Formation Tracking Control Research Articles

Distributed Adaptive Formation Tracking Control of Mobile Robots With Event-Triggered Communication and Denial-of-Service Attacks

This paper focuses on distributed adaptive formation tracking control of mobile robots under event-triggered communication (ETC) and Denial-of-Service (DoS) attacks. Dynamic level of model for mobile robots and directed communication graph condition are considered. To handle the constraint that only part of the robots can access full knowledge of the desired trajectories, distributed event-triggered based estimators are designed. Then, an adaptive tracking control scheme is designed for each robot by utilizing backstepping tech- nique. By analyzing the effects of DoS attacks on ETC, a stability condition constraining the active and suspended durations for each attack period is provided, based on which all closed-loop signals are ensured to be locally uniformly bounded. Moreover, Zeno behaviors are excluded. Experimental results are presented to validate theoretical findings.

Resilient Time-Varying Formation-Tracking of Multi-UAV Systems Against Composite Attacks: A Two-Layered Framework

This paper studies the countermeasure design problems of distributed resilient time-varying formation-tracking control for multi-UAV systems with single-way communications against composite attacks, including denial-of-services (DoS) attacks, false-data injection attacks, camouflage attacks, and actuation attacks (AAs). Inspired by the concept of digital twin, a new two-layered protocol equipped with a safe and private twin layer (TL) is proposed, which decouples the above problems into the defense scheme against DoS attacks on the TL and the defense scheme against AAs on the cyber-physical layer. First, a topology-repairing strategy against frequency-constrained DoS attacks is implemented via a Zeno-free event-triggered estimation scheme, which saves communication resources considerably. The upper bound of the reaction time needed to launch the repaired topology after the occurrence of DoS attacks is calculated. Second, a decentralized adaptive and chattering-relief controller against potentially unbounded AAs is designed. Moreover, this novel adaptive controller can achieve uniformly ultimately bounded convergence, whose error bound can be given explicitly. The practicability and validity of this new two-layered protocol are shown via a simulation example and a UAV swarm experiment equipped with both Ultra-WideBand and WiFi communication channels.

Extended Kalman Filter Based Resilient Formation Tracking Control of Multiple Unmanned Vehicles via Game-Theoretical Reinforcement Learning

In this paper, we discuss the resilient formation tracking control problem of multiple unmanned vehicles (MUV). A dynamic leader-follower distributed control structure is utilized to optimize the performance of the formation tracking. For the follower of the MUV, the leader is a cooperative unmanned vehicle, and the target of formation tracking is a non-cooperative unmanned vehicle with a nonlinear trajectory. Therefore, an extended Kalman filter (EKF) observer is designed to estimate the state of the target. Then the leader of the MUV is adjusted dynamically according to the state of the target. In order to describe the interactions between the follower and dynamic leader, a Stackelberg game model is constructed to handle the hierarchical decision problems. At the lower layer, each follower responds by observing the leader's strategy, and the potential game is used to prove a Nash equilibrium among all followers. At the upper layer, the dynamic leader makes decisions depending on the response of all followers to reaching the Stackelberg equilibrium. Moreover, the Stackelberg-Nash equilibrium of the designed game theoretical model is proven. A novel reinforcement learning-based algorithm is designed to achieve the Stackelberg-Nash equilibrium of the game. Finally, the effectiveness of the method is verified by a variety of formation tracking simulation experiments.

Flexible Formation Tracking Control of Multiple Unmanned Surface Vessels for Navigating Through Narrow Channels with Unknown Curvatures

This article proposes a flexible formation tracking control protocol (FFTC) for multiple unmanned surface vessels (USVs) to pass through narrow water channels with unknown curvatures. An observer is developed to estimate the curvatures of channels. A flexible formation tracking control protocol is, thereby designed to steer USV fleets to pass through narrow channels in a flexible serial formation. Furthermore, the asymptotically stable conditions of the closed-loop multi-USV systems are theoretically derived. Finally, both numerical simulation and experimental results with a fleet of three HUSTER-0.3 USVs are reported to substantiate the effectiveness of the proposed FFTC protocol for navigating through narrow channel in a laboratory context.

Adaptive Constrained Formation-Tracking Control for a Tractor-Trailer Mobile Robot Team With Multiple Constraints

A team of multiple tractor–trailer mobile robots has many applications in areas including agriculture, logistics, transportation, etc. In this article, we propose a novel adaptive constrained formation-tracking control algorithm for the trailers in a tractor–trailer mobile robot team to track a desired formation, while satisfying multiple <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">precision</i> , <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">safety</i> , and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">feasibility</i> constraint requirements during the operation. Both universal barrier function approaches and a novel state transformation scheme are incorporated to deal with constraints of different nature. Adaptive estimators are introduced to estimate the rate of change of the desired trajectories for all trailers. We show that exponential convergence to a small neighborhood of the equilibrium can be guaranteed. In the end, a MATLAB simulation example and a Gazebo simulator study further demonstrate the efficacy of the proposed algorithm.

Spherical Formation Tracking Control of Non-Holonomic UAVs with State Constraints and Time Delays

This paper addresses a novel spherical formation tracking control problem of multiple UAVs with time-varying delays in the directed communication network, where the dynamics of each UAV is non-holonomic and in the presence of spatiotemporal flowfields. The state constraints (that is, position and velocity constraints) are derived from our previous differential geometry method and the F–S formulas. The state constraints and time delays in the directed communication network bring many difficulties to controller design. To this end, a virtual-structure-like design is given to achieve a formation with delayed information by using Lyapunov–Krasovskii functionals, and then proposing a barrier Lyapunov function for the satisfaction of state constraints to design a novel spherical formation tracking algorithm. The general assumption of the rate of change of time-varying delays, and a certain initial position and velocity adjustment range are given. Simulation results show the feasibility and effectiveness of the proposed algorithm.

Third-order consensus for robust distributed formation control of double integrator vehicles

This paper presents the development of a robust distributed and cooperative control algorithm for formation tracking by teams of vehicles modeled as double integrators, and exemplifies its use through the application to multirotor vehicles. To achieve coordination between the vehicles in a distributed manner, in the sense that only local information is either exchanged or perceived, consensus-based protocols are considered. Consensus protocols for agents modeled with up to three integrators are presented, and the third-order protocol is analyzed under any time-invariant sensing or communication topology. The analysis seeks to determine exact bounds on the coupling gains of the protocol that lead to convergence. To that end, an extension of the Routh–Hurwitz criterion to polynomials with complex coefficients is used, leading to novel necessary and sufficient conditions for convergence. Moreover, these novel bounds turn out to be a generalization of the ones described in the literature for second-order consensus, as the latter can be recovered as a special case. The effect of disturbances acting upon the agents is also analyzed and related to their ability to achieve robust consensus in the sense that bounded disturbances do not lead to instability. Further results are derived for the case of constant disturbances, a special case that is particularly relevant for formation control. The third-order consensus protocol is then explored to incorporate integral action in a formation tracking controller used for double integrator vehicles and thereby enable constant disturbance rejection. Finally, experiments resulting from the application of the proposed control algorithms to multirotor vehicles are presented, in order to validate the analysis and demonstrate the usefulness of this approach.

Layered fully distributed formation-containment tracking control for multiple unmanned surface vehicles

This paper addresses the formation-containment tracking control (FCTC) problem for unmanned surface vehicles (USVs) formation systems swarm with multiple leaders. Unlike the general study of the multi-leader case, communication among leaders is considered to endow the system with broader applicability under different mission requirements. Besides, a layered framework is employed here to distinguish the behaviour and role of agents in the formation system. In the first layer, a formation tracking controller is developed for leaders to track the reference trajectory and achieve the desired formation configuration. Then, a containment controller is proposed for followers in the second layer to drive them into the geometric space formed by leaders. Without loss of generality, the state information transmission between the two layers is considered unidirectional and the directed communication networks are designed in both layers. Meanwhile, considering the limitation that the agents in the USV formation system can only access their local information, the FCTC control strategy is designed in a fully distributed manner. Finally, numerical simulation results are represented to demonstrate the validity and feasibility of the proposed control scheme.

Event-Triggered Formation Tracking Control With Application to Multiple Mobile Robots

In this article, we address the distributed event-triggered leader–follower formation tracking control problem of general linear multiagent systems with a dynamic leader in sampled-data settings. A novel locally computable state-estimate-based event generator is established for each follower agent to regulate the interagent communication at each sampling instant. Then, we propose a distributed formation tracking protocol based on the triggered sampled information such that the formation tracking control problem can be formulated as a stability-analysis problem of the closed-loop formation error dynamics. The event generator and formation tracking controller gains can then be co-designed using the feasible linear matrix inequality conditions that are derived from Lyapunov-based stability-analysis methods that guarantee the ultimate boundedness of the closed-loop formation error dynamics. Finally, numerical simulations along with experiment implementations were conducted for a group of linearized unicycle-type mobile robots to demonstrate the effectiveness and advantages of the proposed method.

Active Disturbance Rejection Formation Tracking Control for Uncertain Nonlinear Multi-Agent Systems With Switching Topology via Dynamic Event-Triggered Extended State Observer

In this paper, the time-varying formation tracking (TVFT) control problem is concerned for multi-agent systems (MASs). The primary objective is to achieve asymptotical convergence for formation tracking error subject to nonparametric and nonvanishing uncertainties. Firstly, in order to estimate lumped unmodeled dynamics and external disturbances, an event- triggered fuzzy extended state observer (FESO) inspired by our previous works is established for follower group, in which efficient nonlinear observation pattern and convenient linear numerical tractability are integrated. For rationally scheduling transmission, a dynamic event-triggered mechanism is applied to form adaptively regulating strategy. Secondly, a distributed TVFT control law is developed by utilizing neighborhood formation tracking errors. Different from conventional disturbance-tolerant methodologies, total disturbance compensation is introduced to attenuate uncertainty influence in real time. Consequently, active disturbance rejection formation tracking control architecture is systematically constructed for uncertain MASs. Moreover, considering switching topology, the controller design algorithm is presented by piecewise Lyapunov analysis. Finally, the effectiveness and advantages of the proposed event-triggered FESO-based active disturbance rejection control protocol is illustrated by an numerical example on unmanned aerial vehicle swarm system.

Robust Saturated Formation Tracking Control of Multiple Quadrotors With Switching Communication Topologies

This article deals with distributed formation control for a set of quadrotors subject simultaneously to external disturbances and switching communication topologies. The proposed robust controller incorporates position and attitude control laws for each quadrotor. Both control laws have a nominal part for trajectory tracking and a robust part that compensates for the dynamic model uncertainties and time-varying external disturbances. The devised controller guarantees that the thrust force is bounded with respect to the position error by utilizing saturation functions. The directed communication topology among the quadrotors is considered to be switchable. The formation control performance is guaranteed under switching topologies, and it is demonstrated that all error terms, in closed-loop, converge to a ball centered at the origin with an arbitrarily small radius, achieving uniformly ultimate boundedness. Finally, the performance of the proposed strategy is validated through numerous simulation and experimental examples.

Fault-Tolerant Time-Varying Formation Tracking Control for Multi-Agent Systems With Actuator Faults and Switching Topologies

Fault-Tolerant Time-Varying Formation Tracking Control for Multi-Agent Systems With Actuator Faults and Switching Topologies

Formation Tracking Control for Multi-Agent Systems with Collision Avoidance and Connectivity Maintenance

This paper investigates the formation tracking control of multiple agents with a double-integrator model and presents a novel distributed control framework composed of three items: a potential-based gradient term, a formation term, and a navigation term. Considering the practical situation, each agent is regarded as a rigid-body with a safe radius and a sensing region. To enable collision avoidance and connectivity maintenance among multiple agents, a new potential function with fewer parameters is established. The predetermined formation is also achieved by taking the difference between the actual displacement and the desired displacement as a consensus variable. Lastly, the virtual navigator provides trajectory signals and guides the multiple agent movement. Two instances of an equilateral triangle formation and a hexagonal formation are used in the simulation to verify the proposed method.

Leader-Following Formation Tracking Control of Nonholonomic Mobile Robots Considering Collision Avoidance: A System Transformation Approach

In this paper, the obstacle avoidance problem-based leader–following formation tracking of nonholonomic wheeled mobile robots with unknown parameters of desired trajectory is investigated. First, the under-actuated system is transformed into a fully-actuated system by obtaining an auxiliary control variable using the transverse function. Second, by introducing a potential function for each obstacle, the influence of obstacles is considered in trajectory tracking, and the effect of the potential field on mobile robots is taken into account in the system tracking error. Third, the adaptive laws are designed to estimate the unknown parameters of the desired trajectory. Fourth, the results show that the formation error with respect to the actual position and orientation can be arbitrarily small by selecting appropriate design parameters. Finally, simulation examples are used to demonstrate that the proposed control scheme is effective.

A Multilayer Graph for Multiagent Formation and Trajectory Tracking Control Based on MPC Algorithm.

This article studies the formation and trajectory tracking control of multiagent systems. We present a novel multilayer graph for the multiagent system to enable extensibility of the interaction network. Based on the multilayer graph, a formation control law by using the potential function approach is developed for autonomous formation, formation maintenance, collision, and obstacle avoidance. When the desired formation is achieved, the barycentric of the formation shape is viewed as a virtual leader, and a model predictive control (MPC) scheme is applied to the virtual leader for tracking a reference trajectory; meanwhile, the agents will maintain the desired angles and distances via the formation control law. By applying the proposed schemes, the tasks of formation maintenance and trajectory tracking in a constrained space are fulfilled. Comprehensive simulation studies under different environmental constraints and trajectories confirm the effectiveness of the proposed approaches in addressing the formation and trajectory tracking problems.

Active disturbance rejection formation control for multi-agent systems with multiple leaders

An active disturbance rejection formation tracking problem is studied herein. Aiming at the time-varying formation tracking problem with external disturbance, a distributed control strategy of formation tracking based on extended state observer is presented. Considering the unknown state and external disturbance of single agent, a special extended state observer is produced which uses the output of neighbors. Subsequently, the extended state observer output–based formation protocol is designed to implement a predetermined formation. In addition, the necessary and sufficient condition of formation tracking control is obtained by taking full advantage of matrix transformation and Lyapunov theory. In the end, there are three simulation instances to verify the validity and feasibility of this method, which is mentioned in this article.

Multiple leaders formation tracking with switching topology and aperiodic sampled data under intermittent control scheme

AbstractThis article studies the problem of second‐order formation tracking with multiple leaders under intermittent control scheme in stochastic multi‐agent networked systems. Based on the aperiodic sampled data, the formation tracking control protocol is proposed by considering switching topology and the time‐varying transmission delay of information interaction between each agent. Using the algebraic graph theory, stochastic systems theory, Lyapunov theory, and Halanay inequality, the sufficient conditions of mean square stability for formation tracking with multiple leaders are obtained. To further alleviate the computation resources of the controller, the intermittent control strategy is proposed. Meanwhile, a novel stability analysis method for intermittent control is introduced based on an auxiliary system and comparison principle. Furthermore, the lower bound of the duty cycle for a certain control period is obtained and the desired formation mode is also reached under the designed intermittent control scheme. Finally, numerical examples are given to verify the correctness and effectiveness of the proposed methods.

Collision-free formation tracking control for multiple quadrotors under switching directed topologies: Theory and experiment

Multiple quadrotors are becoming increasingly attractive in many fields, and the formation tracking control of multiple quadrotors is the foundation for performing complex tasks. In this paper, the collision-free formation tracking control problem for multiple quadrotors under switching topology is studied, and the leader has the control command, which is unknown to the followers. A formation tracking control protocol is firstly constructed utilizing local neighboring information, in which the neighbors of the quadrotors can change. Then, inspired by the spring-damping system, a collision avoidance mechanism based on Hooke's law with damping is proposed to avoid collision of multiple quadrotors in a cluttered flight. By using the Lyapunov based stability analysis, it is proved that multiple quadrotors can track the dynamic leader in a dynamic formation using the proposed protocol under formation feasibility and the existence of spanning trees in communication topology. Finally, a lightweight communication protocol is designed in the experimental platform. Several groups of visual simulations are carried out based on the Gazebo simulator. The proposed method is compared with two potential field methods in two scenarios through quantitative studies of task efficiency and error analysis. Overall, the completion time is improved by 86.02% and 31.98%, and the minimum tracking error is improved by 57.24% and 46.20% in scenario 1. The completion time is improved by 86.88% and 30.34%, and the minimum tracking errors are improved by 82.20% and 42.62% in scenario 2. Outdoor experiments on formation tracking are performed to verify the effectiveness of the proposed methods. Furthermore, several outdoor experiments are conducted in the same scenarios to validate the proposed algorithm.

Adaptive Distributed Sliding Mode Control for Multiple Unmanned Aerial Vehicles With Prescribed Performance

In this article, the formation tracking control problem with prescribed performance is studied for multiple unmanned aerial vehicles whose disturbance is bounded with unknown boundary. Different from most existing works where prescribed performance control is realized based on error transformation, a new prescribed performance function-based adaptive strategy is proposed to guarantee both transient and steady state performance, which simplifies the design procedure. Furthermore, the proposed adaptive distributed sliding mode controller is of low complex and easily implementable, without utilizing the information of the external disturbance or any approximating structures to acquire such knowledge. Additionally, collision avoidance constraints among neighbors can be satisfied through appropriately designed performance bounds. Simulation verification also confirms the effectiveness of the proposed approach.

Formation tracking control design for uncertain artificial swarm systems under inequality constraints: Leakage and dead-zone type

The paper proposes a formation tracking control method for the uncertain artificial swarm systems under the inequality constraints. Not only can the agents perform swarm behaviors (e.g., convergence, formation and avoidance of collision), but they can also track the fixed targets in a constrained area (which is formulated as the inequality constraints, such as unilateral constraint and bilateral constraint.). The swarm behaviors are creatively considered as the servo constraints or the control objectives for the swarm agents. Based on the Udwadia–Kalaba (U–K) equation, those prescribed behaviors are realized by a model-based control design (that is the servo constraints force model-based feedforward control). To deal with the inequality constraints in the formation tracking process, a differential homeomorphism transformation is used to relieve the environmental constraints for the swarm agents. Moreover, the uncertainty of the swarm agents (i.e., the parameter uncertainty in modeling and the external disturbances) is considered, which is time-varying and unknown (but bounded). An uncertainty estimation method with dead-zone and leakage term is designed to calculate the possible upper bound of the uncertainty. In virtue of the estimated upper bound of the uncertainty, a robust control is designed for the uncertain swarm agents to obey the prescribed swarm behaviors in the formation tracking task. The system performances of the artificial swarm systems under the proposed control are theoretically guaranteed by a range of rigorous theorems and numerically verified by the simulations of three agents.