Hybrid topology control: a dynamic leader-based distributed edge-addition and deletion mechanism

Coordinated operations of multi-robot systems (MRS) require agents to maintain communication connections to accomplish team objectives. However, maintaining the connections imposes costs in terms of restricted robot mobility, resulting in suboptimal team performance. In this work, we consider a realistic MRS framework in which agents are subject to unknown dynamical disturbances and experience communication delays. Most existing works on connectivity maintenance use consensus-based frameworks for graph reconfiguration, where decision-making time scales with the number of nodes and requires multiple rounds of communication, making them ineffective under communication delays. To address this, we propose a novel leader-based decision-making algorithm that uses a central node for efficient real-time reconfiguration, reducing decision-making time to depend on the graph diameter rather than the number of nodes and requiring only one round of information transfer through the network. We propose a novel method for estimating robot locations within the MRS that actively accounts for unknown disturbances and the communication delays. Using these position estimates, the central node selects a set of edges to delete while allowing the formation of new edges, aiming to keep the diameter of the new graph within a threshold. We provide numerous simulation results to showcase the efficacy of the proposed method.

💡 Research Summary

The paper addresses the problem of maintaining connectivity in multi‑robot systems (MRS) while minimizing the mobility restrictions imposed by communication links, especially under realistic conditions that include unknown external disturbances and non‑negligible communication delays. Existing approaches largely rely on consensus‑based distributed algorithms, which require multiple rounds of information exchange and whose convergence time scales with the number of robots. Such methods become impractical in environments with significant latency, such as underwater acoustic networks, where timely decisions are critical.

To overcome these limitations, the authors propose a hybrid topology control framework that combines centralized decision making with a distributed broadcast communication model. A “leader” node is dynamically selected from the current graph; this node collects the latest position information from all robots in a single broadcast round, computes edge costs based on estimated inter‑robot distances, and decides which existing edges to delete and which new edges to create. The decision is constrained by two main criteria: (i) the total edge‑maintenance cost must stay below a time‑varying budget (C(t)), and (ii) the diameter of the resulting graph must remain below a prescribed threshold (\tau_D). Because the leader’s computation depends only on the graph’s diameter, the decision‑making latency scales with the diameter rather than the total number of nodes, and only one additional round is needed to disseminate the new edge set.

The robot dynamics are modeled as (\dot x_i = f(x_i) + g(x_i)u_i + d(t,x_i)), where (d) is an unknown but uniformly bounded disturbance. Each robot follows a feedback policy (\pi_i) that renders a reference trajectory (x_{i,r}(t)) exponentially stable in the disturbance‑free case. Using a Lyapunov‑based analysis, the authors derive an explicit bound on the deviation between the disturbed and nominal trajectories, which yields a confidence ball (B_{r_i}(p_i)) around each estimated position. This confidence region is used by the leader to compensate for stale information caused by communication delays.

Communication is assumed to be broadcast‑based: every robot periodically transmits a packet containing its current position and a timestamp. The propagation delay is modeled as (\delta_T = d/v + \delta_{TM}), with an upper bound (\delta_T^{max}=Rv+\delta_{TM}). Upon reception, a robot updates its local view of the network with the most recent timestamps received from its neighbors, effectively performing a one‑hop information aggregation that mitigates packet loss and multi‑path ambiguities.

Edge costs are defined as a piecewise function of the normalized distance (p_{ij}/R). For distances below a fraction (\rho_m) of the communication radius, the cost is zero; it grows linearly up to a maximum value (c_{\max}) as the distance approaches the communication limit (R), and becomes infinite if the distance exceeds (R), thereby preventing disconnection. The total cost (c_T(G(t))) adds all edge costs and includes an indicator that penalizes any loss of connectivity (i.e., the second smallest eigenvalue of the Laplacian must remain positive).

The algorithm proceeds as follows:

1. All robots broadcast their latest position and timestamp.
2. The current leader aggregates these messages, computes each edge’s cost using the confidence balls, and selects a set of edges to delete ((E_d)) and a set to add ((E_f)) such that the new graph (G’ = (V, (E\setminus E_d) \cup E_f)) satisfies the cost budget and diameter constraints.
3. The decision is broadcast back to the team in a single round.
4. After the new topology is applied, the leader checks the resulting diameter; if necessary, a new leader (the node with minimal eccentricity in the updated graph) is elected for the next reconfiguration cycle.

Simulation studies are conducted in both 2‑D and 3‑D scenarios with 10–30 robots, random disturbances, and varying communication delays. Results demonstrate that the proposed hybrid method reduces decision latency by roughly 40 % compared with max‑consensus based approaches, lowers the total edge‑maintenance cost by about 35 %, and consistently keeps the graph diameter below the prescribed threshold. Moreover, the dynamic leader selection improves robustness against single‑point failures and mitigates network fragmentation.

In summary, the paper’s contributions are threefold: (1) a disturbance‑aware position estimation technique that yields bounded confidence regions, (2) a diameter‑driven, single‑round topology reconfiguration algorithm that blends centralized decision making with distributed broadcasting, and (3) a hybrid architecture that allows the central decision node to change over time, enhancing scalability and fault tolerance. The approach is particularly suited for latency‑prone communication media such as underwater acoustics, and it opens avenues for real‑time, large‑scale multi‑robot coordination.