Distributed Predictive Control Barrier Functions: Towards Scalable Safety Certification in Modular Multi-Agent Systems

Jonas Ohnemus; Alexandre Didier; Ahmed Aboudonia; Andrea Carron; Melanie N. Zeilinger

eess.SYMar 31, 2026

Distributed Predictive Control Barrier Functions: Towards Scalable Safety Certification in Modular Multi-Agent Systems

Authors: Jonas Ohnemus, Alexandre Didier, Ahmed Aboudonia, Andrea Carron, Melanie N. Zeilinger

Organizations: Institute for Dynamic Systems and Control, ETH Zurich, 8092 Zurich, Switzerland · University of California Berkeley, 94720 CA, USA

Abstract

We consider safety-critical multi-agent systems with distributed control architectures and potentially varying network topologies. While learning-based distributed control enables scalability and high performance, a lack of formal safety guarantees in the face of unforeseen disturbances and unsafe network topology changes may lead to system failure. To address this challenge, we introduce structured control barrier functions (s-CBFs) as a multi-agent safety framework. The s-CBFs are augmented to a distributed predictive control barrier function (D-PCBF), a predictive, optimization-based safety layer that uses model predictions to guarantee recoverable safety at all times. The proposed approach enables a permissive yet formal plug-and-play protocol, allowing agents to join or leave the network while ensuring safety recovery if a change in network topology requires temporarily unsafe behavior. We validate the formulation through simulations and real-time experiments of a miniature race-car platoon.

Figures & tables

Fig. 1: Network-level recoverable safety using s-CBFs. The formulation defines safe sets $\mathcal{S}_{\ell}$ and regions of attraction $\mathcal{D}_{\ell}\setminus\mathcal{S}_{\ell}$ , ensuring constraint satisfaction and network-level convergence even when individual trajectories temporarily have to violate safety.

Fig. 2: Possible distributed predictive control barrier function (D-PCBF) control loop. Local control policies propose inputs $u_{\mathrm{p},\ell}$ that a distributed model predictive safety filter (see [ 16 ] , but with the same constraint formulation as the D-PCBF) subsequently filters to generate the control inputs $u_{\ell}$ , using the slack values $\xi_{\ell}^{i}$ that result from the D-PCBF. The D-PCBF design ensures that the feasible set is forward-invariant and attractive. Instead of using local controllers and a distributed predictive safety filter, distributed MPC can be employed directly by modifying the cost in ( 7 ).

\sum_{\ell\in\mathcal{L}_{\mathrm{new}}}(\xi_{\ell}^{N})^{\star}\leq\gamma_{f}.

Algorithm 1 PnP procedure with D-PCBF certificates

Fig. 3: Platoon example system. Assuming perfect lateral tracking and a kinematic model, the distributed dynamics consider the arc length to the preceding vehicle and the velocity magnitude.

Fig. 4: Synthesis results for the vehicle platoon model when maximizing the safe set for

L=5

agents. The top plots show the resulting s-CBF safe sets (green) and domains (blue) for the second and third car of the platoon. The bottom plots visualize the alternating optimization results described in Section V-A to approximately solve ( 12 ). The safe set size is plotted as the log-determinants of

E

, i.e.,

\log\det(E)=\sum_{\ell}\log\det(E_{\ell})\propto|E|

, while

\gamma_{f}

is used to indicate the size of the terminal region of attraction.

Fig. 5: Simulation results for the vehicle platoon model. The top plots show the state space trajectories (start=dot, end=cross) of the distributed simulation for the first four follower agents, where agents

\ell=1,2

are initialized at an unsafe distance. The top-left plot shows results for 5 agents, and the right plot shows results for 40 agents. In both cases, the network-level system converges to safe operation within the state constraints, although all agents try to accelerate with

a_{\ell}^{\mathrm{p}}=10.0\,\mathrm{m}/\mathrm{s}^{2}

. The bottom plot shows the solve times of ( 6 ) for the centralized solver and the distributed implementation, where the latter is reported as an idealized parallel runtime.

Fig. 6: State and input signals of the platoon experiment. The experiment starts with the configuration

0\leftarrow 1\leftarrow 2

. It consists of the following events: Car 3 approaches with high speed from behind and plugs in at

t\approx 47s

. Then, the leading car 0 plugs out at

t\approx 59s

. Finally, at

t\approx 78s

, this car approaches with high speed from behind and plugs in again. It can be seen that, in both plug-in scenarios, temporary violations of velocity and distance constraints occur, since the cars have limited acceleration. Although the infeasible commands proposed by the unsafe PID controllers (gray signals) would violate state constraints, the framework prevents unsafe operation whenever possible by applying the filtered commands (red signals). Moreover, it enables safety recovery in cases of constraint violations (gray shaded times). The leader vehicle is constrained to a smaller maximum acceleration to generate visible distance-constraint violations.

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Multi-robot systems (MRS) are essential for large-scale applications such as disaster response, material transport, and warehouse logistics, yet ensuring robust, safety-aware formation control in cluttered and dynamic environments remains a major challenge. Existing model predictive control (MPC) approaches suffer from limitations in scalability and provable safety, while control barrier functions (CBFs), though principled for safety enforcement, are difficult to handcraft for large-scale nonlinear systems. This paper presents FORMULA, a safe distributed, learning-enhanced predictive control framework that integrates MPC with Control Lyapunov Functions (CLFs) for stability and neural network-based CBFs for decentralized safety, eliminating manual safety constraint design. This scheme maintains formation integrity during obstacle avoidance, resolves deadlocks in dense configurations, and reduces online computational load. Simulation results demonstrate that FORMULA enables scalable, safety-aware, formation-preserving navigation for multi-robot teams in complex environments.

Abstract

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