A Scalable Adaptive Approach to Multi-Vehicle Formation Control with Obstacle Avoidance

This paper deals with the problem of distributed formation tracking control and obstacle avoidance of multivehicle systems(MVSs)in complex obstacle-laden environments.The MVS under consideration consists of a leader vehicle with an unknown control input and a group of follower vehicles,connected via a directed interaction topology,subject to simultaneous unknown heterogeneous nonlinearities and external disturbances.The central aim is to achieve effective and collisionfree formation tracking control for the nonlinear and uncertain MVS with obstacles encountered in formation maneuvering,while not demanding global information of the interaction topology.Toward this goal,a radial basis function neural network is used to model the unknown nonlinearity of vehicle dynamics in each vehicle and repulsive potentials are employed for obstacle avoidance.Furthermore,a scalable distributed adaptive formation tracking control protocol with a built-in obstacle avoidance mechanism is developed.It is proved that,with the proposed protocol,the resulting formation tracking errors are uniformly ultimately bounded and obstacle collision avoidance is guaranteed.Comprehensive simulation results are elaborated to substantiate the effectiveness and the promising collision avoidance performance of the proposed scalable adaptive formation control approach.

Finite-time Prescribed Performance Time-Varying Formation Control for Second-Order Multi-Agent Systems With Non-Strict Feedback Based on a Neural Network Observer

This paper studies the problem of time-varying formation control with finite-time prescribed performance for nonstrict feedback second-order multi-agent systems with unmeasured states and unknown nonlinearities.To eliminate nonlinearities,neural networks are applied to approximate the inherent dynamics of the system.In addition,due to the limitations of the actual working conditions,each follower agent can only obtain the locally measurable partial state information of the leader agent.To address this problem,a neural network state observer based on the leader state information is designed.Then,a finite-time prescribed performance adaptive output feedback control strategy is proposed by restricting the sliding mode surface to a prescribed region,which ensures that the closed-loop system has practical finite-time stability and that formation errors of the multi-agent systems converge to the prescribed performance bound in finite time.Finally,a numerical simulation is provided to demonstrate the practicality and effectiveness of the developed algorithm.

Adaptive Event-Triggered Time-Varying Output Group Formation Containment Control of Heterogeneous Multiagent Systems

In this paper,a class of time-varying output group formation containment control problem of general linear hetero-geneous multiagent systems(MASs)is investigated under directed topology.The MAS is composed of a number of tracking leaders,formation leaders and followers,where two different types of leaders are used to provide reference trajectories for movement and to achieve certain formations,respectively.Firstly,compen-sators are designed whose states are estimations of tracking lead-ers,based on which,a controller is developed for each formation leader to accomplish the expected formation.Secondly,two event-triggered compensators are proposed for each follower to evalu-ate the state and formation information of the formation leaders in the same group,respectively.Subsequently,a control protocol is designed for each follower,utilizing the output information,to guide the output towards the convex hull generated by the forma-tion leaders within the group.Next,the triggering sequence in this paper is decomposed into two sequences,and the inter-event intervals of these two triggering conditions are provided to rule out the Zeno behavior.Finally,a numerical simulation is intro-duced to confirm the validity of the proposed results.

Formation mechanism and organizational controlling of ultra-fine-grain copper processed by asymmetrical accumulative rolling-bond and annealing

The initial copper with large grain sizes of 60-100 μm was processed by six passes asymmetrical accumulative rolling-bond （AARB） and annealing, the ultra-fine-grained （UFG） copper with grain size of 200 nm was obtained, and the microstructures and properties were studied. The results show that there are large sub-structures and also texture component C for the UFG copper obtained by six passes AARB, possessing high strength and microhardness in company with poor elongation and conductivity. Thereafter, the UFG copper was annealed at 220 °C for 35 min, in which the sub-structures disappear, the grain boundaries are composed of big angle grain boundaries, and the textures are composed of a variety of texture components and parts of twins. Compared with the UFG copper obtained by six passes AARB, the tensile strength and yield strength for the UFG copper obtained by six passes AARB and annealing at 220 °C for 35 min are decreased slightly, the elongation and conductivity are improved obviously.

Robust Adaptive Gain Higher Order Sliding Mode Observer Based Control-constrained Nonlinear Model Predictive Control for Spacecraft Formation Flying

This work deals with the development of a decentralized optimal control algorithm, along with a robust observer,for the relative motion control of spacecraft in leader-follower based formation. An adaptive gain higher order sliding mode observer has been proposed to estimate the velocity as well as unmeasured disturbances from the noisy position measurements.A differentiator structure containing the Lipschitz constant and Lebesgue measurable control input, is utilized for obtaining the estimates. Adaptive tuning algorithms are derived based on Lyapunov stability theory, for updating the observer gains,which will give enough flexibility in the choice of initial estimates.Moreover, it may help to cope with unexpected state jerks. The trajectory tracking problem is formulated as a finite horizon optimal control problem, which is solved online. The control constraints are incorporated by using a nonquadratic performance functional. An adaptive update law has been derived for tuning the step size in the optimization algorithm, which may help to improve the convergence speed. Moreover, it is an attractive alternative to the heuristic choice of step size for diverse operating conditions. The disturbance as well as state estimates from the higher order sliding mode observer are utilized by the plant output prediction model, which will improve the overall performance of the controller. The nonlinear dynamics defined in leader fixed Euler-Hill frame has been considered for the present work and the reference trajectories are generated using Hill-Clohessy-Wiltshire equations of unperturbed motion. The simulation results based on rigorous perturbation analysis are presented to confirm the robustness of the proposed approach.

Leader-following consensus protocols for formation control of multi-agent network

Two protocols are presented,which can make agents reach consensus while achieving and preserving the desired formation in fixed topology with and without communication timedelay for multi-agent network.First,the protocol without considering the communication time-delay is presented,and by using Lyapunov stability theory,the sufficient condition of stability for this multi-agent system is presented.Further,considering the communication time-delay,the effectiveness of the protocol based on Lyapunov-Krasovskii function is demonstrated.The main contribution of the proposed protocols is that,as well as the velocity consensus is considered,the formation control is concerned for multi-agent systems described as the second-order equations.Finally,numerical examples are presented to illustrate the effectiveness of the proposed protocols.

A Novel Multi-agent Formation Control Law With Collision Avoidance

In this paper a stable formation control law that simultaneously ensures collision avoidance has been proposed.It is assumed that the communication graph is undirected and connected.The proposed formation control law is a combination of the consensus term and the collision avoidance term(CAT).The first order consensus term is derived for the proposed model,while ensuring the Lyapunov stability.The consensus term creates and maintains the desired formation shape,while the CAT avoids the collision.During the collision avoidance,the potential function based CAT makes the agents repel from each other.This unrestricted repelling magnitude cannot ensure the graph connectivity at the time of collision avoidance.Hence we have proposed a formation control law,which ensures this connectivity even during the collision avoidance.This is achieved by the proposed novel adaptive potential function.The potential function adapts itself,with the online tuning of the critical variable associated with it.The tuning has been done based on the lower bound of the critical variable,which is derived from the proposed connectivity property.The efficacy of the proposed scheme has been validated using simulations done based on formations of six and thirty-two agents respectively.

Distributed formation control for a multi-agent system with dynamic and static obstacle avoidances

Formation control and obstacle avoidance for multi-agent systems have attracted more and more attention. In this paper, the problems of formation control and obstacle avoidance are investigated by means of a consensus algorithm. A novel distributed control model is proposed for the multi-agent system to form the anticipated formation as well as achieve obstacle avoidance. Based on the consensus algorithm, a distributed control function consisting of three terms （formation control term, velocity matching term, and obstacle avoidance term） is presented. By establishing a novel formation control matrix, a formation control term is constructed such that the agents can converge to consensus and reach the anticipated formation. A new obstacle avoidance function is developed by using the modified potential field approach to make sure that obstacle avoidance can be achieved whether the obstacle is in a dynamic state or a stationary state. A velocity matching term is also put forward to guarantee that the velocities of all agents converge to the same value. Furthermore, stability of the control model is proven. Simulation results are provided to demonstrate the effectiveness of the proposed control.

Time-varying fault-tolerant formation tracking based cooperative control and guidance for multiple cruise missile systems under actuator failures and directed topologies

This paper studies time-varying fault-tolerant formation tracking problems for the multiple cruise missile system under directed topologies subjected to actuator failures. Firstly, the timevarying fault-tolerant formation tracking process for the multiple cruise missile system is divided into the guidance loop and the control loop. Then protocols are constructed to accomplish distributed fault-tolerant formation tracking in the guidance loop with the adaptive updating mechanism, in the condition where neither the knowledge about actuator malfunctions nor any global information of the communication topology remains available. Moreover, sufficient conditions to accomplish formation tracking are presented, and it is shown that the multiple cruise missile system can carry on the predefined time-varying fault-tolerant control (FTC) formation tracking through the active disturbances rejection controller (ADRC) and the proportion integration (PI) controller by the way of the fault-tolerant protocol utilizing the designed strategies, in the event of actuator failures. At last, numerical analysis and simulation are designed to verify the theoretical results.

Optimal Formation Reconfiguration Control of Multiple UCAVs Using Improved Particle Swarm Optimization

Optimal formation reconfiguration control of multiple Uninhabited Combat Air Vehicles （UCAVs） is a complicated global optimum problem. Particle Swarm Optimization （PSO） is a population based stochastic optimization technique inspired by social behaviour of bird flocking or fish schooling. PSO can achieve better results in a faster, cheaper way compared with other bio-inspired computational methods, and there are few parameters to adjust in PSO. In this paper, we propose an improved PSO model for solving the optimal formation reconfiguration control problem for multiple UCAVs. Firstly, the Control Parameterization and Time Diseretization （CPTD） method is designed in detail. Then, the mutation strategy and a special mutation-escape operator are adopted in the improved PSO model to make particles explore the search space more efficiently. The proposed strategy can produce a large speed value dynamically according to the variation of the speed, which makes the algorithm explore the local and global minima thoroughly at the same time. Series experimental results demonstrate the feasibility and effectiveness of the proposed method in solving the optimal formation reconfiguration control problem for multiple UCAVs.

Fixed-time Sliding Mode Formation Control of AUVs Based on a Disturbance Observer

In this paper,we investigate formation tracking control of autonomous underwater vehicles(AUVs)with model parameter uncertainties and external disturbances.The external disturbances due to the wind,waves,and ocean currents are combined with the model parameter uncertainties as a compound disturbance.Then a disturbance observer(DO)is introduced to estimate the compound disturbance,which can be achieved within a finite time independent of the initial estimation error.Based on a DO,a novel fixed-time sliding control scheme is developed,by which the follower vehicle can track the leader vehicle with all the states globally stabilized within a given settling time.The effectiveness and performance of the method are demonstrated by numerical simulations.

Robust Leader-Follower Formation Tracking Control of Multiple Underactuated Surface Vessels

This paper is concerned with the formation control problem of multiple underactuated surface vessels moving in a leader-follower formation. The formation is achieved by the follower to track a virtual target defined relative to the leader. A robust adaptive target tracking law is proposed by using neural network and backstepping techniques. The advantage of the proposed control scheme is that the uncertain nonlinear dynamics caused by Coriolis/centripetal forces, nonlinear damping, unmodeled hydrodynamics and disturbances from the environment can be compensated by on line learning. Based on Lyapunov analysis, the proposed controller guarantees the tracking errors converge to a small neighborhood of the origin. Simulation results demonstrate the effectiveness of the control strategy.

A Software-in-the-Loop Implementation of Adaptive Formation Control for Fixed-Wing UAVs

This paper discusses the design and software-in-theloop implementation of adaptive formation controllers for fixedwing unmanned aerial vehicles(UAVs) with parametric uncertainty in their structure, namely uncertain mass and inertia. In fact, when aiming at autonomous flight, such parameters cannot assumed to be known as they might vary during the mission(e.g.depending on the payload). Modeling and autopilot design for such autonomous fixed-wing UAVs are presented. The modeling is implemented in Matlab, while the autopilot is based on ArduPilot, a popular open-source autopilot suite. Specifically, the ArduP ilot functionalities are emulated in Matlab according to the Ardupilot documentation and code, which allows us to perform software-in-the-loop simulations of teams of UAVs embedded with actual autopilot protocols. An overview of realtime path planning, trajectory tracking and formation control resulting from the proposed platform is given. The software-inthe-loop simulations show the capability of achieving different UAV formations while handling uncertain mass and inertia.

Formation Control for Water-Jet USV Based on Bio-Inspired Method

The formation control problem for underactuated unmanned surface vehicles(USVs) is addressed by a distributed strategy based on virtual leader strategy. The control system takes account of disturbance induced by external environment. With the coordinate transformation, the advantage of the proposed scheme is that the control point can be any point of the ship instead of the center of gravity. By introducing bio-inspired model, the formation control problem is addressed with backstepping method. This avoids complicated computation, simplifies the control law,and smoothes the input signals. The system uniform ultimate boundness is proven by Lyapunov stability theory with Young inequality. Simulation results are presented to verify the effectiveness and robust of the proposed controller.

Consensus tracking protocol and formation control of multi-agent systems with switching topology

Consensus tracking control problems for single-integrator dynamics of multi-agent systems with switching topology are investigated. In order to design effective consensus tracking protocols for a more general class of networks, which are aimed at ensuring that the concerned states of agents converge to a constant or time-varying reference state, new consensus tracking protocols with a constant and time-varying reference state are proposed, respectively. Particularly, by contrast with spanning tree, an improved condition of switching interaction topology is presented. And then, convergence analysis of two consensus tracking protocols is provided by Lyapunov stability theory. Moreover, consensus tracking protocol with a time-varying reference state is extended to achieve the fbrmation control. By introducing formation structure set, each agent can gain its individual desired trajectory. Finally, several simulations are worked out to illustrate the effectiveness of theoretical results. The test results show that the states of agents can converge to a desired constant or time-varying reference state. In addition, by selecting appropriate structure set, agents can maintain the expected formation under random switching interaction topologies.

Insights into Cronobacter sakazakii Biofilm Formation and Control Strategies in the Food Industry

Cronobacter sakazakii(C.sakazakii)is a foodborne opportunistic pathogen that can cause life-threatening invasive diseases,such as necrotizing enterocolitis,meningitis,and sepsis in infants.The potential risk of C.sakazakii contamination of powdered infant formula(PIF)is an issue that has attracted considerable attention from manufacturers,regulators,and consumers.C.sakazakii biofilms on the surfaces of equipment and in diverse food-production environments constitute a mode of cell growth that protects the pathogen from hostile environments,and are an important source of persistent contamination of food products.Bacterial biofilms are difficult to remove due to their resistant properties.Conventional cleaning and sterilizing procedures may be insufficient for biofilm control,and may lead to further biofilm development and dispersal.Consequently,novel control strategies are being developed,such as nanotechnology-based delivery systems,interspecies interactions,antimicrobial molecules of microbial origin,natural extracts,and phages.This review focuses on describing the mechanisms underlying the biofilm formation and behavior of C.sakazakii and discussing potential control strategies.

Geological Controls on the CBM Productivity of No.15 Coal Seam of Carboniferous–Permian Taiyuan Formation in Southern Qinshui Basin and Prediction for CBM High-yield Potential Regions

Coalbed methane(CBM) resources in No.15 coal seam of Taiyuan Formation account for 55% of the total CBM resources in southern Qinshui Basin(SQB), and have a great production potential. This study aims at investigating the CBM production in No.15 coal seam and its influence factors. Based on a series of laboratory experiments and latest exploration and development data from local coal mines and CBM companies, the spatial characteristics of gas production of No.15 coal seam were analyzed and then the influences of seven factors on the gas productivity of this coal seam were discussed, including coal thickness, burial depth, gas content, ratio of critical desorption pressure to original coal reservoir pressure(RCPOP), porosity, permeability, and hydrogeological condition. The influences of hydrological condition on CBM production were analyzed based on the discussions of four aspects: hydrogeochemistry, roof lithology and its distribution, hydrodynamic field of groundwater, and recharge rate of groundwater. Finally, a three-level analytic hierarchy process(AHP) evaluation model was proposed for predicting the CBM potentials of the No.15 coal seam in the SQB. The best prospective target area for CBM production of the No.15 coal seam is predicted to be in the districts of Panzhuang, Chengzhuang and south of Hudi.

Leader-following formation control of multi-agent networks based on distributed observers

To investigate the leader-following formation control, in this paper we present the design problem of control protocols and distributed observers under which the agents can achieve and maintain the desired formation from any initial states, while the velocity converges to that of the virtual leader whose velocity cannot be measured by agents in real time. The two cases of switching topologies without communication delay and fixed topology with time-varying communication delay are both considered for multi-agent networks. By using the Lyapunov stability theory, the issue of stability is analysed for multi-agent systems with switching topologies. Then, by considering the time-varying communication delay, the sufficient condition is proposed for the multi-agent systems with fixed topology. Finally, two numerical examples are given to illustrate the effectiveness of the proposed leader-following formation control protocols.

The Formation Control of Multi-agent Systems on a Circle

This paper investigates the formation control of a class of multi-agent systems moving on a circle, whose topology is a cyclic graph, and presents several new results for the following two cases: Case I, the agents with single-integrator kinematics,and Case II, the agents with double-integrator kinematics. Firstly,for Case I, two control protocols are proposed under which the multiagent systems keep a uniformly-spaced formation. Secondly,we study Case II, and a control protocol is designed for this case, then the stability of the formation is proved. Finally, three simulations are studied by using our presented results. The study of illustrative examples with simulations shows that our results as well as designed control protocols work very well in studying the formation control of this class of multi-agent systems.

Dynamic formation control for autonomous underwater vehicles

Path planning and formation structure forming are two of the most important problems for autonomous underwater vehicles(AUVs) to collaborate with each other.In this work,a dynamic formation model was proposed,in which several algorithms were developed for the complex underwater environment.Dimension changeable particle swarm algorithm was used to find an optimized path by dynamically adjusting the number and the distribution of the path nodes.Position relationship based obstacle avoidance algorithm was designed to detour along the edges of obstacles.Virtual potential point based formation-keeping algorithm was employed by incorporating dynamic strategies which were decided by the current states of the formation.The virtual potential point was used to keep the formation structure when the AUV or the formation was deviated.Simulation results show that an optimal path can be dynamically planned with fewer path nodes and smaller fitness,even with a concave obstacle.It has been also proven that different formation-keeping strategies can be adaptively selected and the formation can change its structure in a narrow area and restore back after passing the obstacle.