In this work, we analyze the decentralized formation control problem for a class of multi-robotic systems evolving on slippery surfaces. Grounded on experimental data of robots moving on a gravel surface inducing slippery, we show that a deterministic model cannot capture the uncertainties resulting from the kinematics of the robots while, instead, a model incorporating stochastic noise is capable of emulating such perturbations on wheel driving speed and turn rate. To account for these uncertainties, we consider a second order non-holonomic unicycle model to capture the full dynamics of individual vehicles where both actuation force and torque are subject to stochastic disturbances. Upon reducing the input-output dynamics of individual robot to a stochastic double integrator, we investigate the effects of these perturbations on the control input using concepts from stochastic stability theory and through numerical simulations. We demonstrated the applicability of the proposed scheme for formation control notably by providing sufficient conditions for exponential mean square convergence and we numerically determined the range of noise intensities for which team of robots can achieve formation stabilization. The promising findings from this work are expected to aid the design of robust control schemes for formation control of non-holonomic robots on off-road or un-paved surfaces.

Developing distributed control algorithms for multi-agent systems is difficult when each agent is modeled as a nonlinear dynamical system. Moreover, the problem becomes far more complex if the agents do not have sufficient number of actuators to track any arbitrary trajectory. In this paper, we present the first fully decentralized approach to formation control for networks of underactuated surface vessels. The vessels are modeled as three degree of freedom planar rigid bodies with two actuators. Algebraic graph theory is used to model the network as a directed graph and employing a leader-follower model. We take advantage of the cascade structure of the combined nonlinear kinematic and dynamic model of surface vessels and develop a reduced-order error dynamic model using a state transformation definition. The error dynamics and consequently all system states are then stabilized using sliding mode control approach. It is shown that the stabilization of the reduced-order error dynamics guarantees uniform global asymptotic stability of the closed-loop system subject to bounded uncertainties. The proposed control method can be implemented in directed time-invariant communication networks without the availability of global position measurements for any of the vehicles participating in the network. An example of a a network of five surface vessels is simulated to verify the effective performance of the proposed control approach.

Effective trajectory planning and cooperative control of multi-agent systems require accurate localization of the agents to perform collaborative missions. Accurate localization may be achieved by Global Positioning System (GPS) and simultaneous localization and mapping. However, GPS signals and fixed features may not be readily available, particularly in remote and unstructured environments. Under these circumstances, Cooperative Localization (CL) has been proposed as a short-term solution that can significantly improve vehicle pose estimation. CL algorithms have been developed and tested mainly on mobile robots and planar vehicles due to complexities of three-dimensional (3D) motion. In this paper, we present a CL algorithm for multi-agent systems comprised of 3D vehicles. Each vehicle’s pose is represented by three position and three orientation variables. Quaternions are employed to represent orientation and avoid singularities associated with Euler angle. Vehicle kinematic velocity relations are used to model vehicle dynamics with respect to a fixed reference frame. It is assumed a vehicle can take relative pose measurements of other neighboring vehicles within an ad hoc network of agents. We then designate the observed as target vehicles and the observers as base vehicles and determine the linearized output matrix of the relative measurements for Extended Kalman Filter (EKF) application. Simulations are presented to discuss the advantages and shortcomings of the algorithm.

Collective behavior refers to the group-level organization arising from interaction among individuals. To exchange information the individuals rely on their sensing modalities. Experimental studies provide evidence that the integration of information from multiple sensory modalities can influence animal navigation and social communication. In this paper, we present a modified Vicsek model with a composite sensing scheme that combines both auditory and visual sensing cues through the set of sensory neighbors. We investigate the combined effect of auditory and visual sensing on the group behavior compared to pure vision and audition using numerical simulation. We observe that taking the advantage of composite modality, the particles get access to more information that enables them to form a single large, cohesive, and perfectly aligned group using a narrow sensing region, which is possible in either vision or audition only using a wider sensing region.

Many multi-agent systems in nature are comprised of agents that interact with, and respond to, the dynamics of their environment. In this paper, we approach the study of such agent environment interactions through the study of passively compliant vehicles coupled to their environment via simple nonholonomic constraints. We first consider a single passively compliant Chaplygin beanie atop a platform having translational compliance, introduce the reduced equations for the system using the notion of nonholonomic momentum, and provide proof for its stability under arbitrary deformations of the elastic element modeling its compliance. We then direct our focus to results concerning the frequency response and control of passive Chaplygin beanies under actuation of the platform, discuss rich dynamical features arising from periodic actuation, and develop rules by which control can be exerted to collect and disperse multiple passive vehicles. We then discuss how the latter of these results clarifies the extent to which stable behavior can be excited in the system through exogenous control.

We present a distributed control law to assemble a cluster of satellites into an equally-spaced, planar constellation in a desired circular orbit about a planet. We assume each satellite only uses local information, transmitted through communication links with neighboring satellites. The same control law is used to maintain relative angular positions in the presence of disturbance forces. The stability of the constellation in the desired orbit is proved using a compositional approach. We first show the existence and uniqueness of an equilibrium of the interconnected system. We then certify each satellite and communication link is equilibrium-independent passive with respective storage functions. By leveraging the skew symmetric coupling structure of the constellation and the equilibrium-independent passivity property of each subsystem, we show that the equilibrium of the interconnected system is stable with a Lyapunov function composed of the individual subsystem storage functions. We further prove that the angular velocity of each satellite converges to the desired value necessary to maintain circular, areostationary orbit. Finally, we present simulation results to demonstrate the efficacy of the proposed control law in acquisition and station-keeping of an equally-spaced satellite constellation in areostationary orbit despite the presence of unmodeled disturbance forces.

Predicting the diffusion of real-world contagion processes requires a simplified description of human-to-human interactions. Temporal networks offer a powerful means to develop such a mathematically-transparent description. Through temporal networks, one may analytically study the co-evolution of the contagion process and the network topology, as well as incorporate realistic feedback-loop mechanisms related to individual behavioral changes to the contagion. Despite considerable progress, the state-of-the-art does not allow for studying general time-varying networks, where links between individuals dynamically switch to reflect the complexity of social behavior. Here, we tackle this problem by considering a temporal network, in which reducible, associated with node-specific properties, and irreducible links, describing dyadic social ties, simultaneously vary over time. We develop a general mean field theory for the Susceptible-Infected-Susceptible model and conduct an extensive numerical campaign to elucidate the role of network parameters on the average degree of the temporal network and the epidemic threshold. Specifically, we describe how the interplay between reducible and irreducible links influences the disease dynamics, offering insights towards the analysis of complex dynamical networks across science and engineering.

This work addresses the observability properties of linear time-invariant systems that are monitored by a sensor network that provides access only to relative measurements and partial absolute observations of the state-space variables. Graph-theoretical tools are deployed to represent the information sharing links between the sensors of the network. The results are extended to multi-agent coordinated systems that are independently controlled or execute distributed control protocols. Explicit analytical conditions are derived that determine the system’s observability with respect to the spectral characteristics of the information-sharing network. The system’s observability is further investigated for multi-agent systems governed by the agreement dynamics where only a singleton measurement is available. The analysis is disseminated to the design of distributed observers where the agents have only available their relative displacement measurement from their neighbors. The distributed observer’s estimation error is rendered globally asymptotically stable by the addition of an anchor node that has access to the absolute motion of a single agent (node). The theoretical analysis is validated through numerical simulations.

Communication inspired by animals is a timely topic of research in the modeling and control of multi-agent systems. Examples of such bio-inspired communication methods include pheromone trails used by ants to forage for food and echolocation used by bats to orient themselves and hunt. Source searching is one of many challenges in the field of swarm robotics that tackles an analogous problem to animals foraging for food. This paper seeks to compare two communication methods, inspired by sonar and pheromones, in the context of a multi-agent foraging problem. We explore which model is more effective at recruiting agents to forage from a found target. The results of this work begin to uncover the complicated relationship between sensing modality, collective tasks, and spontaneous cooperation in groups.

In this paper, the problem of using a limited number of mobile sensors to sense/measure a time-varying distribution of a field over a multi dimensional space is considered. As the number of sensors, in general, is not adequate for capturing the dynamic distribution with the needed spatial resolution, the sensors are required to be transited between the sampled locations, resulting in intermittent measurement at each sampled location. Therefore, it becomes challenging to use the measured data to recover/restore not only the dynamic process at each sampled/measured location, but also the dynamic distribution over the entire measured space, with high temporal and spatial resolutions. Such a multi-mobile sensing problem, however, cannot be addressed by using existing methods directly. In this work, we propose to tackle this problem through the compressed sensing framework. The randomness requirement of the compressed sensing, however, results in the temporal-spatial coupling, and the constraints in selecting the sampled locations due to the limit of the sensor speed. We propose a spatial-temporal pairing method to avoid the temporal-spatial coupling, and a checking-and-removal process to remove the sensor speed constraint. Simulation results of a video recovery example is presented and discussed to illustrate the proposed method.

This paper addresses an energy-balanced leader-switching policy for formation rotation control of multi-agent systems inspired by bird flocks. Birds that flock in V-formation with a leader rotation strategy are able to travel longer distances due to reduced drag and therefore less energy expenditure. This flocking behavior with a leader rotation will result in more conservation of overall energy and will be particularly beneficial to migrating birds that should fly long distances without landing. In this paper, we propose an energy-balanced leader-switching policy inspired by this bird flocking behavior in order to increase the flight range for multi-agent systems. The formation control of multi-agent systems is achieved by the consensus algorithm, which is fully decentralized through the use of information exchanges between agents. The proposed leader-switching method is not necessarily incorporated with the consensus dynamics and thus, the leader-switching algorithm can be decoupled from formation control dynamics. Therefore, the proposed method can simplify the leader-switching algorithm, making it easy to implement. Moreover, we propose the analytic flight distance based on the energy consumption model for each agent. To test the validity of the developed method, several simulation results are presented.

Publisher’s Note: This paper was selected for publication in ASME Letters in Dynamic Systems and Control . https://www.asmedigitalcollection.asme.org/lettersdynsys/article/doi/10.1115/1.4046580/1075681/Thermodynamics-Inspired-Macroscopic-States-of

This work is concerned with stability analysis of stationary and time-varying equilibria in a class of mean-field games that relate to multi-agent control problems of flocking and swarming. The mean-field game framework is a non-cooperative model of distributed optimal control in large populations, and characterizes the optimal control for a representative agent in Nash-equilibrium with the population. A mean-field game model is described by a coupled PDE system of forward-in-time Fokker-Planck (FP) equation for density of agents, and a backward-in-time Hamilton-Jacobi-Bellman (HJB) equation for control. The linear stability analysis of fixed points of these equations typically proceeds via numerical computation of spectrum of the linearized MFG operator. We explore the Evans function approach that provides a geometric alternative to solving the characteristic equation.

In this paper, we explore a model of collective behavior using EUGENE, an algorithm for automated discovery of so-called “dynamical kinds”. Two systems are of the same dynamical kind if their underlying causal dynamics are similar, as defined using dynamical symmetry. We apply EUGENE to simulation data from a model capable of generating a range of qualitatively different collective behaviors, from aligned motion to circular milling. These behaviors are measured using both global and local order parameters, and this data is analyzed with EUGENE. We find that EUGENE is capable of differentiating between these systems when global order parameters are used, and can only identify more coarse characteristics when local order parameters are considered.

In this paper a periodic event-based repetitive controller with dynamic output feedback is designed for linear systems with exogenous disturbances. The periodic event mechanism is designed such that within any two event triggering instants, the dynamic output feedback controller is open which substantially reduces the control and communication burden when the output does not change significantly. First, by employing the input delay approach, the overall system consisting of the physical plant, the repetitive controller, and the dynamic output feedback controller with periodic event-triggering mechanism is modeled as a closed-loop time-varying delay system. Then, sufficient conditions in terms of linear matrix inequalities are derived to ensure that the closed-loop system is asymptotically stable with a prescribed H ∞ attenuation performance level. The controller gains are synthesized by using a matrix decomposition technique. A numerical example is provided to evaluate the proposed design approach.

The swashplate of a model helicopter consists of stationary and rotating plates separated by ball bearings. This mechanism enables the swashplate to tilt in all directions and move vertically as one unit. The lower stationary plate is mounted on the main rotor mast and connected to the cyclic and collective controls by a series of pushrods. There are similar pushrods known as pitch links connected to the upper rotating plate. These pitch links are connected to the pitch horns and control the pitch of individual blades. In this study, the pitch links of the model helicopter are replaced by a semi compliant mechanism. This mechanism is directly connected to the pitch horns to control the pitch of the individual blades. The actuation of the bars can be achieved by using high torque stepper or servo motors. These precise low and high amplitude outputs are specifically required for the cyclic and collective controls of the helicopter swashplate. The compliant swashplate mechanism can be fabricated as a single piece using an injection molding technique or by 3D printing. The mechanism is modeled by two similar vector loops in two different planes. The mathematical model of the plate motion and the forces on the mechanism links are developed and simulated using MATLAB and Simulink, and initial results are discussed in this paper. This mechanism would be applied to the helicopter directional control where the plate in the pitch-roll mechanism would serve as the swash plate of the helicopter.

This paper presents a human-robot trust integrated task allocation and motion planning framework for multi-robot systems (MRS) in performing a set of parallel subtasks. Parallel subtask specifications are conjuncted with MRS to synthesize a task allocation automaton. Each transition of the task allocation automaton is associated with the total trust value of human in corresponding robots. A dynamic Bayesian network (DBN) based human-robot trust model is constructed considering individual robot performance, safety coefficient, human cognitive workload and overall evaluation of task allocation. Hence, a task allocation path with maximum encoded human-robot trust can be searched based on the current trust value of each robot in the task allocation automaton. Symbolic motion planning (SMP) is implemented for each robot after they obtain the sequence of actions. The task allocation path can be intermittently updated with this DBN based trust model. The overall strategy is demonstrated by a simulation with 5 robots and 3 parallel subtask automata.

In this paper, a novel switched systems approach is taken to enable the distributed coordination of a multi-agent system with intermittent communication. A mobile information service provider switches between various (follower) agents in the network to provide them with state feedback when they are within close proximity. The follower agents do not have navigational sensors but are still proven to converge to a desired goal through open-loop control with intermittent error correction by the leader. A switched systems stability analysis is performed to determine the maximum dwell-time the mobile information service provider can intermittently communicate information to the agents to ensure convergence to the desired goal. Simulation results are included to demonstrate the development.

In previous work, a (smooth) finite-time distributed control algorithm with time transformation was introduced for first-order multiagent systems, which guarantees convergence of the single state of agents to a time-varying leader at a-priori given, user-defined time T from any arbitrary initial conditions with bounded local control signals. In this paper, we present an extension of this previous work to second-order multiagent systems. Specifically, utilizing a user-defined finite-time interval of interest t ∈ [0, T), we time transform this class of multiagent systems subject to the considered (smooth) distributed control algorithm to an infinite-time interval s ∈ [0, ∞) with s being the stretched time. Based on a property of this time transformation, this results in finite-time convergence as the regular time t approaches to T from any arbitrary initial conditions with bounded local control and internal signals. Finally, two numerical examples illustrate the efficacy of the proposed algorithm.

Collective behavior emerges from local interactions in a group, has been observed in many natural systems, and is of significant interests for engineering applications. The Vicsek model is a mathematical tool to study collective alignment in a group of self-propelled particles based on local interaction, which has been well-studied in the literature for its simple algorithm and complex global behaviors. Several studies show that particles reach alignment faster when the directionality of particle interaction is restricted by an optimal view angle. This result seems counterintuitive, since each particle is expected to get more information through omnidirectional interaction. This work seeks to explore the possible causes of this optimal view angle by studying interaction dynamics in Vicsek model with restricted view angle through numerical simulation.