Twinkle Tripathy

Kushal Pratap Singh, Twinkle Tripathy

In this paper, we present a class of bearing based distributive nonlinear guidance laws for the cooperative circumnavigation of a stationary target by a heterogeneous team of asymmetric Dubins vehicles. In such a vehicle, the maximal left and right turn capabilities are non uniform. In the given framework, the location of the target is known only to a small subset of the vehicles, called the leaders. The uninformed vehicles, called the followers, use information from their out neighbours in the communication graph, constructed using the nearest neighbour rule. A class of guidance laws is formulated that relies solely on the heading angle and line of sight angles of a designated out neighbour of the vehicle in the graph. Using Zubov theorem, we prove that the proposed guidance laws achieve global asymptotic stability under angular speed only control and ensure the convergence of the trajectories of all the Dubins vehicles to a common centre. The proposed results are validated through numerical simulations.

Kushal Pratap Singh, Manvi Bengani, Darshit Mittal et al.

In this paper, we address the problem of circumnavigation of a stationary target by a heterogeneous group comprising of $\textbf{n}$ autonomous agents, having unicycle kinematics. The agents are assumed to have constant linear speeds, we control only the angular speeds. Assuming limited sensing capabilities of the agents, only a subset of agents, termed as \textit{leaders}, know the target location. The rest, termed as \textit{followers}, do not. We propose a distributed guidance law which drives all the agents towards the desired objective; global asymptotic stability (GAS) is ensured by using Zubov's theorem. The efficacy of the approach is demonstrated through both numerical simulations and hardware experiments.

Pradeep M, Twinkle Tripathy

This paper investigates structural herdability in a special class of temporally switching networks with fixed topology. We show that when the underlying digraph remains unchanged across all snapshots, the network attains complete SS herdability even in the presence of signed or layer dilations, a condition not applicable to static networks. This reveals a fundamental structural advantage of temporal dynamics and highlights a novel mechanism through which switching can overcome classical obstructions to herdability. To validate these conclusions, we utilize a more relaxed form of sign matching within each snapshot of the temporal network. Furthermore, we show that when all snapshots share the same underlying topology, the temporally switching network achieves $\mathcal{SS}$ herdability within just two snapshots, which is fewer than the number required for structural controllability. Several examples are included to demonstrate these results.

Aashi Shrinate, Twinkle Tripathy

The convergence of opinions in the Friedkin-Johnsen (FJ) framework is well studied, but the topological conditions leading to opinion clustering remain less explored. To bridge this gap, we examine the role of topology in the emergence of opinion clusters within the network. The key contribution of the paper lies in the introduction of the notion of topologically prominent agents, referred to as Locally Topologically Persuasive (LTP) agents. Interestingly, each LTP agent is associated with a unique set of (non-influential) agents in its vicinity. Using them, we present conditions to obtain opinion clusters in the FJ framework in any arbitrarily connected digraph. A key advantage of the proposed result is that the resulting opinion clusters are independent of the edge weights and the stubbornness of the agents. Finally, we demonstrate using simulation results that, by suitably placing LTP agents, one can design networks that achieve any desired opinion clustering.

Aashi Shrinate, Twinkle Tripathy, Laxmidhar Behera

The Friedkin-Johnsen (FJ) model is a popular opinion dynamics model that explains the disagreement that can occur even among closely interacting individuals. Cluster consensus is a special type of disagreement, where agents in a network split into subgroups such that those within a subgroup agree and those in different subgroups disagree. In large-scale social networks, users often distribute into echo chambers (i.e. groups of users with aligned views) while discussing contested issues such as electoral politics, social norms, etc. Additionally, they are exposed only to opinions and news sources that align with their existing beliefs. Hence, the interaction network plays a key role in the formation of an echo chamber. Since cluster consensus can represent echo chambers in a social network, we examine the conditions for cluster consensus under the FJ model with the objective of determining the properties of the interaction network that lead to echo chamber formation. We present topology-based necessary and sufficient conditions for cluster consensus under the FJ model, regardless of the edge weights in the network and stubbornness values (which are difficult to estimate parameters in a social network). A major advantage of the proposed results is that they are applicable to arbitrary digraphs. Moreover, using the proposed conditions, we explain the emergence of bow-tie structures which are often observed in real-world echo chambers. Finally, we also develop a computationally feasible methodology to verify the proposed conditions for cluster consensus.