- The paper introduces a distributed optimization-based control framework employing a truncation function and two-time-scale dynamics for safety-critical coordination.
- It utilizes control barrier and Lyapunov functions to enforce inter-agent and obstacle safety while preserving connectivity under fluctuating communication links.
- Simulations validate that the method achieves uniform global asymptotic stability and maintains positive algebraic connectivity even during topology transitions.
Distributed Safety-Critical Control of Multi-Agent Systems with Time-Varying Communication Topologies
Problem Setting and Motivation
This work addresses distributed control synthesis for multi-agent systems tasked with reach-avoid missions under inter-agent collision, obstacle avoidance, and connectivity preservation constraints, where communication between agents is predicated on relative state-dependent proximity and, hence, induces a time-varying communication topology. Classical distributed CBF-based approaches regularly presume a fixed communication graph and thus are insufficient when the underlying communication topology potentially experiences discontinuities as agents dynamically enter or exit each other's communication range. Handling such hybrid scenarios with scalable, robust distributed coordination and explicit safety assurances is a nontrivial, critical challenge in cooperative robotics, large-scale autonomy, and distributed sensor networks.
Methodological Contributions
The paper constructs a distributed optimization-based scheme incorporating two essential innovations to guarantee invariant safety and convergence properties under dynamically evolving graphs:
- Truncation Function for Topology Transitions: To address the discontinuity in both constraints and controller states as links are created or dropped, a smooth truncation function is introduced. This function guarantees continuity of constraints, and crucially, maintains the well-posedness of mismatch variables at topology transitions, avoiding the pathologies arising from instantaneous edge addition/removal in auxiliary variable structures.
- Auxiliary Mismatch Variables with Two-Time-Scale Dynamics: By introducing fast-evolving constraint decoupling variables, the method decouples globally coupled constraints (such as connectivity and collision avoidance) into local algebraic conditions. The resulting two-timescale (singularly perturbed) dynamical system enables each agent to solve a local optimization problem with only local and neighbor information, but the collective ensures that global constraints are maintained.
The framework rigorously leverages control barrier functions (CBFs) for safety requirements—encoding both inter-agent and obstacle avoidance—and control Lyapunov functions (CLFs) for target convergence. Connectivity preservation is encoded using algebraic graph properties and CBFs. The decomposition to distributed, locally consistent enforcement of constraints is enabled by the mismatch-variable formalism augmented for state-dependent graphs.
Theoretical Results
Singular perturbation analysis demonstrates uniform global asymptotic stability (UGAS) and forward invariance of safety sets for the interconnected, hybrid system. The analysis is nontrivial due to the necessity to show that the fast subsystem (consisting of mismatch variables) remains well-defined and that equilibria of the saddle-point dynamics for the agent-level problems persist under arbitrary topology changes.
Key claims proven include:
- If all local feasibility, smoothness, and Lipschitz conditions hold (see Assumptions 1–5), the distributed controller ensures inter-agent and obstacle safety, algebraic connectivity of the communication graph, and convergence to the collective target domain for all system trajectories.
- The error induced by the two-time-scale decomposition can be made arbitrarily small for sufficiently small time-scale parameter, ensuring negligible loss in global constraint satisfaction.
- The distributed algorithm remains robust to and well-posed under instantaneous addition and removal of edges due to the truncation function and appropriately updated mismatch variable dimensions.
Numerical Results
Simulations with five kinematic agents in the plane confirm that the proposed framework enables all agents to reach the target set while keeping clear of obstacles and avoiding inter-agent collisions, with communication connectivity maintained at all time steps. The algebraic connectivity (Fiedler value) of the induced communication Laplacian is shown to remain strictly positive throughout, even as edges of the communication graph are created or removed dynamically, confirming the efficacy of the approach under realistic, state-driven topology variations.
Implications and Future Directions
Practical Impact: The proposed method is immediately relevant to autonomous vehicle swarms, multi-robot exploration, and surveillance systems, where maintaining robust, scalable, and safe distributed coordination with limited-range, state-dependent wireless or sensing topologies is fundamental.
Theoretical Significance: This work generalizes the class of safety-critical distributed control schemes for multi-agent systems beyond static graphs, offering a rigorous framework for hybrid, edge-driven dynamic networks, a scenario common in realistic deployments. The approach subsumes existing distributed quadratic programming and saddle-point CBF/CLF schemes as special cases but provides new technical machinery to handle the hybrid nature of real-world systems.
Future Research: Extending these tools for asynchronous updates, stochastic topology evolution, or cyber-physical adversarial settings is natural. Integration with estimation algorithms to tolerate sensing/communication uncertainty and further reductions in conservativeness via adaptive, learning-based constraint set refinement is likely to improve performance and applicability.
Conclusion
The paper presents a distributed, optimization-based control architecture for multi-agent systems under time-varying, state-dependent communication topologies. The core advances—a truncation function for edge discontinuity management and two-time-scale mismatch variable dynamics—enable fully distributed, safe, and connectivity-preserving convergence to target sets, with theoretical guarantees established via singular perturbation analysis and validated in systematic simulations. This framework is a robust, scalable solution for safety-critical multi-agent coordination under realistic communication constraints (2604.00429).