This paper presents a distributed model predictive control (DMPC) approach for a virtually coupled train set (VCTS) with communication delays. Specifically, we stabilize the real-time states of VCTS and guarantee the satisfaction of safety constraints in automatic train protection systems with delayed states, which fills the gap in the existing literature. First, using the predicted trajectories at previous instants, the real-time states of VCTS are estimated from delayed states obtained through communication. Then, compatibility constraints are designed to regulate predicted control inputs, such that the error between the predicted and actual trajectories in the prediction horizon can be confined in a sequence of sets. Next, linear matrix inequalities are derived to tune cost functions, terminal sets and terminal controllers, which guarantee the stability and recursive feasibility of DMPC. Finally, experimental results demonstrate the performance of our approach in both cruising and speed-varying operations. The minimal spacing policies are evaluated with different communication delays and parameters in DMPC based on our mathematical designs.

In this article, a class of distributed nonlinear placement problems is considered for a multicluster system. The task is to determine the positions of the agents in each cluster subject to the constraints on agent positions and the network topology. In particular, the agents in each cluster are placed to form the desired shape and minimize the sum of squares of the Euclidean lengths of the links amongst the center of each cluster and its corresponding cluster members. The problem is converted into a time-varying noncooperative game and then a distributed Nash equilibrium-seeking algorithm is designed based on a distributed observer method. A new iterative approach is employed to prove the convergence with the aid of the Lyapunov stability theorem. The effectiveness of the distributed algorithm is validated by numerical examples.

This article considers the distributed time-varying optimal resource allocation problem with time-varying quadratic cost functions and a time-varying coupled equality constraint for multiagent systems. The objective is to design a distributed algorithm for agents with single-integrator dynamics to cooperatively satisfy the coupled equality constraint and minimize the sum of all local cost functions. Here, both the coupled equality constraint and cost functions depend explicitly on time. The cost functions are in quadratic form and may have nonidentical time-varying Hessians. To solve the problem in a distributed manner, an estimator based on the distributed average tracking method is first developed for each agent to estimate certain global information. By leveraging the estimated global information and an adaptive gain scheme, a distributed continuous-time algorithm is proposed, which ensures the agents to find and track the time-varying optimal trajectories with vanishing errors. We illustrate the applicability of the proposed method in the optimal hose transportation problem using multiple quadrotors.

This paper studies the problem of multi-robot cooperative visual-inertial localization where each robot is equipped with only a single camera and IMU. We develop two cooperative visual-inertial odometry (C-VIO) algorithms within the multi-state constraint Kalman filter (MSCKF) framework, in which each robot utilizes not only its own measurements but constraints of common features co-observed with its neighbors within the current sliding window in order to improve the localization accuracy. The first centralized-equivalent algorithm tracks the robot-to-robot cross correlations and prioritizes the pose accuracy while requiring full capacity communication among all the robots during update. The second distributed algorithm ignores the robot-to-robot cross correlations to obtain a scalable, robust and efficient fully distributed structure where each robot only keeps its own states and communicates with its neighbors, while a covariance intersection (CI)-based update strategy is leveraged to guarantee consistency. The proposed algorithms are validated extensively in both Monte-Carlo simulations and real-world datasets, and shown to be able to achieve better accuracy with competitive efficiency.

In this paper we present a consistent and distributed state estimator for multi-robot cooperative localization (CL) which efficiently fuses environmental features and loop-closure constraints across time and robots. In particular, we leverage covariance intersection (CI) to allow each robot to only estimate its own state and autocovariance and compensate for the unknown correlations between robots. Two novel multi-robot methods for utilizing common environmental SLAM features are introduced and evaluated in terms of accuracy and efficiency. Moreover, we adapt CI to enable drift-free estimation through the use of loop-closure measurement constraints to other robots’ historical poses without a significant increase in computational cost. The proposed distributed CL estimator is validated against its non-realtime centralized counterpart extensively in both simulations and real-world experiments.

This paper addresses the mean-square leader-follower consensus problem for the multiagent Markov jump linear systems. The leader has the general linear dynamics while the followers are subject to parameter changes modeled by Markov jump. By using the output measurement of the leader, two types of observers, namely, the common observer and the distributed adaptive observer, are first constructed together to estimate the leader state. Then based on the estimated state and the follower self information, two kinds of controllers, namely, the synchronous controller and the asynchronous controller, are designed to achieve the mean-square leader-follower consensus. Finally, the simulation results are given to illustrate the feasibility and effectiveness of the proposed approaches.

This paper focuses on studying the differentially private consensus problem in multiagent networks under a quantized communication environment, where the exact real-value state is not available for transmission due to the range limitation of digital channels. We first extend the differentially private consensus model to the case of a quantized communication environment integrated with a dynamic encoding/decoding scheme and propose a differentially private communication algorithm utilizing the quantized state with a bounded quantizer instead of the exact real-value state to reach an agreement while protecting the initial or current states of the participants from information disclosure. Then, the convergence analysis of mean square consensus in the case of an unbounded quantizer is given to explain the sufficiency of the extended model and convergence conditions. To overcome the uncertainty of saturation in the case of a bounded quantizer, we also give a statistical analysis on the boundedness of quantization that the bounded quantizer with a finite number of bits can remain unsaturated with a desired high probability under certain conditions. Furthermore, we provide the statistical analysis on the convergent accuracy, which shows that the agreement value just converges to a random variable that falls in the neighboring range of the initial state average and the expectation of the agreement value is equal to the initial state average exactly. In addition, we provide the differential privacy analysis for individual agents and the whole network, and then establish the potential relationship between the dynamic encoding/decoding scheme and the differential privacy mechanism. Finally, the simulation results visually show that the proposed algorithm and the main theoretical results are effective and correct.

This article focuses on the fault-tolerant constrained consensus problem for multiagent systems with communication delays. The communication graphs are first assumed to be directed and fixed. Then, a novel delay-dependent fault-tolerant controller is designed such that, in the presence of communication delays and randomly occurring actuator failures, the influence of the projections and the initial states on the closed-loop system can be attenuated with a prespecified level. Based on the provided performance requirement, the initial state of each agent does not need to be identical. The proposed control algorithms ensure that sufficient conditions are met for the fault-tolerant constrained consensus to be achieved according to the prespecified performance index. After this, the controller gains are computed by employing an iterative linear matrix inequality scheme. Finally, a numerical example is provided to show the effectiveness of the proposed method.

In this paper, the finite-time output consensus problem is considered for a class of second-order multiagent systems (MASs), where the mismatched disturbance exists in the dynamics of each agent, and the communication topology is directed. First of all, a basic backstepping control protocol is proposed to solve the finite-time consensus problem without mismatched disturbance. Then, a finite-time disturbance observer is designed to estimate the mismatched disturbance, based on which, two adaptive finite-time consensus protocols are proposed to solve the finite-time output consensus and tracking consensus problems without using any global information with respect to the communication topology. Finally, two simulation examples are illustrated to verify the theoretical results.

In this paper, the containment problem with nonconvex velocity constraints is studied for second-order discrete-time multiagent systems. A distributed projection-based algorithm is proposed for all followers to be gathered in the convex area formed by multiple stationary leaders. It is revealed that the algorithm can solve the velocity-constrained containment problem with communication delays and switching networks provided that each follower has at least a directed path from some leaders to itself in the union of graphs. The main analysis approaches include model transformation techniques, Lyapunov function, and convexity analysis. A simulation example is also included to elucidate the obtained result.

This paper investigates the resource allocation problem for a group of agents communicating over a strongly connected directed graph, where the total objective function of the problem is composted of the sum of the local objective functions incurred by the agents. With local convex sets, we first design a continuous-time projection algorithm over a strongly connected and weight-balanced directed graph. Our convergence analysis indicates that when the local objective functions are strongly convex, the output state of the projection algorithm could asymptotically converge to the optimal solution of the resource allocation problem. In particular, when the projection operation is not involved, we show the exponential convergence at the equilibrium point of the algorithm. Second, we propose an adaptive continuous-time gradient algorithm over a strongly connected and weight-unbalanced directed graph for the reduced case without local convex sets. In this case, we prove that the adaptive algorithm converges exponentially to the optimal solution of the considered problem, where the local objective functions and their gradients satisfy strong convexity and Lipachitz conditions, respectively. Numerical simulations illustrate the performance of our algorithms.

In this paper, we present a novel distributed algorithm to track a moving object's state by utilizing a heterogenous mobile robot network in a three-dimensional (3-D) environment, wherein the robots' poses (positions and orientations) are unknown. Each robot is equipped with a monocular camera and an inertial measurement unit (IMU), and has the ability to communicate with its neighbors. Rather than assuming a known common global frame for all the robots (which is often the case in the literature regarding multi-robot systems), we allow each robot to perform motion estimation locally. For localization, we propose a multi-robot visual-inertial navigation systems (VINS) where one robot builds a prior map and then the map is used to bound the long-term drifts of the visual-inertial odometry (VIO) running on the other robots. Moreover, a novel distributed Kalman filter is introduced and employed to cooperatively track the six degree-of-freedom (6-DoF) motion of the object which is represented as a point cloud. Further, the object can be totally invisible to some robots during the tracking period. The proposed algorithm is extensively validated in Monte-Carlo simulations.

This paper investigates the H∞ output consensus problem for multiagent systems with Markov jump and external disturbance in both continuous-time and discrete-time domains. The communication network is directed and fixed with uncertainties. Based on the hidden Markov model, an output feedback controller is constructed. Then, the original system is transformed into a reduced-order system, which features the error dynamics. By using a Lyapunov function, sufficient conditions are developed to ensure that all agents can reach the consensus with the desired H∞ performance in the mean-square sense. Finally, simulation results are presented to illustrate the efficiency of the proposed approaches.

The objective of this paper is to design the protocols with a final consensus value and settling time estimations for finite-time consensus of multiagent systems. A couple of new edge-based protocols are developed for multiple second-order nonlinear agents under bounded or Lipschitz-type nonlinear functions, respectively. The final consensus value of the multiagent system is obtained as an average expression. Further, to obtain the estimation of the finite settling time, a special Lyapunov function is constructed. Through the construction processes, both the final consensus value and the settling time are obtained. Finally, as applications, a finite-time formation controller based on the first protocol is designed for multiple mini-spacecraft, verified by simulations.

This paper presents some necessary and sufficient conditions for the synchronization of second-order interconnected networks, where fixed inner-linked connections with information communication exist. First, a novel derivation of the conditions for a second-order polynomial with complex coefficients to be Hurwitz is provided. Based on this, a sufficient and necessary condition is proposed for the synchronization of the coupled complex network. Next, the design method of the synchronization protocol is constructively given, where the upper and lower bounds of the control gains are obtained through the properties of the polynomial. In addition, we consider some special cases where the second-order model is a double integrator, or general multiagent model without fixed interactions. Finally, the simulation result is given to verify the theoretical analysis.

This paper presents both algorithms and experimental results to solve a distributed rendezvous problem with shortest distance to convex regions. In a multiagent network, each agent is assigned to a certain convex region and has information about only its own region. All these regions might not have an intersection. Through local interaction with their neighbors, multiple agents collectively rendezvous at an optimal location that is a priori unknown to each agent and has the shortest total squared distance to these regions. First, a distributed time-varying algorithm is introduced, where a corresponding condition is given to guarantee that all agents rendezvous at the optimal location asymptotically for bounded convex regions. Then a distributed tracking algorithm combined with a distributed estimation algorithm is proposed. It is first shown that for general possibly unbounded convex regions, all agents rendezvous in finite time and then collectively slide to the optimal location asymptotically. Then it is shown that for convex regions with certain projection compressibility, all agents collectively rendezvous at the optimal location in finite time, even when the regions are time varying. The algorithms are experimentally implemented on multiple ground robots to illustrate the obtained theoretical results.

This paper studies a containment problem with communication delays and switching topologies. A nonlinear projection containment control algorithm for followers with single-integrator discrete-time dynamics is proposed. The main approach is to use the convexity of the convex hull spanned by multiple stationary leaders to show the nonincreasing monotonicity of the largest distance from the agents to the convex hull. It is shown that the nonlinear projection containment control algorithm is robust to arbitrarily bounded communication delays as long as each follower jointly has a path from some leaders to itself. Finally, a numerical example is implemented to show the obtained theoretical results.

This paper studies the inherent connection between dynamic region-following formation control (DRFFC) and distributed average tracking (DAT). We propose a fixed-gain DAT algorithm with robustness to initialization errors for linear multiagent systems, which is capable of achieving DAT with a zero tracking error for a large class of reference signals. In the case that the fixed gain cannot be chosen properly, we present an adaptive control gain design, under which each agent simply chooses its own gain and the restriction on knowing the upper bounds on the reference signals and their inputs is removed. We show that the proposed DAT algorithms can be employed to solve the DRFFC problem. This is an attempt on the applications of DAT algorithms to achieve distributed control; existing works most use DAT as distributed estimation algorithms. For single-integrator, double-integrator, higher-order linear dynamics, we derive the corresponding DRFFC algorithms from the DAT algorithm. Compared with existing DRFFC algorithms, the DAT-based DRFFC algorithms do not require the desired region to have a regular shape and is capable of generating a much richer formation behavior. Numerical examples are also included to show the validity of the derived results.

This paper considers the robustness analysis and distributed 'I-1∞(H-infinity) controller synthesis for a platoon of connected vehicles with undirected topologies. We first formulate a unified model to describe the collective behavior of homogeneous platoons with external disturbances using graph theory. By exploiting the spectral decomposition of a symmetric matrix, the collective dynamics of a platoon is equivalently decomposed into a set of subsystems sharing the same size with one single vehicle. Then, we provide an explicit scaling trend of robustness measure γ-gain, and introduce a scalable multistep procedure to synthesize a distributed 'I-1∞controller for large-scale platoons. It is shown that communication topology, especially the leader's information, exerts great influence on both robustness performance and controller synthesis. Furthermore, an intuitive optimization problem is formulated to optimize an undirected topology for a platoon system, and the upper and lower bounds of the objective are explicitly analyzed, which hints us that coordination of multiple mini-platoons is one reasonable architecture to control large-scale platoons. Numerical simulations are conducted to illustrate our findings.

This paper studies the coverage problem in an unknown environment by a Mobile Sensor Network (MSN). Each agent in the MSN has communication, sensing, moving, and computation capabilities to complete sensing tasks. These agents would have some limitations on time and energy to accomplish their tasks that need to be considered by the designers. Here, the agents need to relocate themselves, from their initial random locations, to their optimal configuration. An algorithm based on game theory is proposed, where a collection of distributed agents communicate with local neighbors and use their local information make decisions. A state-based potential game is defined in which each agent's utility function is designed to consider the trade-off between the worth of the covered area and the energy consumption. The agents employ binary log-linear learning to update their actions in each iteration in order to converge to the Nash equilibrium. As the agents do not have the knowledge of the sensing area, a Gaussian Mixture Model (GMM) is used to model the distributions of the worth in the sensing area. To estimate the unknown parameters of the GMM, a Maximum Likelihood (ML) estimation scheme is employed, where an expectation-maximization algorithm is used as a tool to solve the ML recursively. Then, in order to feed the estimation algorithm with more informative data, a mutual information term is added to the agents' utility functions. The mutual information is utilized to determine which observation can improve the agent's knowledge of the unobserved area more. Both simulation results and experimental results on a multi-robot platform are provided to validate the performance of the proposed algorithm.

This paper presents a distributed adaptive finite-time control solution to the formation-containment problem for multiple networked systems with uncertain nonlinear dynamics and directed communication constraints. By integrating the special topology feature of the new constructed symmetrical matrix, the technical difficulty in finite-time formation-containment control arising from the asymmetrical Laplacian matrix under single-way directed communication is circumvented. Based upon fractional power feedback of the local error, an adaptive distributed control scheme is established to drive the leaders into the prespecified formation configuration in finite time. Meanwhile, a distributed adaptive control scheme, independent of the unavailable inputs of the leaders, is designed to keep the followers within a bounded distance from the moving leaders and then to make the followers enter the convex hull shaped by the formation of the leaders in finite time. The effectiveness of the proposed control scheme is confirmed by the simulation.

This paper is concerned with the consensus problem of general linear dynamic multiagent systems with stochastic sampling. In this paper, the sampling intervals randomly switch between two different values. The communication topology between agents is fixed and directed. Full- and reduced-order observers are designed based on neighbor agents' relative output information. The algorithms to construct such observers are also provided. By using the estimated states of the agents, the observer-based consensus protocol with stochastic sampling are presented. Sufficient conditions to ensure consensus in mean square are derived by using Lyapunov stability theory. Finally, simulations are given to examine the effectiveness of the proposed methods.

In this paper, a framework of convex optimization algorithm with a fixed time convergence rate is investigated. Given a strongly convex optimization problem, two control algorithms are developed to solve the problem within a fixed time of which the upper bound is theoretically obtained. Moreover, the fixed time convergence rate based algorithms are extended into the distributed manner which is applied to two typical distributed optimization problems including the resource allocation problem and the coordination optimization problem. Laplacian graph matrix is employed to the weighted gradient based and the coordination based distributed optimization algorithms. By developing the characteristic of the objective function, the upper bound of the fixed time convergence is derived. Two numerical examples are given to verify the main results.

The consensus problem for second-order multiagent systems with absolute velocity damping under directed topologies is investigated. In contrast to the existing results, which rely on a sufficiently large common absolute velocity damping gain above a lower bound dependent on global information, this paper focuses on novel algorithms to overcome this limitation. A novel consensus algorithm, where different agents use different absolute velocity damping gains, is first proposed. In the absence of delays, based on a system transformation method, the consensus problem for second-order multiagent systems is converted into that for first-order multiagent systems with the agent number doubled. Necessary and sufficient conditions are then derived under directed topologies by relating the topologies associated with the doubled number of agents and the original team of agents. In the presence of multiple constant delays, based on a further system transformation method, the consensus problem for second-order multiagent systems is converted into the stability problem for corresponding systems. Necessary and sufficient conditions are presented to guarantee consensus under a directed fixed topology. For systems with a uniform constant delay, more concrete necessary and sufficient conditions on how large the delay can be to guarantee consensus is given. Numerical simulations are provided to illustrate the effectiveness of the obtained theoretical results.

This paper studies the containment control of multiagent systems (MASs) with multiple dynamic leaders in both continuous-time domain and discrete-time domain. The leaders' motions are described by the nth-order polynomial trajectories. This setting makes practical sense because given some critical points, the leaders' trajectories are usually planned by the polynomial interpolations. In order to drive all followers into the convex hull spanned by the leaders, a PIn-type containment algorithm is proposed (P and I are short for proportional and integral, respectively; Inimplies that the algorithm includes up to the n-thorder integral terms). It is theoretically proved that the PIn-type containment algorithm is able to solve the containment problem of MASs where the followers are described by any order integral dynamics. Compared to the previous results on the MASs with dynamic leaders, the distinguished features of this paper are that: 1) the containment problem is studied not only in the continuoustime domain but also in the discrete-time domain while most existing results only work in the continuous-time domain; 2) to deal with the leaders with the nth-order polynomial trajectories, existing results require the follower's dynamics to be the (n + 1)th-order integral while the followers considered in this paper can be described by any-order integral dynamics; 3) the “sign” function is not employed in the proposed algorithm, which avoids the chattering phenomenon; and 4) both disturbance and measurement noise are taken into account. Finally, some simulation examples are given to demonstrate the effectiveness of the proposed algorithm.

In this paper, we consider the distributed containment control problem for multiagent systems with unknown nonlinear dynamics. More specifically, we focus on multiple second-order nonlinear systems and networked Lagrangian systems. We first study the distributed containment control problem for multiple second-order nonlinear systems with multiple dynamic leaders in the presence of unknown nonlinearities and external disturbances under a general directed graph that characterizes the interaction among the leaders and the followers. A distributed adaptive control algorithm with an adaptive gain design based on the approximation capability of neural networks is proposed. We present a necessary and sufficient condition on the directed graph such that the containment error can be reduced as small as desired. As a byproduct, the leaderless consensus problem is solved with asymptotical convergence. Because relative velocity measurements between neighbors are generally more difficult to obtain than relative position measurements, we then propose a distributed containment control algorithm without using neighbors' velocity information. A two-step Lyapunov-based method is used to study the convergence of the closed-loop system. Next, we apply the ideas to deal with the containment control problem for networked unknown Lagrangian systems under a general directed graph. All the proposed algorithms are distributed and can be implemented using only local measurements in the absence of communication. Finally, simulation examples are provided to show the effectiveness of the proposed control algorithms.

This paper reviews some main results and progress in distributed multi-agent coordination, focusing on papers published in major control systems and robotics journals since 2006. Distributed coordination of multiple vehicles, including unmanned aerial vehicles, unmanned ground vehicles, and unmanned underwater vehicles, has been a very active research subject studied extensively by the systems and control community. The recent results in this area are categorized into several directions, such as consensus, formation control, optimization, and estimation. After the review, a short discussion section is included to summarize the existing research and to propose several promising research directions along with some open problems that are deemed important for further investigations.

This paper presents an implementation of autonomous indoor aerial gripping using a low-cost, custom-built quadrotor. Such research extends the typical functionality of micro air vehicles (MAV) from passive observation and sensing to dynamic interaction with the environment. To achieve this, three major challenges are overcome: precise positioning, sensing and manipulation of the object, and stabilization in the presence of disturbance due to interaction with the object. Navigation in unstructured, GPS-denied environments is achieved using a visual SLAM algorithm that relies on an onboard monocular camera. A secondary camera, capable of detecting infrared light sources, is used to estimate the 3D location of the object, while an under-actuated and passively compliant manipulator is designed for effective gripping under uncertainty. The system utilizes nested PID controllers for attitude stabilization, vision-based navigation and gripping. The quadrotor is therefore able to autonomously navigate, locate and grasp an object, using only onboard sensors.

In this paper, time-domain (Lyapunov theorems) and frequency-domain (the Nyquist stability criterion) approaches are used to study leaderless and leader-following consensus algorithms with communication and input delays under a directed network topology. We consider both the first-order and second-order cases and present stability or boundedness conditions. Several interesting phenomena are analyzed and explained. Simulation results are presented to support the theoretical results.

This paper studies the distributed coordination of networked fractional-order systems over a directed interaction graph. A general fractional-order coordination model is introduced by summarizing three different cases: 1) fractional-order agent dynamics with integer-order coordination algorithms; 2) fractional-order agent dynamics with fractional-order coordination algorithms; and 3) integer-order agent dynamics with fractional-order coordination algorithms. We show sufficient conditions on the interaction graph and the fractional order such that coordination can be achieved using the general model. The coordination equilibrium is also explicitly given. In addition, we characterize the relationship between the number of agents and the fractional order to ensure coordination. Furthermore, we compare the convergence speed of coordination for fractional-order systems with that for integer-order systems. It is shown that the convergence speed of the fractional-order coordination algorithms can be improved by varying the fractional orders with time. Finally, simulation results are presented as a proof of concept.

Laplacian matrices play an important role in linear-consensus algorithms. This paper studies optimal linear-consensus algorithms for multivehicle systems with single-integrator dynamics in both continuous-time and discrete-time settings. We propose two global cost functions, namely, interaction-free and interaction-related cost functions. With the interaction-free cost function, we derive the optimal (nonsymmetric) Laplacian matrix by using a linear-quadratic-regulator-based method in both continuous-time and discrete-time settings. It is shown that the optimal (nonsymmetric) Laplacian matrix corresponds to a complete directed graph. In addition, we show that any symmetric Laplacian matrix is inverse optimal with respect to a properly chosen cost function. With the interaction-related cost function, we derive the optimal scaling factor for a prespecified symmetric Laplacian matrix associated with the interaction graph in both continuous-time and discrete-time settings. Illustrative examples are given as a proof of concept.

In this paper, we experimentally implement and validate distributed consensus algorithms on a mobile actu- ator and sensor network platform under directed, possibly switching interaction topologies to explore issues and challenges in distributed multi-vehicle cooperative control. Distributed consensus algorithms are applied to three target applications namely rendezvous, axial alignment, and formation maneu- vering. In the rendezvous application, multiple mobile robots simultaneously arrive at a common a priori unknown target location determined through team negotiation. In the axial alignment application, multiple mobile robots collectively align their final positions along a line. In the formation maneuvering application, multiple mobile robots form a rigid geometric shape and maneuver as a group with a given group velocity. The experimental results show the effectiveness and robustness of the consensus algorithms even in the presence of platform physical limitations, packet loss, information delay, etc.