Capability-Aware Heterogeneous Control Barrier Functions for Decentralized Multi-Robot Safe Navigation

Joonkyung Kim; Yanze Zhang; Wenhao Luo; Yiwei Lyu

cs.ROApr 14, 2026

Capability-Aware Heterogeneous Control Barrier Functions for Decentralized Multi-Robot Safe Navigation

Authors: Joonkyung Kim, Yanze Zhang, Wenhao Luo, Yiwei Lyu

Organizations: Department of Computer Science and Engineering, Texas A&M University · Department of Computer Science, University of Illinois Chicago

Abstract

Safe navigation for multi-robot systems requires enforcing safety without sacrificing task efficiency under decentralized decision-making. Existing decentralized methods often assume robot homogeneity, making shared safety requirements non-uniformly interpreted across heterogeneous agents with structurally different dynamics, which could lead to avoidance obligations not physically realizable for some robots and thus cause safety violations or deadlock. In this paper, we propose Capability-Aware Heterogeneous Control Barrier Function (CA-HCBF), a decentralized framework for consistent safety enforcement and capability-aware coordination in heterogeneous robot teams. We derive a canonical second-order control-affine representation that unifies holonomic and nonholonomic robots under acceleration-level control via canonical transformation and backstepping, preserving forward invariance of the safe set while avoiding relative-degree mismatch across heterogeneous dynamics. We further introduce a support-function-based directional capability metric that quantifies each robot's ability to follow its motion intent, deriving a pairwise responsibility allocation that distributes the safety burden proportionally to each robot's motion capability. A feasibility-aware clipping mechanism further constrains the allocation to each agent's physically achievable range, mitigating infeasible constraint assignments common in dense decentralized CBF settings. Simulations with up to 30 heterogeneous robots and a physical multi-robot demonstration show improved safety and task efficiency over baselines, validating real-world applicability across robots with distinct kinematic constraints.

Figures & tables

Panel of Figure 1 — Figure 1: (a) Five mobile robots with heterogeneous kinematic classes (DI, UNI, DD, CL, FO) navigate toward individual goals. Each robot’s statement reflects its directional motion capability, ranging from the unconstrained DI to the restricted CL and FO, motivating the capability-aware responsibility allocation in Section IV . (b) Feasible control sets $\mathcal{U}_{i}$ in the $(v,\omega)$ space and their analytical definitions for the four nonholonomic kinematic classes (Section III-B ). The DI is omitted as it is holonomic and not parameterized by $(v,\omega)$ .

	$N=10$			$N=20$			$N=30$
Method	AR (%) $\uparrow$	# Viol $\downarrow$	Mean V $\downarrow$	AR (%) $\uparrow$	# Viol $\downarrow$	Mean V $\downarrow$	AR (%) $\uparrow$	# Viol $\downarrow$	Mean V $\downarrow$
CA-HCBF (Ours)	97.4	0.1 (0.5)	0.001 (0.008)	94.7	1.2 (2.0)	0.003 (0.008)	89.6	5.1 (9.6)	0.018 (0.035)
APF + Tracking ( $w{=}0.9$ )	94.2	4.3 (2.8)	0.273 (0.112)	90.9	22.7 (6.4)	0.280 (0.075)	87.1	59.7 (11.6)	0.279 (0.066)
APF + Tracking( $w{=}0.5$ )	89.4	2.1 (2.0)	0.200 (0.147)	86.1	13.5 (3.8)	0.267 (0.064)	80.7	37.9 (9.4)	0.271 (0.048)
APF + Tracking( $w{=}0.1$ )	46.2	0.0 (0.1)	0.005 (0.034)	22.5	0.1 (0.4)	0.041 (0.124)	15.5	1.0 (1.3)	0.179 (0.206)
APF + HOCBF	42.4	2.5 (1.6)	0.196 (0.124)	36.6	11.5 (7.3)	0.271 (0.086)	29.9	25.2 (9.9)	0.264 (0.065)

Table I : Performance comparison across team sizes (

N\in\{10,20,30\}

, 50 trials each).

Figure 2: Random start–goal scenario with 30 robots (5 per model) at multiple timestamps. At $t=0$ , robots start from random positions; × marks indicate assigned goals. UNI (blue circle), DI (light-blue circle), DD (green diamond), CL (red rectangle), FO (purple sector). The dashed circle denotes $r_{i}^{\mathrm{cbf}}$ (Section IV-E ), with its center representing the robot’s reference point (operational state position)

Parameter	DI	UNI	DD	CL	FO
Look-ahead $x_{r}^{i}$ (m)	–	0.1	0.1	0.2	0.2
$v_{\max}$ (m/s)	1.0	1.0	1.0	1.0	1.0
$a_{\max}$ (m/s 2 )	2.0	2.0	–	2.0	2.0
$\dot{\omega}_{\max}$ (rad/s 2 )	–	8.0	–	10.0	10.0
Wheelbase $\ell$ (m)	–	–	0.5	0.5	0.5
Physical radius (m)	0.3	0.3	0.3	–	–

Table II : Per-agent kinematic and physical parameters.

Figure 3: Average QP infeasibility events per trial across

N\in\{10,20,30\}

for three allocation strategies. The proposed capability- and feasibility-aware allocation reduces failures, with the gap widening as

N

increases.

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This paper proposes a fully decentralized model predictive control (MPC) framework with control barrier function (CBF) constraints for safety-critical trajectory planning in multi-robot legged systems. The incorporation of CBF constraints introduces explicit inter-agent coupling, which prevents direct decomposition of the resulting optimal control problems. To address this challenge, we reformulate the centralized safety-critical MPC problem using a structured distributed optimization framework based on the alternating direction method of multipliers (ADMM). By introducing a novel node-edge splitting formulation with consensus constraints, the proposed approach decomposes the global problem into independent node-local and edge-local quadratic programs that can be solved in parallel using only neighbor-to-neighbor communication. This enables fully decentralized trajectory optimization with symmetric computational load across agents while preserving safety and dynamic feasibility. The proposed framework is integrated into a hierarchical locomotion control architecture for quadrupedal robots, combining high-level distributed trajectory planning, mid-level nonlinear MPC enforcing single rigid body dynamics, and low-level whole-body control enforcing full-order robot dynamics. The effectiveness of the proposed approach is demonstrated through hardware experiments on two Unitree Go2 quadrupedal robots and numerical simulations involving up to four robots navigating uncertain environments with rough terrain and external disturbances. The results show that the proposed distributed formulation achieves performance comparable to centralized MPC while reducing the average per-cycle planning time by up to 51% in the four-agent case, enabling efficient real-time decentralized implementation.

Abstract

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