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.
Figures & tables
Figure 1: Real-robot trajectory comparison, recovery-certificate margin, and model-dependent velocity sets. Five heterogeneous robots (DI, UNI, DD, CL, and FO) navigate to individual goals. (a) With CA-BRF (ours), the robots navigate successfully while maintaining the prescribed pairwise safety condition. (b) Directly applying the HOCBF candidate controls without CA-BRF violates this condition. Darker trajectory colors indicate later times. (c) Backup safety margin Bijψ(x) for the CL–FO pair under the candidate and CA-BRF applied controls. Values below zero indicate that the prescribed backup maneuvers no longer certify safe separation. The candidate control crosses below zero, whereas the CA-BRF applied control remains nonnegative, preserving backup recoverability. The shaded interval marks the active CL–FO interaction during which CA-BRF modifies the candidate control. (d) Feasible (v,ω) velocity sets and constraints for four representative nonholonomic kinematic classes [ 1 ] ; DI is omitted as holonomic.
Table 2
Figure 2: Random start–goal navigation with N=30 heterogeneous robots (six per model) at multiple timestamps. Robots start from randomly sampled positions, and × markers denote their assigned goals. UNI, DI, DD, CL, and FO robots are shown as blue circles, light-blue circles, green diamonds, red rectangles, and purple sectors, respectively. Dashed outlines show the operational-space safety radii ri centered at the corresponding operational points (Sec. II ).
Metric
N=20
N=30
Decision differs (%)
4.74
11.61
Shared accepts / CA-BRF rejects (%)
4.58
11.25
Shared rejects / CA-BRF accepts (%)
0.21
0.48
Table III : Same-state comparison of model-specific and shared recovery evaluation. All controller components are fixed except for the backup rollout used to evaluate recoverability.
N=20
N=30
Certificate
Recall (%)
Lead (s)
Recall (%)
Lead (s)
Bh only
76.9
0.15
67.0
0.10
Bh and Bψ
100.0
0.85
97.8
0.85
Table IV : Early-warning ability of the recovery certificate on HOCBF-only trajectories. Recall is the fraction of safety-buffer breaches preceded by a certificate violation within the previous 40 control steps ( 2.0 s), and lead time is the median time from certificate violation to breach.
Figure 3: Effect of coordinating filter decisions across simultaneously interacting robots. CA-BRF uses one common candidate–backup interpolation factor within each connected interaction component, whereas the comparison variant selects factors independently. (a) Fraction of trials with composition failures, in which locally accepted decisions fail the pairwise backup-recoverability test when executed together. (b) Fraction of active robot control steps applying the full backup ( λ=0 ). Coordinated selection removes the observed composition failures while requiring more frequent full-backup activation in dense interactions.
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
Multi-robot Control Barrier Function (CBF) safety filters can become infeasible, but a failed quadratic program (QP) does not indicate why the conflict occurred or how to resolve it. To address this, we develop an exact feasibility certificate for multi-agent CBF filters with heterogeneous control-affine dynamics and convex input sets. The certificate quantifies a feasibility reserve by separating the demand imposed by safety constraints from the available actuator supply. This decomposition shows when CBF gain tuning or increased actuation can and cannot resolve infeasibility, and identifies the agents and interactions responsible for the conflict. We further propose an algorithm to optimally allocate shared safety constraints by maximizing the worst local feasibility margin, yielding a linear program for polyhedral input sets. In 320 paired closed-loop simulations, the proposed allocation reduces infeasible control steps from roughly 50% to 6.2%, and reduces safety-violating runs from 118/160 to 24/160. In addition, across 52 infeasibility events, the certificate identifies an interaction whose relaxation restores feasibility in 94% of cases.
Chandan Kumar Sah, Jishnu Keshavan
Department of Mechanical Engineering, Indian Institute of Science, Bengaluru 560012, India
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.
Joonkyung Kim, Janghyun Cho, Jeehyun Lee +2
Dept. of Computer Science and Engineering, Texas A&M University. · Dept. of Artificial Intelligence, Sogang University. · Dept. of Electronic Engineering, Sogang University.