In swarm robotics, agents interact through local roles to solve complex tasks beyond an individual's ability. Even though swarms are capable of carrying out some operations without the need for human intervention, many safety-critical applications still call for human operators to control and monitor the swarm. There are novel challenges to effective Human-Swarm Interaction (HSI) that are only beginning to be addressed. Explainability is one factor that can facilitate effective and trustworthy HSI and improve the overall performance of Human-Swarm team. Explainability was studied across various Human-AI domains, such as Human-Robot Interaction and Human-Centered ML. However, it is still ambiguous whether explanations studied in Human-AI literature would be beneficial in Human-Swarm research and development. Furthermore, the literature lacks foundational research on the prerequisites for explainability requirements in swarm robotics, i.e., what kind of questions an explainable swarm is expected to answer, and what types of explanations a swarm is expected to generate. By surveying 26 swarm experts, we seek to answer these questions and identify challenges experts faced to generate explanations in Human-Swarm environments. Our work contributes insights into defining a new area of research of eXplainable Swarm (xSwarm) which looks at how explainability can be implemented and developed in swarm systems. This paper opens the discussion on xSwarm and paves the way for more research in the field.

Swarm robotic systems utilize collective behaviour to achieve goals that might be too complex for a lone entity, but become attainable with localized communication and collective decision making. In this paper, a behaviour-based distributed approach to shape formation is proposed. Flocking into strategic formations is observed in migratory birds and fish to avoid predators and also for energy conservation. The formation is maintained throughout long periods without collapsing and is advantageous for communicating within the flock. Similar behaviour can be deployed in multi-agent systems to enhance coordination within the swarm. Existing methods for formation control are either dependent on the size and geometry of the formation or rely on maintaining the formation with a single reference in the swarm (the leader). These methods are not resilient to failure and involve a high degree of deformation upon obstacle encounter before the shape is recovered again. To improve the performance, artificial force-based interaction amongst the entities of the swarm to maintain shape integrity while encountering obstacles is elucidated.

A novel distributed algorithm is proposed for finite-time converging to a feasible consensus solution satisfying global optimality to a certain accuracy of the distributed robust convex optimization problem (DRCO) subject to bounded uncertainty under a uniformly strongly connected network. Firstly, a distributed lower bounding procedure is developed, which is based on an outer iterative approximation of the DRCO through the discretization of the compact uncertainty set into a finite number of points. Secondly, a distributed upper bounding procedure is proposed, which is based on iteratively approximating the DRCO by restricting the constraints right-hand side with a proper positive parameter and enforcing the compact uncertainty set at finitely many points. The lower and upper bounds of the global optimal objective for the DRCO are obtained from these two procedures. Thirdly, two distributed termination methods are proposed to make all agents stop updating simultaneously by exploring whether the gap between the upper and the lower bounds reaches a certain accuracy. Fourthly, it is proved that all the agents finite-time converge to a feasible consensus solution that satisfies global optimality within a certain accuracy. Finally, a numerical case study is included to illustrate the effectiveness of the distributed algorithm.

This article studies the distributed estimation problem of a multi-agent system with bounded absolute and relative range measurements. Parts of the agents are with high-accuracy absolute measurements, which are considered as anchors; the other agents utilize lowaccuracy absolute and relative range measurements, each derives an uncertain range that contains its true state in a distributed manner. Different from previous studies, we design a distributed algorithm to handle the range measurements based on extended constrained zonotopes, which has low computational complexity and high precision. With our proposed algorithm, agents can derive their uncertain range sequentially along the chain topology, such that agents with low-accuracy sensors can benefit from the high-accuracy absolute measurements of anchors and improve the estimation performance. Simulation results corroborate the effectiveness of our proposed algorithm and verify our method can significantly improve the estimation accuracy. Keywords: Set-membership estimation, constrained zonotope, absolute and relative measurements.

This paper addresses a Multi-Agent Collective Construction (MACC) problem that aims to build a three-dimensional structure comprised of cubic blocks. We use cube-shaped robots that can carry one cubic block at a time, and move forward, reverse, left, and right to an adjacent cell of the same height or climb up and down one cube height. To construct structures taller than one cube, the robots must build supporting stairs made of blocks and remove the stairs once the structure is built. Conventional techniques solve for the entire structure at once and quickly become intractable for larger workspaces and complex structures, especially in a multi-agent setting. To this end, we present a decomposition algorithm that computes valid substructures based on intrinsic structural dependencies. We use Mixed Integer Linear Programming (MILP) to solve for each of these substructures and then aggregate the solutions to construct the entire structure. Extensive testing on 200 randomly generated structures shows an order of magnitude improvement in the solution computation time compared to an MILP approach without decomposition. Additionally, compared to Reinforcement Learning (RL) based and heuristics-based approaches drawn from the literature, our solution indicates orders of magnitude improvement in the number of pick-up and drop-off actions required to construct a structure. Furthermore, we leverage the independence between substructures to detect which sub-structures can be built in parallel. With this parallelization technique, we illustrate a further improvement in the number of time steps required to complete building the structure. This work is a step towards applying multi-agent collective construction for real-world structures by significantly reducing solution computation time with a bounded increase in the number of time steps required to build the structure.

This paper proposes a distributed algorithm for average consensus in a multi-agent system under a fixed bidirectional communication topology, in the presence of malicious agents (nodes) that may try to influence the average consensus outcome by manipulating their updates. The proposed algorithm converges asymptotically to the average of the initial values of the non-malicious nodes, which we refer to as the trustworthy average, as long as the underlying topology that describes the information exchange among the non-malicious nodes is connected. We first present a distributed iterative algorithm that assumes that each node receives (at each iteration or periodically) side information about the trustworthiness of the other nodes, and it uses such trust assessments to determine whether or not to incorporate messages received from its neighbors, as well as to make proper adjustments in its calculation depending on whether a previously trustworthy neighbor becomes untrustworthy or vice-versa. We show that, as long as the trust assessments for each non-malicious node eventually reflect correctly the status (malicious or non-malicious) of its neighboring nodes, the algorithm guarantees asymptotic convergence to the trustworthy average. We subsequently discuss how the proposed algorithm can be enhanced with functionality that enables each node to obtain trust assessments about its neighbors by utilizing information that it receives from its two-hop neighbors at infrequent, perhaps randomly chosen, time instants.

The recent deployment of multi-agent systems in a wide range of scenarios has enabled the solution of learning problems in a distributed fashion. In this context, agents are tasked with collecting local data and then cooperatively train a model, without directly sharing the data. While distributed learning offers the advantage of preserving agents' privacy, it also poses several challenges in terms of designing and analyzing suitable algorithms. This work focuses specifically on the following challenges motivated by practical implementation: (i) online learning, where the local data change over time; (ii) asynchronous agent computations; (iii) unreliable and limited communications; and (iv) inexact local computations. To tackle these challenges, we introduce the Distributed Operator Theoretical (DOT) version of the Alternating Direction Method of Multipliers (ADMM), which we call the DOT-ADMM Algorithm. We prove that it converges with a linear rate for a large class of convex learning problems (e.g., linear and logistic regression problems) toward a bounded neighborhood of the optimal time-varying solution, and characterize how the neighborhood depends on~$\text{(i)--(iv)}$. We corroborate the theoretical analysis with numerical simulations comparing the DOT-ADMM Algorithm with other state-of-the-art algorithms, showing that only the proposed algorithm exhibits robustness to (i)--(iv).

Collective perception is a foundational problem in swarm robotics, in which the swarm must reach consensus on a coherent representation of the environment. An important variant of collective perception casts it as a best-of-$n$ decision-making process, in which the swarm must identify the most likely representation out of a set of alternatives. Past work on this variant primarily focused on characterizing how different algorithms navigate the speed-vs-accuracy tradeoff in a scenario where the swarm must decide on the most frequent environmental feature. Crucially, past work on best-of-$n$ decision-making assumes the robot sensors to be perfect (noise- and fault-less), limiting the real-world applicability of these algorithms. In this paper, we derive from first principles an optimal, probabilistic framework for minimalistic swarm robots equipped with flawed sensors. Then, we validate our approach in a scenario where the swarm collectively decides the frequency of a certain environmental feature. We study the speed and accuracy of the decision-making process with respect to several parameters of interest. Our approach can provide timely and accurate frequency estimates even in presence of severe sensory noise.

This paper studies a class of strongly monotone games involving non-cooperative agents that optimize their own time-varying cost functions. We assume that the agents can observe other agents' historical actions and choose actions that best respond to other agents' previous actions; we call this a best response scheme. We start by analyzing the convergence rate of this best response scheme for standard time-invariant games. Specifically, we provide a sufficient condition on the strong monotonicity parameter of the time-invariant games under which the proposed best response algorithm achieves exponential convergence to the static Nash equilibrium. We further illustrate that this best response algorithm may oscillate when the proposed sufficient condition fails to hold, which indicates that this condition is tight. Next, we analyze this best response algorithm for time-varying games where the cost functions of each agent change over time. Under similar conditions as for time-invariant games, we show that the proposed best response algorithm stays asymptotically close to the evolving equilibrium. We do so by analyzing both the equilibrium tracking error and the dynamic regret. Numerical experiments on economic market problems are presented to validate our analysis.

Can social power endow social robots with the capacity to persuade? This paper represents our recent endeavor to design persuasive social robots. We have designed and run three different user studies to investigate the effectiveness of different bases of social power (inspired by French and Raven's theory) on peoples' compliance to the requests of social robots. The results show that robotic persuaders that exert social power (specifically from expert, reward, and coercion bases) demonstrate increased ability to influence humans. The first study provides a positive answer and shows that under the same circumstances, people with different personalities prefer robots using a specific social power base. In addition, social rewards can be useful in persuading individuals. The second study suggests that by employing social power, social robots are capable of persuading people objectively to select a less desirable choice among others. Finally, the third study shows that the effect of power on persuasion does not decay over time and might strengthen under specific circumstances. Moreover, exerting stronger social power does not necessarily lead to higher persuasion. Overall, we argue that the results of these studies are relevant for designing human--robot-interaction scenarios especially the ones aiming at behavioral change.