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.
Safe decentralized navigation in heterogeneous robot teams is challenging because robots with different dynamics and control limits cannot satisfy identical collision-avoidance obligations equally well. Existing methods often rely on model-specific safety formulations or allocate avoidance responsibility without considering whether the assigned control is physically realizable, possibly leading to safety-constrained QP infeasibility and safety violations. We propose Capability-Aware Heterogeneous Control Barrier Functions (CA-HCBF), a decentralized framework for consistent safety enforcement and capability-aware responsibility allocation. We derive a unified operational-space second-order control-affine formulation for holonomic and nonholonomic mobile robots through canonical transformation and backstepping, addressing the relative-degree mismatch while preserving forward invariance of the pairwise safe set. Second, we quantify each robot's achievable control authority along the safety-critical direction using a support-function-based capability metric and use it to distribute pairwise avoidance responsibility. A feasibility-aware clipping mechanism further mitigates physically unrealizable responsibility assignments. Simulations with up to 30 heterogeneous robots and hardware experiments demonstrate high task completion with low safety violations and reduction in local QP infeasibility.
Joonkyung Kim, Yanze Zhang, Wenhao Luo +1
Department of Computer Science and Engineering, Texas A&M University · Department of Computer Science, University of Illinois Chicago
Safe navigation in heterogeneous multi-robot teams faces two coupled challenges: differences in robots' braking and turning capabilities limit how each robot can respond to an approaching neighbor, while simultaneous interactions require a single control action to satisfy multiple collision-avoidance constraints. Together, these challenges can make local safety constraints incompatible with a robot's admissible controls, leaving a decentralized safety controller without a feasible action. We propose a Capability-Aware Backup-Recoverability Filter (CA-BRF), based on the insight that navigation actions should preserve access to a certified recovery maneuver. First, we construct a backup-recoverable set in a shared Cartesian operational space by evaluating whether prescribed backup maneuvers maintain pairwise safety until the robots come to rest. Each maneuver respects the corresponding robot's kinematic and actuation constraints, making the recovery certificate capability-dependent. Second, CA-BRF filters candidate controls by selecting admissible interpolations between candidate and backup actions while coordinating the selection across simultaneous interactions. This preserves backup recoverability while retaining as much of the candidate action as possible and ensures that all pairwise recovery conditions are satisfied by a single executable control for each robot. Together, we establish recursive feasibility and safety for the discrete-time closed-loop system even when the nominal safety-constrained optimization becomes infeasible. The validity and effectiveness of the proposed CA-BRF are validated in simulations with up to 30 heterogeneous robots and experiments of robots with five different kinematic classes.
Joonkyung Kim, Yanze Zhang, Wenhao Luo +1
Department of Computer Science and Engineering, Texas A&M University · Department of Computer Science, University of Illinois Chicago
As the number of autonomous robots continues to grow, safety becomes increasingly important. Control barrier functions (CBFs) provide a theoretically grounded framework for ensuring safety, but existing design methods often face limitations in effectiveness, scalability, or interpretability, and may result in overly conservative safe sets. In this paper, we propose VertexCBF, a framework for learning neural CBFs in a scalable, systematic, and explainable way. We approximate the stationary Hamilton--Jacobi value function using a neural network trained via a combination of physics-informed and sparsely supervised learning. By exploiting control-affine dynamics and a convex polytope control set, under which the Hamiltonian is maximized at the control vertices, we efficiently generate supervision points via GPU-parallel vertex-restricted tree search, while a residual architecture guarantees that the learned CBF is never larger than the specified constraint function. We evaluate the method on 15 systems and compare it against relevant baselines, showing that it reliably recovers large safe sets where the baselines are conservative or fail completely. In addition, we perform a hardware experiment in which a mobile robot safely avoids pedestrians using a neural CBF trained with our method.
Bojan Derajić, Sebastian Bernhard, Wolfgang Hönig
Technical University of Berlin, Germany · AUMOVIO, Germany · Technical University of Applied Sciences Augsburg, Germany +1