.
Figure 2: Overview of the proposed CC-HGCBF framework. 1 Heterogeneous robot motion is mapped into a shared reference-point operational space. 2 The RCF represents each robot’s state-dependent finite-horizon motion capability in this common space. 3 These capability features are embedded into the local interaction graph and incorporated into neighboring robots’ safety reasoning through graph message passing. 4 The shared barrier and decentralized policy are jointly trained using proactive safety labeling and neural CBF-QP supervision. 5 During decentralized execution, each robot constructs its local capability-conditioned graph and applies the learned policy through its model-specific control interface.
Figure 3: Capability representation and training procedure. (a) State-dependent RCF representations for DI, UNI, DD, and CL in the shared operational-velocity space [ 20 ] . Colored regions show the K=8 RCFs at vi∈{0.2,0.5,0.8} m/s with ωi=0 . Circular markers denote the current operational velocities, and black dashed boundaries denote the model-specific feasible velocity sets mapped into the shared space. (b) Joint barrier–policy training pipeline [ 7 ] with proactive safety labeling. The data collection example visualizes the learned barrier hθ around an ego robot as a local safety map, with lower barrier values near detected obstacles and along the motion directions of neighboring robots. Policy rollouts generate interaction data, proactive safety labels supervise the graph barrier, and the neural CBF-QP provides supervisory actions for policy learning.
Figure 4: Experimental settings and results. (a) Random start–goal evaluation settings in a 22m×22m workspace with N=128 robots ( 32 per model) in Free , and N=32 robots ( 8 per model) with Nobs=32 static obstacles in Obs . Colored markers denote DI, UNI, DD, and CL robots. (b) Scalable heterogeneous navigation with seen robot models. In Free , performance is evaluated as team size increases; in Obs , performance is evaluated as obstacle density increases with N=32 . (c) Effect of proactive safety labeling and safe-label horizon H compared with velocity-cone-based labeling. Results are shown under increasing team size in Free and increasing obstacle density in Obs .
DI
UNI
DD
CL
∣vx∣∣vy∣≤vmax≤vmax
∣v∣∣ω∣≤vmax≤ωmax
vmax∣v∣+ωmax∣ω∣≤1
∣ω∣≤l∣v∣tan(ϕmax)
Table 5
Env.
Setting
Maximum steering angle, ϕmax
30∘
40∘†
50∘
Free
N=16
99.0 / 100.0
98.8 / 100.0
99.8 / 100.0
N=32
99.1 / 100.0
99.7 / 100.0
99.9 / 100.0
N=64
98.0 / 99.4
99.1 / 99.7
99.5 / 100.0
N=96
96.0 / 99.0
97.2 / 99.1
98.6 / 99.9
N=128
92.5 / 97.6
95.2 / 98.9
97.3 / 99.2
Table I : RCF generalization to maximum steering-angle variations across team sizes and obstacle densities. Trained only at ϕmax=40∘ ( † ), the policy is evaluated without retraining. Entries report Success / Safety (%).
Evaluation
Metric
K=4
K=8
K=12
K=16
ΔK
Seen models
Success
94.8
94.5
94.7
94.9
0.4
Safety
98.2
97.7
97.7
97.5
0.7
Held-out FO
Success
94.5
95.0
95.0
95.2
0.7
Safety
98.3
98.2
98.1
97.7
0.6
Held-out CL
Success
82.4
80.9
80.6
82.7
2.1
Safety
85.1
86.1
86.1
86.0
1.0
Table II : Ablation on Fourier order K . Performance (%) is averaged over the corresponding evaluation configurations and five training seeds; ΔK denotes the range across K .
Figure 5: Zero-shot generalization to unseen CL and FO models. For unseen CL, all methods are trained on DI, UNI, and DD; 5(a) – 5(b) report performance over all agents, whereas 5(d) – 5(e) report performance for the unseen CL agents only. For unseen FO, methods are trained on DI, UNI, DD, and CL; 5(c) and 5(f) report performance for the unseen FO agents only. Shaded regions denote variance.