Consensus-based Formation Control Research Articles

Global Consensus-Based Formation Control of Nonholonomic Mobile Robots With Time-Varying Delays and Without Velocity Measurements

We propose a solution to the full consensus-based formation problem for torque-controlled nonholonomic mobile robots under time-varying communication delays and without velocity measurements. Under the assumptions of static and undirected communication topologies, and smooth and bounded delays, we propose a distributed smooth, time-varying control law which achieves the goal of acquiring a global formation pattern in a common consensus point for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">both</i> position and orientation. The controller is a combination of a simple Proportional-Plus-Damping scheme and a simple globally exponentially convergent velocity observer. Consensus is reached independently of all initial conditions. Realistic simulations in the Gazebo-ROS environment illustrate the effectiveness of the proposed algorithm and the robustness with respect to measurement noise, non-smooth delays and uncertain dynamics.

Global consensus-based formation control of perturbed nonholonomic mobile robots with time varying delays

This paper proposes a smooth time-variant PID-like control scheme for networks composed of nonholonomic vehicles modeled as differential drive robots affected by unknown input constant disturbances and transmission variable time-delays in the communication channel. Using Barbalat’s Lemma and under the fact that the interconnecting graph is undirected and connected, it is proved that all robots positions asymptotically converge to a position in a given desired formation and they all agree on the center of this formation, while the orientations asymptotically reach a consensus value. Besides, it is proved that given the structure of the proposed new integral action, the external constant disturbances are rejected (exactly estimated) and that velocities converge to zero. Simulation results, with a robot network composed of eight nonholonomic vehicles and considering disturbances subjected to step changes, are presented to illustrate the robustness of the proposed control scheme.

Distributed Formation Control for a Multirobotic Fish System With Model-Based Event-Triggered Communication Mechanism

This paper confronts the formation control problem for a multi-robotic fish system with event-triggered communication mechanism. A three-dimensional (3-D) distributed formation control framework is proposed to drive the robotic fish agents to an anticipated configuration aligning with a moving target. In particular, a consensus-based formation control law is intended to realize the two-stage formation control process. Taking the energy-constrained occasions into consideration, the communication structure and event-triggered protocols are initially tailored. Meanwhile, the Lyapunov function is employed and the globally asymptotic stability of the proposed method is fully demonstrated. Afterwards, making use of the local measurements of triggering times, the unscented Kalman filter (UKF) is introduced and a novel model-based event-triggered mechanism is put forward to further mitigate otiose communication consumption. Finally, adequate simulations and experiments are carried out to verify the effectiveness and robustness of the proposed scheme. Thereby, the proposed formation control frame offers great potential for future practical marine operations of the underwater multi-agent systems.

Robust Consensus-based Formation Control of a Group of UAV

Consensus-based formation control (CFC) is one of the most phenomenal formation control methods designed to achieve consensus between any vehicles that using and sharing their position and/or linear velocity with each other in a swarm mission. In this paper, a robust CFC (R-CFC) has been designed and proposed to realize pre-defined formation shapes with a team of unmanned aerial vehicles (UAVs). First, the double integrator dynamics of an UAV is presented. Second, the graph theory is explained briefly to understand any adjacency between UAVs. Then, the proposed R-CFC algorithm has been derived and the stability analysis has been proven via algebraic Riccati stability theory based on Lyapunov stability theorem. After that, the effectiveness of the proposed controller has been tested in real time outdoor tests. The experimental results show that the UAVs have been able to create the desired formation shapes and are less affected by external disturbances such as wind thanks to the proposed control algorithm.

Edge-Weighted Consensus-Based Formation Control with Collision Avoidance for Mobile Robots Based on Multi-Strategy Mutation Differential Evolution

An edge-weighted consensus-based formation control strategy is presented for mobile robots. In the edge-weighted strategy, a desired formation pattern is achieved by adjusting gain weights related to the distance between robots. Moreover, the edge-weighted formation control exploits the properties of weighted graphs to allow the formation to rotate and adapt its shape to avoid collision among robots. However, formation patterns are commonly defined by biases with respect to the centroid of the consensus rather than gain weights. This work proposes to optimize the gain weights in edge-weighted graphs, given a formation pattern in terms of biases. A multi-strategy mutation differential evolution algorithm is introduced to solve the optimization problem. Simulation and real-world experiments are performed considering multi-robot systems composed of differential drive robots. Additionally, the experimental setup includes Turtlebot3® Waffle Pi robots and an OptiTrack® motion capture system for control purposes. The experimental results verify the effectiveness of the proposed approach.

Event-Trigger-Based Finite-Time Privacy-Preserving Formation Control for Multi-UAV System

Privacy-preserving has been crucial technique of multi-UAV systems, including cooperative detection, cooperative penetration and strike. Unprocessed interactive information poses a serious privacy threat to UAV swarm collaborative tasks. Considering not only privacy-preserving but also bandwidth constraints and the convergence performance of multi-UAV systems, this paper comprehensively proposes an original event-triggered-based finite-time privacy-preserving formation control scheme to resolve these three factors. Firstly, this paper adopted a local, deterministic, time-varying output mapping function for a privacy mask, which encodes the internal states of the UAV prior to its public transmission, and the initial true value of each UAV’s states is kept indecipherable for honest-but-curious UAVs and other malicious eavesdropping attackers. Then, considering the limited communication bandwidth and channels, we employed a distributed event-triggered strategy and deduced the triggering condition for consensus-based formation control, which effectively reduces the excessive consumption of communication and computational resources in contrast to time-triggered strategy. In terms of the convergence performance of the UAVs, finite-time stability theory was introduced to make the system reach the desired formation in finite time and obtain a settling time related to the initial state. Compared with the existing literature, this paper systematically took into account the above three factors for multi-UAV systems and provides a convergence analysis and a privacy analysis in detail. Finally, the effectiveness of the finite-time privacy-preserving protocol based on an event-triggered strategy was demonstrated by numerical simulation examples and comparative experiments. The proposed method achieves the formation control under privacy-preserving, improves the convergence rate and reduces the frequency of controller updates and information transmission.

Observerless Output-Feedback Consensus-Based Formation Control of Second-Order Nonholonomic Systems

We present a solution to the problem of formation consensus control of second-order nonholonomic systems via output feedback. We contribute with a distributed consensus controller for force-controlled nonholonomic systems under the assumption that the forward and angular velocities are not measurable. Our main statement establishes uniform global asymptotic stability for the closed-loop system; this guarantees robustness with respect to bounded disturbances, in the sense of Malkin’s total stability, also known as local input-to-state stability.

Consensus Problem and Formation Control for Heterogeneous Multi-Agent Systems with Switching Topologies

The cooperative control problem of discrete-time multi-agent systems (MASs) is discussed, and bounded uncertain time-delays and directed switching topologies are considered. By applying model transformations and matrix theory, an augmented system method is introduced to handle a heterogeneous time-delay MAS. Then, the consensus problem of the system is turned to the convergence issue of the product of innumerable row stochastic matrices. Sufficient conditions for asymptotic consensus of the system under directed switching topologies are obtained. Moreover, a novel consensus-based formation control strategy is designed to gain sufficient and necessary conditions for the formation control of a second-order differential robot system. Finally, the effectiveness of the obtained results is verified through simulations.

Leaderless maneuver guidance and event-triggered formation control for distributed multi-space-robot systems

In this paper, the distributed displacement-based formation and leaderless maneuver guidance control problems of multi-space-robot systems are investigated by introducing event-triggered control update mechanism. A distributed formation and leaderless maneuver guidance control framework is first constructed, which includes two parallel controllers, namely an improved linear quadratic regulator and a distributed consensus-based formation controller. By applying this control framework, the desired formation configuration of multi-space-robot systems can be achieved and the center of leaderless formation can converge to the target point globally. Second, a pull-based event triggering mechanism is introduced to the distributed formation controller, which makes the control update independent of the events of neighboring robots, avoids unnecessary control updates, and saves the extremely limited energy of space robots. Furthermore, the potential Zeno behaviors have been excluded by proving a positive lower bound for the inter-event times. Finally, numerical simulation verifies the effectiveness of the theoretical results.

Formation control for discrete-time multi-agent system with input and output delays under network attacks

This paper addresses the mean square consensus-based formation control for multiple agent system (MAS) with input and output delays under network attacks, process noise, and measurement noise in MAS. Firstly, a time delay-free transformation approach for a multi-agent system with input and output delays is presented. The MAS is transformed into a formal delay-free discrete-time system using the delay-free transformation method. Then a state observer based on Kalman filter is presented to estimate the states of agents. A distributed predictive consensus protocol based on the estimated states of each MAS is proposed for the leader-following MAS. The sufficient and necessary conditions of mean square consensus for MAS under DoS attacks are derived. Finally, a numerical example of consensus-based formation control for multi-agent systems is provided to verify the correctness and effectiveness of the proposed consensus control protocol.

Consensus-based formation control using a novel signed protocol

This paper aims to achieve formation control over a group of agents, modeled as single integrators, that exchange state information over an undirected graph. The information available to each agent is the sign of its relative displacement with respect to its neighbors, along different axis of a common frame of reference. It is shown that using a consensus protocol that uses only these signs, and not the magnitudes, of the relative positions, the agents may achieve desired formations shapes at various points in the Euclidean space. Additionally, the sign of this relative displacement is weighted, in the control law, by an edge weight. It is shown that consensus is achievable even when some of these edge weights are negative. Simulations vindicate the analytical claims in the paper.

Consensus-Based Formation Control of Multiple Nonholonomic Vehicles Under Input Constraints

We address the open problem of consensus-based formation control of nonholonomic multiagent vehicles with pre-imposed input constraints. That is the problem of stabilizing a group of second-order differential-drive nonholonomic robots, making them acquire a determined formation pattern around a non pre-specified point on the plane and a common non pre-specified orientation. This problem is also known as leaderless full consensus. Our controller is smooth and time-varying, and fully distributed. Its design is a natural modification of another controller proposed earlier, which relies on proportional feedback, damping injection, and a smooth time-varying term that injects persistency of excitation in the system to overcome the effects of nonholonomicity. It is assumed that the robots communicate over a network with an undirected-graph topology.

Robust PID consensus-based formation control of nonholonomic mobile robots affected by disturbances

In this work, we report a novel controller to solve (globally) the position and orientation consensus-based formation problem of multiple nonholonomic vehicles modelled as differential drive robots affected by external disturbances. The controller has the structure of a simple to implement Proportional Integral Derivative (PID) scheme. In order to satisfy the well-known Brocket stabilisation theorem for nonholonomic systems, we also incorporate a time-varying persistency of excitation term in the angular velocity dynamics. Our proposal reports the first solution to the robust formation problem using a smooth time-varying controller. Simulations are shown to evidence the theoretical findings of this work.

Bipartite consensus-based formation control of high-order multi-robot systems with time-varying delays

This paper considers a multi-robot formation control scheme for high-order bipartite consensus under time-varying delays. First, a third-order bipartite consensus protocol under time-varying delays is presented, and then a high-order bipartite consensus protocol is extended from it. Then, necessary and sufficient conditions for third-order and high-order multi-agent systems without time-delays are given to attain bipartite consensus following the protocols. Communication time-delays are added to the protocols, and the theory of Lyapunov asymptotic stability is used to obtain sufficient conditions for the multi-agent systems with communication delays to ultimately attain a bipartite consensus. Furthermore, the given protocol is employed for the formation control of multi-robot systems, and a formation control scheme for multi-robot systems with time-varying delays is proposed. Finally, a few simulations are implemented to demonstrate the rationality and availability of the method.

SDP-Based Robust Formation-Containment Coordination of Swarm Robotic Systems with Input Saturation

There are many potential applications of swarm robotic systems in real-world scenarios. In this paper, formation-containment controller design for single-integrator and double-integrator swarm robotic systems with input saturation is investigated. The swarm system contains two types of robots—leaders and followers. A novel control protocol and an implementation algorithm are proposed that enable the leaders to achieve the desired formation via semidefinite programming (SDP) techniques. The followers then converge into the convex hull formed by the leaders simultaneously. In contrast to conventional consensus-based formation control methods, the relative formation reference signal is not required in the real-time data transmission, which provides greater feasibility for implementation on hardware platforms. The effectiveness of the proposed formation-containment control algorithm is demonstrated with both numerical simulations and experiments using real robots that utilize the miniature mobile robot, Mona.

Distributed Formation Control Using Fuzzy Self-Tuning of Strictly Negative Imaginary Consensus Controllers in Aerial Robotics

Wind gusts are significant barriers to the outdoor operations of networked multiple unmanned aerial vehicles (UAVs), which fly in close proximity to each other or around obstacles. As such, traditional control methods such as PID control may not perform adequately. Based on the strictly negative imaginary (SNI) systems theory, this article presents a novel decentralized and adaptive consensus-based formation control law that drives multiple UAVs to follow the desired formation in the presence of limited bandwidth for information exchange and dynamically changing environmental conditions. To be consistent with a decentralized approach, each UAV only measures its relative position with respect to its neighbors according to a fixed information graph. As a result, the required formation is obtained by maintaining the desired relative positions among UAVs. Moreover, to deal with the challenging dynamics of flight environments, we also employ a knowledge-based fuzzy inference system to automatically adjust the parameters of the SNI consensus controllers, leading to the development of a fast and robust adaption method. In this article, we conduct a stability analysis based on the SNI theorem and rigorously compare the performance of our controllers with respect to the performance of conventional PID controllers. The efficacy of the overall closed loop control system is highlighted in real-time flight tests.

Multi-vehicle formation control and obstacle avoidance using negative-imaginary systems theory

This paper presents a compelling combination of the two negative-imaginary (NI) control systems: a consensus-based formation control framework for a hybrid multi-vehicle system and a new dynamic obstacle detection and avoidance algorithm. The incorporation of the two techniques permits robots to self-detect collisions and then self-create a safe path to overcome any unexpected obstacles while traveling to the destination in a given formation. Moreover, owing to the distributed and dynamic architecture, our NI obstacle avoidance method has better adaptability to the change of environment conditions or obstacle/robot dynamics. Also, a rigorous comparative study on the performance of our obstacle avoidance method with respect to that of the artificial potential field function and switching formation-based NI obstacle avoidance algorithms is performed as a benchmark. Finally, simulation and experimental results are then implemented to demonstrate the effectiveness of the proposed theories.

Consensus-Based Formation Control of Networked Nonholonomic Vehicles With Delayed Communications

For a network of nonholonomic vehicles communicating according to an undirected connected graph, a consensus-based formation control problem is solved via a smooth time-varying, proportional-derivative, δ-persistently-exciting, controller. It is assumed that the communication among agents is affected by time-varying, nondifferentiable, communication delays and uniform global asymptotic stability is demonstrated. This goes beyond the more-often encountered property of nonuniform convergence and, what is more, for the first time in the literature, a strict Lyapunov-Krasovskii functional is provided.

Leadership Hierarchy-based Formation Control via Adaptive Chaotic Pigeon-inspired Optimization

Abstract Formation control of multi-agent systems (MASs) is a significant research subject in the field of cooperative control. In this paper, we propose a novel consensus-based formation control approach with minimal resource cost and excellent adaptability for second-order nonlinear multi-agent systems. Specifically, an improved constrained adaptive chaotic pigeon-inspired optimization algorithm (ACPIO) is proposed for tuning parameters, which promotes the automation of controller design and alleviates the workload of conventional designer. Moreover, a variant of pinning control method integrating with hierarchical leadership model of pigeon flocks is introduced, which achieves excellent adaptability and reduces computational complexity simultaneously. Additionally, sufficient conditions are derived for achieving the desired formation pattern based on Lyapunov stability theory and matrix theory. Numerical simulation results demonstrate the feasibility and effectiveness of the proposed method for formation control of second-order nonlinear MASs.

Consensus-based adaptive guaranteed-performance formation control for second-order multi-agent systems

Adaptive guaranteed-performance formation analysis and design problems for second-order multi-agent systems are studied, where the global information is not required, which means the main results of this article are fully distributed. First, an adaptive guaranteed-performance formation control protocol is presented for second-order multi-agent systems, where the control input is constructed using neighboring state errors and adaptively adjustable interaction weights. Then, an adaptive guaranteed-performance formation control is proposed based on Riccati inequalities. Furthermore, the guaranteed-performance cost is determined and the adjusting approach of the formation control gain is presented in terms of linear matrix inequalities. Finally, a numerical simulation is provided to demonstrate the effectiveness of the theoretical results.