Application of Collective Movement in Real Life Scenarios: Overview of Current Flocking Solutions
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paper_title: Spatially balanced topological interaction grants optimal cohesion in flocking models

paper_content:

Models of self-propelled particles (SPPs) are an indispensable tool to investigate collective animal behaviour. Originally, SPP models were proposed with metric interactions, where each individual coordinates with neighbours within a fixed metric radius. However, recent experiments on bird flocks indicate that interactions are topological: each individual interacts with a fixed number of neighbours, irrespective of their distance. It has been argued that topological interactions are more robust than metric ones against external perturbations, a significant evolutionary advantage for systems under constant predatory pressure. Here, we test this hypothesis by comparing the stability of metric versus topological SPP models in three dimensions. We show that topological models are more stable than metric ones. We also show that a significantly better stability is achieved when neighbours are selected according to a spatially balanced topological rule, namely when interacting neighbours are evenly distributed in angle around the focal individual. Finally, we find that the minimal number of interacting neighbours needed to achieve fully stable cohesion in a spatially balanced model is compatible with the value observed in field experiments on starling flocks.
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paper_title: Outdoor flocking and formation flight with autonomous aerial robots

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We present the first decentralized multi-copter flock that performs stable autonomous outdoor flight with up to 10 flying agents. By decentralized and autonomous we mean that all members navigate themselves based on the dynamic information received from other robots in the vicinity. We do not use central data processing or control; instead, all the necessary computations are carried out by miniature on-board computers. The only global information the system exploits is from GPS receivers, while the units use wireless modules to share this positional information with other flock members locally. Collective behavior is based on a decentralized control framework with bio-inspiration from statistical physical modelling of animal swarms. In addition, the model is optimized for stable group flight even in a noisy, windy, delayed and error-prone environment. Using this framework we successfully implemented several fundamental collective flight tasks with up to 10 units: i) we achieved self-propelled flocking in a bounded area with self-organized object avoidance capabilities and ii) performed collective target tracking with stable formation flights (grid, rotating ring, straight line). With realistic numerical simulations we demonstrated that the local broadcast-type communication and the decentralized autonomous control method allows for the scalability of the model for much larger flocks.
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paper_title: Flocking algorithm for autonomous flying robots

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Animal swarms displaying a variety of typical flocking patterns would not exist without the underlying safe, optimal and stable dynamics of the individuals. The emergence of these universal patterns can be efficiently reconstructed with agent-based models. If we want to reproduce these patterns with artificial systems, such as autonomous aerial robots, agent-based models can also be used in their control algorithms. However, finding the proper algorithms and thus understanding the essential characteristics of the emergent collective behaviour requires thorough and realistic modeling of the robot and also the environment. In this paper, we first present an abstract mathematical model of an autonomous flying robot. The model takes into account several realistic features, such as time delay and locality of communication, inaccuracy of the on-board sensors and inertial effects. We present two decentralized control algorithms. One is based on a simple self-propelled flocking model of animal collective motion, the other is a collective target tracking algorithm. Both algorithms contain a viscous friction-like term, which aligns the velocities of neighbouring agents parallel to each other. We show that this term can be essential for reducing the inherent instabilities of such a noisy and delayed realistic system. We discuss simulation results on the stability of the control algorithms, and perform real experiments to show the applicability of the algorithms on a group of autonomous quadcopters. In our case, bio-inspiration works in two ways. On the one hand, the whole idea of trying to build and control a swarm of robots comes from the observation that birds tend to flock to optimize their behaviour as a group. On the other hand, by using a realistic simulation framework and studying the group behaviour of autonomous robots we can learn about the major factors influencing the flight of bird flocks.
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paper_title: The marXbot, a miniature mobile robot opening new perspectives for the collective-robotic research

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Collective and swarm robotics explores scenarios involving many robots running at the same time. A good platform for collective-robotic experiments should provide certain features among others: it should have a large battery life, it should be able to perceive its peers, and it should be capable of interacting with them. This paper presents the marXbot, a miniature mobile robot that addresses these needs. The marXbot uses differential-drive treels to provide rough-terrain mobility. The marXbot allows continuous experiments thanks to a sophisticated energy management and a hotswap battery exchange mechanism. The marXbot can self-assemble with peers using a compliant attachment mechanism. The marXbot provides high-quality vision, using two cameras directly interfaced with an ARM processor. Compared to the related work, the marXbot has better energy management, vision, and interaction capabilities. By allowing complex tasks in large environments for long durations, the marXbot opens new perspectives for the collective-robotic research.
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paper_title: Flocking of multiple autonomous agents with preserved network connectivity and heterogeneous nonlinear dynamics

paper_content:

Abstract This paper investigates a flocking problem of multiple agents with heterogeneous nonlinear dynamics. In order to avoid fragmentation, we construct a potential function and a connectivity-preserving flocking algorithm to enable the multiple agents to move with the same velocity while preserving the connectivity of underlying networks with a mild assumption that the initial network is connected and the coupling strength of the initial network of the nonlinear velocity consensus term is larger than a threshold value. Furthermore the proposed flocking algorithm is extended to solve the problem of multi-agent systems with a nonlinear dynamical virtual leader. The result is that all agents' velocities asymptotically approach to the velocity of the virtual leader, and the distance between any two agents is asymptotically stabilized to avoid collisions among agents. Finally, some numerical simulations are presented to illustrate the effectiveness of the theoretical results.
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paper_title: Adaptive second-order consensus of networked mobile agents with nonlinear dynamics

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We investigate second-order consensus of multiple nonlinear dynamical mobile agents with a virtual leader in a dynamic proximity network. We assume that only a small fraction of agents in the group have access to the information about the position and velocity of the virtual leader through, for example, certain pre-designed communication mechanism such as wireless broadcasting or sensing. To avoid fragmentation, we propose a connectivity-preserving second-order consensus algorithm. Under the assumption that the initial network is connected, we introduce local adaptation strategies for both the weights on the velocity navigational feedback and the velocity coupling strengths that enable all agents to synchronize with the virtual leader even when only one agent is informed, without requiring any knowledge of the agent dynamics. We finally provide some convincing simulation results to illustrate the theoretical results.
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paper_title: Distributed, Physics-Based Control of Swarms of Vehicles

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We introduce a framework, called “physicomimetics,” that provides distributed control of large collections of mobile physical agents in sensor networks. The agents sense and react to virtual forces, which are motivated by natural physics laws. Thus, physicomimetics is founded upon solid scientific principles. Furthermore, this framework provides an effective basis for self-organization, fault-tolerance, and self-repair. Three primary factors distinguish our framework from others that are related: an emphasis on minimality (e.g., cost effectiveness of large numbers of agents implies a need for expendable platforms with few sensors), ease of implementation, and run-time efficiency. Examples are shown of how this framework has been applied to construct various regular geometric lattice configurations (distributed sensing grids), as well as dynamic behavior for perimeter defense and surveillance. Analyses are provided that facilitate system understanding and predictability, including both qualitative and quantitative analyses of potential energy and a system phase transition. Physicomimetics has been implemented both in simulation and on a team of seven mobile robots. Specifics of the robotic embodiment are presented in the paper.
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paper_title: Neural-Network-Based Adaptive Leader-Following Control for Multiagent Systems With Uncertainties

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A neural-network-based adaptive approach is proposed for the leader-following control of multiagent systems. The neural network is used to approximate the agent's uncertain dynamics, and the approximation error and external disturbances are counteracted by employing the robust signal. When there is no control input constraint, it can be proved that all the following agents can track the leader's time-varying state with the tracking error as small as desired. Compared with the related work in the literature, the uncertainty in the agent's dynamics is taken into account; the leader's state could be time-varying; and the proposed algorithm for each following agent is only dependent on the information of its neighbor agents. Finally, the satisfactory performance of the proposed method is illustrated by simulation examples.
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paper_title: On consensus algorithms for double-integrator dynamics without velocity measurements and with input constraints

paper_content:

This note deals with consensus strategy design for double-integrator dynamics. Specifically, we consider the case where the control inputs are required to be a priori bounded and the velocity (second state) is not available for feedback. Two different design methods are proposed. First, based on the auxiliary system approach, we propose a consensus algorithm that extends some of the existing results in the literature to account for actuator saturations and the lack of velocity measurement. The proposed velocity-free control scheme, using local information exchange, achieves consensus among the team members with an a priori bounded control law, whose upper bound depends on the number of neighbors of the vehicle. Second, we propose another approach based on the use of a high order dynamic auxiliary system such that the upper bound of the control law is independent of the number of neighbors of the vehicle, and the performance of the closed loop system is improved in terms of the response damping. Finally, simulation results are provided to illustrate the effectiveness of the proposed algorithms.
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paper_title: Decentralized Robust Adaptive Control for the Multiagent System Consensus Problem Using Neural Networks

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A robust adaptive control approach is proposed to solve the consensus problem of multiagent systems. Compared with the previous work, the agent's dynamics includes the uncertainties and external disturbances, which is more practical in real-world applications. Due to the approximation capability of neural networks, the uncertain dynamics is compensated by the adaptive neural network scheme. The effects of the approximation error and external disturbances are counteracted by employing the robustness signal. The proposed algorithm is decentralized because the controller for each agent only utilizes the information of its neighbor agents. By the theoretical analysis, it is proved that the consensus error can be reduced as small as desired. The proposed method is then extended to two cases: agents form a prescribed formation, and agents have the higher order dynamics. Finally, simulation examples are given to demonstrate the satisfactory performance of the proposed method.
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paper_title: Steering self-organized robot flocks through externally guided individuals

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In this paper, we study how a self-organized mobile robot flock can be steered toward a desired direction through externally guiding some of its members. Specifically, we propose a behavior by extending a previously developed flocking behavior to steer self-organized flocks in both physical and simulated mobile robots. We quantitatively measure the performance of the proposed behavior under different parameter settings using three metrics, namely, (1) the mutual information metric, adopted from Information Theory, to measure the information shared between the individuals during steering, (2) the accuracy metric from directional statistics to measure the angular deviation of the direction of the flock from the desired direction, and (3) the ratio of the largest aggregate to the whole flock and the ratio of informed individuals remaining with the largest aggregate, as a metric of flock cohesion. We conducted a systematic set of experiments using both physical and simulated robots, analyzed the transient and steady-state characteristics of steered flocking, and evaluate the parameter conditions under which a swarm can be successfully steered. We show that the experimental results are qualitatively in accordance with the ones that were predicted in Couzin et al. model (Nature, 433:513–516, 2005) and relate the quantitative differences to the differences between the models.
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paper_title: Second-order consensus in multi-agent dynamical systems with sampled position data

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This paper studies second-order consensus in multi-agent dynamical systems with sampled position data. A distributed linear consensus protocol with second-order dynamics is designed, where both the current and some sampled past position data are utilized. It is found that second-order consensus in such a multi-agent system cannot be reached without any sampled position data under the given protocol while it can be achieved by appropriately choosing the sampling period. A necessary and sufficient condition for reaching consensus of the system in this setting is established, based on which consensus regions are then characterized. It is shown that if all the eigenvalues of the Laplacian matrix are real, then second-order consensus in the multi-agent system can be reached for any sampling period except at some critical points depending on the spectrum of the Laplacian matrix. However, if there exists at least one eigenvalue of the Laplacian matrix with a nonzero imaginary part, second-order consensus cannot be reached for sufficiently small or sufficiently large sampling periods. In such cases, one nevertheless may be able to find some disconnected stable consensus regions determined by choosing appropriate sampling periods. Finally, simulation examples are given to verify and illustrate the theoretical analysis.
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paper_title: Spatially balanced topological interaction grants optimal cohesion in flocking models

paper_content:

Models of self-propelled particles (SPPs) are an indispensable tool to investigate collective animal behaviour. Originally, SPP models were proposed with metric interactions, where each individual coordinates with neighbours within a fixed metric radius. However, recent experiments on bird flocks indicate that interactions are topological: each individual interacts with a fixed number of neighbours, irrespective of their distance. It has been argued that topological interactions are more robust than metric ones against external perturbations, a significant evolutionary advantage for systems under constant predatory pressure. Here, we test this hypothesis by comparing the stability of metric versus topological SPP models in three dimensions. We show that topological models are more stable than metric ones. We also show that a significantly better stability is achieved when neighbours are selected according to a spatially balanced topological rule, namely when interacting neighbours are evenly distributed in angle around the focal individual. Finally, we find that the minimal number of interacting neighbours needed to achieve fully stable cohesion in a spatially balanced model is compatible with the value observed in field experiments on starling flocks.
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paper_title: A framework for the collective movement of mobile robots based on distributed decisions

paper_content:

Abstract A novel framework for the control of the collective movement of mobile robots is presented and analyzed in this article. It allows a group of robots to move as a unique entity performing the following functions: obstacle avoidance at group level, speed control and modification of the inter-robot distance. Its flocking controller is distributed among the robots, allowing them to move in the desired common direction and maintain a desired inter-robot distance. The framework is made up of different modules that modify the behavior of the group thus allowing different functions. They are based on consensus algorithms that allow the robots to agree on different parameters, taking into account which robot has more relevant information. New modules can be easily designed and incorporated into the framework in order to augment its capabilities. It can be easily implemented on any mobile robot capable of measuring the relative positions of neighboring robots and communicating with them. It has been successfully tested using 8 real robots and in simulation with up to 40 robots, demonstrating experimentally its scalability with an increasing number of robots.
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paper_title: Virtual leader approach to coordinated control of multiple mobile agents with asymmetric interactions

paper_content:

Abstract This paper considers the collective dynamics of a group of mobile autonomous agents moving in Euclidean space with a virtual leader. We introduce a set of coordination control laws that enable the group to generate the desired stable flocking motion. The control laws are a combination of attractive/repulsive and alignment forces, and the control law acting on each agent relies on the state information of its flockmates and the external reference signal (or “virtual leader”). Using the control laws, all agent velocities asymptotically approach the desired velocity, collisions can be avoided between the agents, and the final tight formation minimizes all agent global potentials. Moreover, we show that the velocity of the center of mass either is equal to the desired velocity or exponentially converges to it. Furthermore, when the velocity damping is taken into account, we can appropriately modify the control laws to generate the same stable flocking motion. Subsequently, for the case where not all agents know the desired common velocity, we show that the desired flocking motion can still be guaranteed. Numerical simulations are worked out to illustrate our theoretical results. Additionally, we consider the effect of white noise on the collective dynamics of the group, and demonstrate numerically that the desired flocking motion can be kept for weak noise and, as the noise intensity increases, the flocking motion can be destroyed.
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paper_title: Global Synchronization of Linearly Hybrid Coupled Networks with Time-Varying Delay

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Many real-world large-scale complex networks demonstrate a surprising degree of synchronization. To unravel the underlying mechanics of synchronization in these complex networks, a generally linearly hybrid coupled network with time-varying delay is proposed, and its global synchronization is then further investigated. Several effective sufficient conditions of global synchronization are attained based on the Lyapunov function and a linear matrix inequality (LMI). Both delay-independent and delay-dependent conditions are deduced. In particular, the coupling matrix may be nonsymmetric or nondiagonal. Moreover, the derivative of the time-varying delay is extended to any given value. Finally, a small-world network, a regular network, and scale-free networks with network size are constructed to show the effectiveness of the proposed synchronous criteria.
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paper_title: Adaptive flocking with a virtual leader of multiple agents governed by nonlinear dynamics

paper_content:

We investigate the flocking problem of multiple nonlinear dynamical mobile agents with a virtual leader in a dynamic proximity network. We assume that only a fraction of agents in the network are informed and propose a connectivity-preserving flocking algorithm. Under the assumption that the initial network is connected, we introduce local adaptation strategies for both the weights on the velocity navigational feedback and the coupling strengths that enable all agents to track the virtual leader, without requiring the knowledge of the agent dynamics. The resulting flocking algorithm works even for the case where only one agent is informed.
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paper_title: On pinning synchronization of complex dynamical networks

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There exist some fundamental and yet challenging problems in pinning control of complex networks: (1) What types of pinning schemes may be chosen for a given complex network to realize synchronization? (2) What kinds of controllers may be designed to ensure the network synchronization? (3) How large should the coupling strength be used in a given complex network to achieve synchronization? This paper addresses these technique questions. Surprisingly, it is found that a network under a typical framework can realize synchronization subject to any linear feedback pinning scheme by using adaptive tuning of the coupling strength. In addition, it is found that the nodes with low degrees should be pinned first when the coupling strength is small, which is contrary to the common view that the most-highly-connected nodes should be pinned first. Furthermore, it is interesting to find that the derived pinning condition with controllers given in a high-dimensional setting can be reduced to a low-dimensional condition without the pinning controllers involved. Finally, simulation examples of scale-free networks are given to verify the theoretical results.
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paper_title: Adaptive synchronization for delayed neural networks with stochastic perturbation

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In this paper, an adaptive feedback controller is designed to achieve complete synchronization of unidirectionally coupled delayed neural networks with stochastic perturbation. LaSalle-type invariance principle for stochastic differential delay equations is employed to investigate the globally almost surely asymptotical stability of the error dynamical system. An example and numerical simulation are given to demonstrate the effectiveness of the theory results.
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paper_title: Second-Order Consensus for Multiagent Systems With Directed Topologies and Nonlinear Dynamics

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This paper considers a second-order consensus problem for multiagent systems with nonlinear dynamics and directed topologies where each agent is governed by both position and velocity consensus terms with a time-varying asymptotic velocity. To describe the system's ability for reaching consensus, a new concept about the generalized algebraic connectivity is defined for strongly connected networks and then extended to the strongly connected components of the directed network containing a spanning tree. Some sufficient conditions are derived for reaching second-order consensus in multiagent systems with nonlinear dynamics based on algebraic graph theory, matrix theory, and Lyapunov control approach. Finally, simulation examples are given to verify the theoretical analysis.
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paper_title: Adaptive flocking with a virtual leader of multiple agents governed by locally Lipschitz nonlinearity

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Abstract This paper investigates adaptive flocking of multi-agent systems (MASs) with a virtual leader. All agents and the virtual leader share the same intrinsic nonlinear dynamics, which satisfies a locally Lipschitz condition and depends on both position and velocity information for the agent itself. Under the assumption that the initial network is connected, an approach to preserving the connectivity of the network is proposed. On the basis of the Lyapunov stability theory, an adaptive flocking control law is derived, for making the MASs track the virtual leader without collision. Finally, a numerical example is presented to illustrate the effectiveness of the theoretical results.
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paper_title: Velocity-free compact rigid flock control with input saturations

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It is often encountered in industrial multi-agent systems the unavailability of velocity sensors or the imprecise measurements of velocities. This work addresses the velocity-free flock control problem with input saturation. Using algebraic graph theory and Barbalat's Lemma, we prove that the algorithm guarantees the system to converge to a rigid flock behavior where all the agents in the group move with the same velocity. Moreover, the flock will converge to a prescribed tight formation which minimizes all agents' global potentials. Finally, the proposed flock control method are examined by numerical simulations to show its effectiveness.
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paper_title: Flocking and turning: a new model for self-organized collective motion

paper_content:

Birds in a flock move in a correlated way, resulting in large polarization of velocities. A good understanding of this collective behavior exists for linear motion of the flock. Yet observing actual birds, the center of mass of the group often turns giving rise to more complicated dynamics, still keeping strong polarization of the flock. Here we propose novel dynamical equations for the collective motion of polarized animal groups that account for correlated turning including solely social forces. We exploit rotational symmetries and conservation laws of the problem to formulate a theory in terms of generalized coordinates of motion for the velocity directions akin to a Hamiltonian formulation for rotations. We explicitly derive the correspondence between this formulation and the dynamics of the individual velocities, thus obtaining a new model of collective motion. In the appropriate overdamped limit we recover the well-known Vicsek model, which dissipates rotational information and does not allow for polarized turns. Although the new model has its most vivid success in describing turning groups, its dynamics is intrinsically different from previous ones in a wide dynamical regime, while reducing to the hydrodynamic description of Toner and Tu at very large length-scales. The derived framework is therefore general and it may describe the collective motion of any strongly polarized active matter system.
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paper_title: Flocking in Multi-agent Systems with a Bounded Control Input

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Recently, the broad applications of multi-agent systems in many areas have stimulated a great deal of interests in studying coordinated control problems. Previous flocking protocols do not consider the input saturation. In this paper, we investigate the flocking problem with a bounded control input. Under the assumption that the underlying network is connected, all agents can attain the same velocity vector, and distances between the agents are stabilized. Numerical simulations are worked out to illustrate theoretical results.
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paper_title: Distributed leader–follower flocking control for multi-agent dynamical systems with time-varying velocities

paper_content:

Using tools from algebraic graph theory and nonsmooth analysis in combination with ideas of collective potential functions, velocity consensus and navigation feedback, a distributed leader-follower flocking algorithm for multi-agent dynamical systems with time-varying velocities is developed where each agent is governed by second-order dynamics. The distributed leader-follower algorithm considers the case in which the group has one virtual leader with time-varying velocity. For each agent i, this algorithm consists of four terms: the first term is the self nonlinear dynamics which determines the final time-varying velocity, the second term is determined by the gradient of the collective potential between agent i and all of its neighbors, the third term is the velocity consensus term, and the fourth term is the navigation feedback from the leader. To avoid an impractical assumption that the informed agents sense all the states of the leader, the new designed distributed algorithm is developed by making use of observer-based pinning navigation feedback. In this case, each informed agent only has partial information about the leader, yet the velocity of the whole group can still converge to that of the leader and the centroid of those informed agents, having the leader's position information, follows the trajectory of the leader asymptotically. Finally, simulation results are presented to demonstrate the validity and effectiveness of the theoretical analysis. Surprisingly, it is found that the local minimum of the potential function may not form a commonly believed a lattice. (C) 2010 Elsevier B.V. All rights reserved.
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paper_title: Complex Networks: Topology, Dynamics and Synchronization

paper_content:

This report is a recompilation of the research done during my visit to FernUniversitat in Hagen from April 2005 to April 2006. It consists of a tutorial review of the background of Complex Dynamical Networks and some ideas set forward during this research period. The intension is for this manuscript to serve as a complement to the report for the DAAD Research Grant that I received to visit Germany and at the same time as a documental reference and background for future work. 1 Financially Supported by DAAD -Research Scholarship 2005-
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paper_title: On consensus algorithms design for double integrator dynamics

paper_content:

This paper considers the consensus problem of double integrator multi-agent systems where: (i) each agent is subject to input saturations, and (ii) the velocity (second state) of each agent is not available for feedback. We present new consensus algorithms that handle simultaneously the above mentioned situations. Sufficient conditions are derived such that consensus algorithms developed for first- and second-order multi-agent systems in ideal situations can be used to account for input saturations and remove the requirement of velocity measurements. To illustrate the effectiveness of the proposed approach, we propose solutions to two different second-order consensus problems in the case where the input is saturated and the velocity states are not available for feedback and simulation results are provided in each case.
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paper_title: Flocking with fixed-wing UAVs for distributed sensing: A stochastic optimal control approach

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This work focuses on enabling multiple UAVs to flock together in order to distribute and collectively perform a given sensing task. Flocking is performed in a leader-follower fashion, and the leader is assumed to already have an effective control policy for the particular task. The UAVs are small fixed-wing aircraft cruising at a constant speed and fixed altitude, but experience stochasticity in their dynamics. Accordingly, the control problem for each follower is addressed in the context of stochastic optimal control, wherein the cost is a function of distance and heading with respect to the leader. The problem is solved offline via dynamic programming to minimize the expected cost over a finite horizon and generate a receding horizon optimal control policy. This flocking algorithm was successfully applied in the field, where three camera-equipped UAVs flocked together to perform vision-based target tracking. The experimental results verify the efficacy of the approach and show the benefits of flocking with multiple UAVs to distribute sensing tasks, which include a dramatic reduction in overall sensing error and robustness to individual sensor faults.
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paper_title: Flocking of multi-agents with a virtual leader part I: with a minority of informed agents

paper_content:

All agents being informed and the virtual leader traveling at a constant velocity are the two critical assumptions seen in the recent literature on flocking in multi-agent systems. Under these assumptions, Olfati-Saber in a recent IEEE Transactions on Automatic Control paper proposed a flocking algorithm which by incorporating a navigational feedback enables a group of agents to track a virtual leader. This paper revisits the problem of multi-agent flocking in the absence of the above two assumptions. In particular, in Part I, we show that, even when only a fraction of agents are informed, the Olfati-Saber flocking algorithm still enables all the informed agents to move with the desired constant velocity, and an uninformed agent to also move with the same desired velocity if it can be directly or indirectly influenced by the informed agents during the evolution. Numerical simulation demonstrates that a very small group of the informed agents can cause most of the agents to move with the desired velocity and the larger the informed group is the bigger portion of agents will move with the desired velocity. In Part II, we will address the situation when the virtual leader travels at a varying velocity.
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paper_title: Coordinated Control of Multi-Agent Systems with a Varying-Velocity Leader and Input Saturation

paper_content:

In this paper, we investigate a leader-following tracking problem for multi-agent systems with bounded inputs. We propose a distributed bounded protocol for each follower to track a leader whose states may not be completely measured. We theoretically prove that each agent can follow the leader with estimable track errors. Finally, some numerical simulations are presented to illustrate our theoretical results.
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paper_title: Consensus of heterogeneous multi-agent systems without velocity measurements

paper_content:

This article considers the consensus problem of heterogeneous multi-agent system composed of first-order and second-order agents, in which the second-order integrator agents cannot obtain the velocity (second state) measurements for feedback. Two different consensus protocols are proposed. First, we propose a consensus protocol and discuss the consensus problem of heterogeneous multi-agent system. By applying the graph theory and the Lyapunov direct method, some sufficient conditions for consensus are established when the communication topologies are undirected connected graphs and leader-following networks. Second, due to actuator saturation, we propose another consensus protocol with input constraint and obtain the consensus criterions for heterogeneous multi-agent system. Finally, some examples are presented to illustrate the effectiveness of the obtained criterions.
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paper_title: Flocking of multi-agents with a virtual leader part II: with a virtual leader of varying velocity

paper_content:

All agents being informed and the virtual leader traveling at a constant velocity are the two critical assumptions seen in the recent literature on flocking in multi-agent systems. Under these assumptions, Olfati-Saber in a recent IEEE Transactions on Automatic Control paper proposed a flocking algorithm which by incorporating a navigational feedback enables a group of agents to track a virtual leader. This paper revisits the problem of multi-agent flocking in the absence of the above two assumptions. In an earlier part, Part I, of this paper, we showed that, even when only a fraction of agents are informed, the Olfati-Saber flocking algorithm still enables all the informed agents to move with the desired constant velocity, and an uninformed agent to also move with the same desired velocity if it can be directly or indirectly influenced by the informed agents during the evolution. This part, Part II, of the paper considers the situation where the virtual leader travels with a varying velocity. In particular, we propose modification to the Olfati-Saber algorithm and show that the resulting algorithm enables the asymptotic tracking of the virtual leader. That is, the position and velocity of the center of mass of all agents will converge exponentially to those of the virtual leader. The convergent rate is also given.
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paper_title: 1 Flocking of Multi-agent Dynamical Systems Based on Pseudo-leader Mechanism

paper_content:

Flocking behavior of multiple agents can be widely observed in nature such as schooling fish and flocking birds. Recent literature has proposed the possibility that flocking is possible even only a small fraction of agents are informed of the desired position and velocity. However, it is still a challenging problem to determine which agents should be informed or have the ability to detect the desired information. This paper aims to address this problem. By combining the ideas of virtual force and pseudo-leader mechanism, where a pseudo-leader represents an agent who can detect the desired information, we propose a scheme for choosing pseudo-leaders in a multi-agent group. The presented scheme can be applied to a multi-agent group even with an unconnected or switching neighbor graph. Experiments are given to show that the methods presented in this paper are of high accuracy and perform well.
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paper_title: A Connectivity-preserving flocking algorithm for multi-agent dynamical systems with bounded potential function

paper_content:

Without assuming that the communication topology can remain its connectivity frequently enough and the potential function can provide an infinite force during the evolution of agents, the flocking problem of multi-agent systems with second-order non-linear dynamics is investigated in this study. By combining the ideas of collective potential functions and velocity consensus, a connectivity-preserving flocking algorithm with bounded potential function is proposed. Using tools from the algebraic graph theory and matrix analysis, it is proved that the designed algorithm can guarantee the group of multiple agents to asymptotically move with the same velocity while preserving the network connectivity if the coupling strength of the velocity consensus term is larger than a threshold value. Furthermore, the flocking algorithm is extended to solve the flocking problem of multi-agent systems with a dynamical virtual leader by adding a navigation feedback term. In this case, each informed agent only has partial velocity information about the leader, yet the present algorithm not only can guarantee the velocity of the whole group to track that of the leader asymptotically, and also can preserve the network connectivity. Finally, some numerical simulations are provided to illustrate the theoretical results.
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paper_title: Exploring the Split and Join Capabilities of a Robotic Collective Movement Framework

paper_content:

The splitting and joining capabilities of a previously designed framework for the collective movement of mobile robots are studied. This framework is implemented in a distributed manner among the robots and allows scalability with increasing number of robots. It is expandable with new functionalities through the inclusion of new modules. Splitting functionality is created by including a new module, while joining does not need new structures. A total of 130 systematic experiments, grouped in six different sets, were undertaken to test the splitting and joining functions of the framework, yielding results in which robots behaved as expected. Four of the sets correspond to experiments in simulation using up to 40 robots. The remaining sets use eight real robots.
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paper_title: Flocking of multiple autonomous agents with preserved network connectivity and heterogeneous nonlinear dynamics

paper_content:

Abstract This paper investigates a flocking problem of multiple agents with heterogeneous nonlinear dynamics. In order to avoid fragmentation, we construct a potential function and a connectivity-preserving flocking algorithm to enable the multiple agents to move with the same velocity while preserving the connectivity of underlying networks with a mild assumption that the initial network is connected and the coupling strength of the initial network of the nonlinear velocity consensus term is larger than a threshold value. Furthermore the proposed flocking algorithm is extended to solve the problem of multi-agent systems with a nonlinear dynamical virtual leader. The result is that all agents' velocities asymptotically approach to the velocity of the virtual leader, and the distance between any two agents is asymptotically stabilized to avoid collisions among agents. Finally, some numerical simulations are presented to illustrate the effectiveness of the theoretical results.
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paper_title: Flocks, herds and schools: A distributed behavioral model

paper_content:

The aggregate motion of a flock of birds, a herd of land animals, or a school of fish is a beautiful and familiar part of the natural world. But this type of complex motion is rarely seen in computer animation. This paper explores an approach based on simulation as an alternative to scripting the paths of each bird individually. The simulated flock is an elaboration of a particle systems, with the simulated birds being the particles. The aggregate motion of the simulated flock is created by a distributed behavioral model much like that at work in a natural flock; the birds choose their own course. Each simulated bird is implemented as an independent actor that navigates according to its local perception of the dynamic environment, the laws of simulated physics that rule its motion, and a set of behaviors programmed into it by the "animator." The aggregate motion of the simulated flock is the result of the dense interaction of the relatively simple behaviors of the individual simulated birds.
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paper_title: Steering self-organized robot flocks through externally guided individuals

paper_content:

In this paper, we study how a self-organized mobile robot flock can be steered toward a desired direction through externally guiding some of its members. Specifically, we propose a behavior by extending a previously developed flocking behavior to steer self-organized flocks in both physical and simulated mobile robots. We quantitatively measure the performance of the proposed behavior under different parameter settings using three metrics, namely, (1) the mutual information metric, adopted from Information Theory, to measure the information shared between the individuals during steering, (2) the accuracy metric from directional statistics to measure the angular deviation of the direction of the flock from the desired direction, and (3) the ratio of the largest aggregate to the whole flock and the ratio of informed individuals remaining with the largest aggregate, as a metric of flock cohesion. We conducted a systematic set of experiments using both physical and simulated robots, analyzed the transient and steady-state characteristics of steered flocking, and evaluate the parameter conditions under which a swarm can be successfully steered. We show that the experimental results are qualitatively in accordance with the ones that were predicted in Couzin et al. model (Nature, 433:513–516, 2005) and relate the quantitative differences to the differences between the models.
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paper_title: Self-organized Flocking with Conflicting Goal Directions

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In flocking, a large number of individuals move cohesively in a common direction. Many examples can be found in nature: from simple organisms such as crickets and locusts to more complex ones such as birds, fish and quadrupeds. In this paper, we study the flocking behavior of a swarm of robots where information about two distinct goal directions is present in the swarm. In general, we can identify three different macroscopic objectives that we might want to attain: (a) a swarm that moves to the average direction among the two (for example to avoid the obstacle) without splitting; (b) a swarm that selects the most important of the two directions (for example the direction to avoid danger) and follows it without splitting; (c) a swarm that splits in a controlled fashion in the two directions (for example, in the parallel task execution case). This paper proposes a solution for the first objective: a method for moving the swarm along the average between the two conflicting goal directions. We show that this objective can be attained by simply using a similar methodology as the one proposed in earlier work. We execute systematic experiments using a realistic robotics simulator. In the experiments, a small proportion of robots is informed about one goal direction, another small proportion about the other goal direction, and the rest of the swarm is non-informed. We study the effect of what we believe are the critical parameters: the overall proportion of informed robots, the difference between the size of the two groups of informed robots and the difference between the two goal direction. We show that, using the proposed method, the system is always able to follow the average direction between the two.
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paper_title: ARGoS: a modular, parallel, multi-engine simulator for multi-robot systems

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We present a novel multi-robot simulator named ARGoS. ARGoS is designed to simulate complex experiments involving large swarms of robots of different types. ARGoS is the first multi-robot simulator that is at the same time both efficient (fast performance with many robots) and flexible (highly customizable for specific experiments). Novel design choices in ARGoS have enabled this breakthrough. First, in ARGoS, it is possible to partition the simulated space into multiple sub-spaces, managed by different physics engines running in parallel. Second, ARGoS’ architecture is multi-threaded, thus designed to optimize the usage of modern multi-core CPUs. Finally, the architecture of ARGoS is highly modular, enabling easy addition of custom features and appropriate allocation of computational resources. We assess the efficiency of ARGoS and showcase its flexibility with targeted experiments. Experimental results demonstrate that simulation run-time increases linearly with the number of robots. A 2D-dynamics simulation of 10,000 e-puck robots can be performed in 60 % of the time taken by the corresponding real-world experiment. We show how ARGoS can be extended to suit the needs of an experiment in which custom functionality is necessary to achieve sufficient simulation accuracy. ARGoS is open source software licensed under GPL3 and is downloadable free of charge.
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paper_title: A framework for the collective movement of mobile robots based on distributed decisions

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Abstract A novel framework for the control of the collective movement of mobile robots is presented and analyzed in this article. It allows a group of robots to move as a unique entity performing the following functions: obstacle avoidance at group level, speed control and modification of the inter-robot distance. Its flocking controller is distributed among the robots, allowing them to move in the desired common direction and maintain a desired inter-robot distance. The framework is made up of different modules that modify the behavior of the group thus allowing different functions. They are based on consensus algorithms that allow the robots to agree on different parameters, taking into account which robot has more relevant information. New modules can be easily designed and incorporated into the framework in order to augment its capabilities. It can be easily implemented on any mobile robot capable of measuring the relative positions of neighboring robots and communicating with them. It has been successfully tested using 8 real robots and in simulation with up to 40 robots, demonstrating experimentally its scalability with an increasing number of robots.
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paper_title: Outdoor flocking and formation flight with autonomous aerial robots

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We present the first decentralized multi-copter flock that performs stable autonomous outdoor flight with up to 10 flying agents. By decentralized and autonomous we mean that all members navigate themselves based on the dynamic information received from other robots in the vicinity. We do not use central data processing or control; instead, all the necessary computations are carried out by miniature on-board computers. The only global information the system exploits is from GPS receivers, while the units use wireless modules to share this positional information with other flock members locally. Collective behavior is based on a decentralized control framework with bio-inspiration from statistical physical modelling of animal swarms. In addition, the model is optimized for stable group flight even in a noisy, windy, delayed and error-prone environment. Using this framework we successfully implemented several fundamental collective flight tasks with up to 10 units: i) we achieved self-propelled flocking in a bounded area with self-organized object avoidance capabilities and ii) performed collective target tracking with stable formation flights (grid, rotating ring, straight line). With realistic numerical simulations we demonstrated that the local broadcast-type communication and the decentralized autonomous control method allows for the scalability of the model for much larger flocks.
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paper_title: Distributed coordination of a formation of heterogeneous agents with individual regrets and asynchronous communications

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We consider a flotilla composed of N autonomous mobile agents. Each agent ignores its absolute position but collects noisy measurements of the relative position of other agents. It has a convex utility function which depends on its control variables and on some global variables, typically, the average motion of all agents during a unit of time. The utility function of an agent is unknown by other agents. The aim is to determine the control variables which minimize the sum of all utility functions. The minimization is subject to constraints: speed limitations, collision avoidance and maintenance of the flock. We provide sufficient convex and separable conditions which guarantee that constraints are satisfied. These conditions allow to search for a minimizer of the aggregate utility function in a distributed fashion. The proposed algorithm simultaneously involves a gradient descent locally performed by the agents and a random gossip step which allows to find an agreement on the global motion strategy. In the case when there is a large number of transmissions during each unit of time, the algorithm is proved to converge almost surely to the desired minimizer, under mild conditions on the gossip protocol. When transmissions become less frequent, the minimization problem is no longer likely to be solved exactly. However, we propose an adaptive algorithm capable of tracking the minimizer. Its behavior is characterized through detailed simulations.
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paper_title: Flooding in wireless ad hoc networks

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In an ad hoc network, each host assumes the role of a router and relays packets toward final destinations. This paper studies efficient routing mechanisms for packet flooding in ad hoc wireless networks. Because a packet is broadcast to all neighboring nodes, the optimality criteria of wireless network routing are different from that of the wired network routing. We show that the minimum cost flooding tree problem is similar to MCDS (Minimum Connected Dominating Set) problem and prove the NP-completeness of the minimum cost flooding tree problem. Then, we propose two flooding methods: self-pruning and dominant pruning. Both methods utilize the neighbor information to reduce redundant transmissions. Performance analysis shows that both methods perform significantly better than the blind flooding. Especially, dominant pruning performs close to the practically achievable best performance limit.
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paper_title: Quadrotor Using Minimal Sensing For Autonomous Indoor Flight

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This paper presents a Miniature Aerial Vehicle (MAV) capable of hands- off autonomous operation within indoor environments. Our prototype is a Quadrotor weighing approximately 600g, with a diameter of 550mm, which carries the necessary electronics for stability control, altitude control, collision avoidance and anti-drift control. This MAV is equipped with three rate gyroscopes, three accelerometers, one ultrasonic sensor, four infrared sensors, a high-speed motor controller and a flight computer. Autonomous flight tests have been carried out in a 7x6-m room.
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paper_title: Flocking and turning: a new model for self-organized collective motion

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Birds in a flock move in a correlated way, resulting in large polarization of velocities. A good understanding of this collective behavior exists for linear motion of the flock. Yet observing actual birds, the center of mass of the group often turns giving rise to more complicated dynamics, still keeping strong polarization of the flock. Here we propose novel dynamical equations for the collective motion of polarized animal groups that account for correlated turning including solely social forces. We exploit rotational symmetries and conservation laws of the problem to formulate a theory in terms of generalized coordinates of motion for the velocity directions akin to a Hamiltonian formulation for rotations. We explicitly derive the correspondence between this formulation and the dynamics of the individual velocities, thus obtaining a new model of collective motion. In the appropriate overdamped limit we recover the well-known Vicsek model, which dissipates rotational information and does not allow for polarized turns. Although the new model has its most vivid success in describing turning groups, its dynamics is intrinsically different from previous ones in a wide dynamical regime, while reducing to the hydrodynamic description of Toner and Tu at very large length-scales. The derived framework is therefore general and it may describe the collective motion of any strongly polarized active matter system.
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paper_title: Flocking algorithm for autonomous flying robots

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Animal swarms displaying a variety of typical flocking patterns would not exist without the underlying safe, optimal and stable dynamics of the individuals. The emergence of these universal patterns can be efficiently reconstructed with agent-based models. If we want to reproduce these patterns with artificial systems, such as autonomous aerial robots, agent-based models can also be used in their control algorithms. However, finding the proper algorithms and thus understanding the essential characteristics of the emergent collective behaviour requires thorough and realistic modeling of the robot and also the environment. In this paper, we first present an abstract mathematical model of an autonomous flying robot. The model takes into account several realistic features, such as time delay and locality of communication, inaccuracy of the on-board sensors and inertial effects. We present two decentralized control algorithms. One is based on a simple self-propelled flocking model of animal collective motion, the other is a collective target tracking algorithm. Both algorithms contain a viscous friction-like term, which aligns the velocities of neighbouring agents parallel to each other. We show that this term can be essential for reducing the inherent instabilities of such a noisy and delayed realistic system. We discuss simulation results on the stability of the control algorithms, and perform real experiments to show the applicability of the algorithms on a group of autonomous quadcopters. In our case, bio-inspiration works in two ways. On the one hand, the whole idea of trying to build and control a swarm of robots comes from the observation that birds tend to flock to optimize their behaviour as a group. On the other hand, by using a realistic simulation framework and studying the group behaviour of autonomous robots we can learn about the major factors influencing the flight of bird flocks.
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paper_title: The Hand-Bot, a Robot Design for Simultaneous Climbing and Manipulation

paper_content:

We present a novel approach to mobile object manipulation for service in indoor environments. Current research in service robotics focus on single robots able to move, manipulate objects, and transport them to various locations. Our approach differs by taking a collective robotics perspective: different types of small robots perform different tasks and exploit complementarity by collaborating together. We propose a robot design to solve one of these tasks: climbing vertical structures and manipulating objects. Our robot embeds two manipulators that can grasp both objects or structures. To help climbing, it uses a rope to compensate for the gravity force. This allows it to free one of its manipulators to interact with an object while the other grasps a part of a structure for stabilization. Our robot can launch and retrieve the rope autonomously, allowing multiple ascents. We show the design and the implementation of our robot and demonstrate the successful autonomous retrieval of a book from a shelf.
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paper_title: The marXbot, a miniature mobile robot opening new perspectives for the collective-robotic research

paper_content:

Collective and swarm robotics explores scenarios involving many robots running at the same time. A good platform for collective-robotic experiments should provide certain features among others: it should have a large battery life, it should be able to perceive its peers, and it should be capable of interacting with them. This paper presents the marXbot, a miniature mobile robot that addresses these needs. The marXbot uses differential-drive treels to provide rough-terrain mobility. The marXbot allows continuous experiments thanks to a sophisticated energy management and a hotswap battery exchange mechanism. The marXbot can self-assemble with peers using a compliant attachment mechanism. The marXbot provides high-quality vision, using two cameras directly interfaced with an ARM processor. Compared to the related work, the marXbot has better energy management, vision, and interaction capabilities. By allowing complex tasks in large environments for long durations, the marXbot opens new perspectives for the collective-robotic research.
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paper_title: Consensus of heterogeneous multi-agent systems without velocity measurements

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This article considers the consensus problem of heterogeneous multi-agent system composed of first-order and second-order agents, in which the second-order integrator agents cannot obtain the velocity (second state) measurements for feedback. Two different consensus protocols are proposed. First, we propose a consensus protocol and discuss the consensus problem of heterogeneous multi-agent system. By applying the graph theory and the Lyapunov direct method, some sufficient conditions for consensus are established when the communication topologies are undirected connected graphs and leader-following networks. Second, due to actuator saturation, we propose another consensus protocol with input constraint and obtain the consensus criterions for heterogeneous multi-agent system. Finally, some examples are presented to illustrate the effectiveness of the obtained criterions.
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paper_title: Exploring the Split and Join Capabilities of a Robotic Collective Movement Framework

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The splitting and joining capabilities of a previously designed framework for the collective movement of mobile robots are studied. This framework is implemented in a distributed manner among the robots and allows scalability with increasing number of robots. It is expandable with new functionalities through the inclusion of new modules. Splitting functionality is created by including a new module, while joining does not need new structures. A total of 130 systematic experiments, grouped in six different sets, were undertaken to test the splitting and joining functions of the framework, yielding results in which robots behaved as expected. Four of the sets correspond to experiments in simulation using up to 40 robots. The remaining sets use eight real robots.
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paper_title: The e-puck, a robot designed for education in engineering

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Mobile robots have the potential to become the ideal tool to teach a broad range of engineering disciplines. Indeed, mobile robots are getting increasingly complex and accessible. They embed elements from diverse ﬁelds such as mechanics, digital electronics, automatic control, signal processing, embedded programming, and energy management. Moreover, they are attractive for students which increases their motivation to learn. However, the requirements of an effective education tool bring new constraints to robotics. This article presents the e-puck robot design, which specifically targets engineering education at university level. Thanks to its particular design, the e-puck can be used in a large spectrum of teaching activities, not strictly related to robotics. Through a systematic evaluation by the students, we show that the e-puck ﬁts this purpose and is appreciated by 90 percent of a large sample of students.
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paper_title: WebotsTM: Professional Mobile Robot Simulation

paper_content:

Cyberbotics Ltd. develops WebotsTM, a mobile robotics simulation software that provides you with a rapid prototyping environment for modelling, programming and simulating mobile robots. The provided robot libraries enable you to transfer your control programs to several commercially available real mobile robots. WebotsTM lets you define and modify a complete mobile robotics setup, even several different robots sharing the same environment. For each object, you can define a number of properties, such as shape, color, texture, mass, friction, etc. You can equip each robot with a large number of available sensors and actuators. You can program these robots using your favorite development environment, simulate them and optionally transfer the resulting programs onto your real robots. WebotsTM has been developed in collaboration with the Swiss Federal Institute of Technology in Lausanne, thoroughly tested, well documented and continuously maintained for over 7 years. It is now the main commercial product available from Cyberbotics Ltd.
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Title: Application of Collective Movement in Real Life Scenarios: Overview of Current Flocking Solutions

Section 1: Introduction
Description 1: Provide background information on collective movement and the importance of flocking algorithms in real-life scenarios.

Section 2: The Examined Properties of Flocking Solutions
Description 2: Discuss the criteria used to analyze and evaluate flocking algorithms, emphasizing the environmental models and constraints that impact their applicability in real-world scenarios.

Section 3: Control Mechanisms for Flocking
Description 3: Detail the various control mechanisms used in flocking algorithms, such as unit-centre referenced, neighbour-referenced, and leader-follower models, and their implications for real-life applications.

Section 4: Physical Models for Flocking Algorithms
Description 4: Examine the different physical models used in flocking algorithms, ranging from simple linear models to more complex nonlinear models that account for real-world dynamics and external disturbances.

Section 5: Communication Between the Nodes
Description 5: Describe the communication methods used in flocking algorithms, including passive and active communication, and discuss the challenges presented by real-world wireless communication environments.

Section 6: Closer to Real Life: Simulation and Demonstration of Flocking Systems
Description 6: Review the existing simulators and physical experiments conducted to test flocking algorithms, analyzing their effectiveness and limitations in replicating real-life conditions.

Section 7: Conclusion
Description 7: Summarize the findings of the survey, highlighting the current state of flocking algorithms, their limitations, and the areas requiring further research to enhance their practical applicability.