Formation Tracking Control Research Articles

Distributed formation tracking with connectivity preservation and orientation alignment

This paper investigates the formation tracking problem incorporating connectivity preservation and orientation alignment for multi-agent systems. Consider the body-fixed frame of each agent in the multi-agent system is initialized with different orientations. To achieve formation controller design by relative position in the body-fixed frame, the orientation of the frames should be aligned first. A distributed passive-based orientation controller is proposed to ensure convergence of all body-fixed frames toward a unified desired orientation. Once the frames are aligned, a barrier Lyapunov function (BLF)-based formation tracking controller is proposed utilizing the displacement of the agent to ensure the distances between agents always satisfy predefined distance constraints. This strategy guarantees inter-agent collision avoidance and connectivity preservation throughout the formation. Numerical simulations are conducted to validate the efficacy of the proposed approach.

Observer-based leader-centric time-varying formation tracking control for nonlinear multi-agent systems with collision avoidance

The article introduces a novel control design methodology to achieve leader-centric time-varying formation tracking (TVFT) with collision avoidance in Lipschitz nonlinear multi-agent systems (MASs) equipped with a leader-driven formation system. This methodology addresses challenges such as actuator bias faults and leader maneuvering within this MASs setup. It employs two control schemes: collision avoidance and a novel formation observer-based time-varying formation tracking (FO-based TVFT) control. These control schemes work in tandem. The collision avoidance scheme ensures safe operation by preventing inter-agent collisions, while the novel FO-based TVFT control scheme enables followers to achieve leader-driven formations while tracking the leader’s movements. To achieve this capability, each follower employs a formation observer (FO) that continuously estimates the leader’s dynamically driven formations throughout runtime, facilitating responsive formation tracking by the followers. Notably, this FO-based TVFT control scheme establishes a novel framework for integrated leader-driven formation switching and leader tracking (i.e., leader-centric TVFT) in MASs. Furthermore, this control methodology is specifically designed for Lipschitz nonlinear MASs susceptible to challenges like actuator bias faults and leader maneuvering. It guarantees that the followers’ collective formation tracking error is uniformly ultimately bounded (UUB), based on Lyapunov’s stability theory. Finally, an illustrative example validates the proposed approach’s effectiveness.

Resilient Time-Varying Formation Tracking Control for General Linear Multiagent Systems With a Nonautonomous Leader and Adversarial Followers.

This article is concerned with resilient formation tracking problems for general linear multiagent systems, where the leader's control input is unavailable to all the followers and partial followers' behaviors are malicious due to the node attacks. Despite the presence of the nonautonomous leader and the adversarial followers, the remaining benign followers are still expected to track the leader's trajectory with the prescribed time-varying formation. To this end, a resilient scheme comprising an attack detection and isolation strategy and a formation tracking protocol is proposed. The detection strategy enables every benign follower to identify its adversarial neighbors with two-hop communication information, as long as the underlying topology meets given conditions. Then, the detected adversarial agents are directly removed to avoid the spread of their influence, which induces a new problem called node loss. To accommodate possible node loss events, the designed tracking protocol is independent of certain global knowledge, and its convergence is demonstrated by means of the impulsive Lyapunov functions. Finally, the proposed resilient scheme is verified by two simulation examples.

Robust Formation Tracking Control for Noncooperative Heterogeneous Multiagent Systems.

The robust formation tracking problems (FTPs) are investigated for noncooperative heterogeneous multiagent systems (MASs). The parameters and state dimensions of each agent in the MASs can be heterogeneous. The leader is noncooperative and has an unknown external input. The followers are affected by uncertainties and disturbances. A distributed extended state observer is designed to estimate the leader's state and the unknown external input. Then a robust formation tracking control method is proposed. It turns out that the output formation tracking error can reduce to any size neighborhood near the origin by selecting appropriate parameters. Finally, the effectiveness of the proposed observer and controller is demonstrated by a numerical simulation example and a hardware-in-the-loop (HITL) simulation example.

Adaptive Imune Fuzzy Quasi-Sliding Mode Formation Tracking Control for Wheeled Mobile Robots with Obstacle Avoidance Under Incidence of Uncertainties and Disturbances: An Artificial Immune Systems Inspired Approach

This paper presents an adaptive immune fuzzy quasi-sliding mode kinematic control integrated with a PD dynamic control for the trajectory tracking and the leader-follower formation control by nonholonomic differential-drive wheeled mobile robots under incidence of uncertainties and disturbances. An immune regulation mechanism bio-inspired approach with reaction effect established by novel fuzzy rules set to adjust the control effort adaptively is designed, also using a fuzzy boundary layer and introducing an adaptation law for the immune portion gain online adjustment in such a way that they can also avert parameter drift, dealing with the drawbacks of a classic first-order sliding mode control, suppressing chattering and still maintaining the robustness with no a priori knowledge of the bounds of the disturbances. An obstacle avoidance strategy with a reactive method and variable avoidance radius is also proposed. The stability analysis is performed based on the Lyapunov theory. Simulation results demonstrate the proposed control effectiveness.

Prescribed Performance Formation Tracking Control for Underactuated AUVs under Time-Varying Communication Delays

Achieving formation tracking control of underactuated autonomous underwater vehicles (AUVs) under communication delays presents a significant challenge. To address this challenge, a distributed prescribed performance control protocol based on a real-time state information online predictor (RSIOP) is proposed in this paper. First, we innovatively designed an RSIOP to achieve active compensation for the delayed state information of neighboring AUVs. Next, considering formation performance and safety, a low-complexity and practical nonlinear mapping function was used to implement prescribed performance tracking control for the AUV formation. Additionally, the adverse effects of external disturbance uncertainties and input saturation are also considered. Finally, the simulation tests demonstrated that the proposed formation control protocol can successfully achieve the predetermined formation tracking tasks in the presence of time-varying communication delays and external disturbances, while also enabling real-time changes in formation configuration during the process. Throughout, the protocol maintains input saturation limits, and the actual control inputs remain smooth, with no significant oscillations. Furthermore, comparative simulation tests verified the necessity of the RSIOP developed in this study and quantitatively demonstrated that the proposed control method exhibits superior performance in terms of formation control accuracy, error convergence speed, and transient-state constraints.

Finite-time hybrid impulsive formation tracking control of multi-agent systems via aperiodic intermittent communication

This article studies the problem of formation tracking control in multi-agent systems, achieved in finite time, under challenging conditions such as strong nonlinearity, aperiodic intermittent communication, and time-delay effects, all within a hybrid impulsive framework. The impulses are categorized as either stabilizing control impulses or disruptive impulses. Furthermore, by integrating Lyapunov-based stability theory, graph theory, and the linear matrix inequality (LMI) method, new stability criteria are established. These criteria ensure finite-time intermittent formation tracking while considering weak Lyapunov inequality conditions, intermittent communication rates, and time-varying gain strengths. Additionally, the approach manages an indefinite number of impulsive moments and adjusts the control domain’s width based on the average impulsive interval and state-dependent control width. Numerical simulations are provided to validate the applicability and effectiveness of the proposed formation tracking control protocols.

Formation Tracking Control of the Traffic Cone Robots System Under the Environmental Constraints

Formation Tracking Control of the Traffic Cone Robots System Under the Environmental Constraints

Complex Laplacian approach for formation tracking without velocity measurements

This paper is focused on formation tracking control of multi-agent systems in a leader–follower setting. The objective is to introduce control algorithms to steer a team of mobile agents into a desired, moving geometrical pattern while the agents are unaware of their own and other agents' velocity information during the entire process. We introduce a formation control law under which the agents asymptotically shape a desired geometrical pattern and track a constant reference velocity. Another control law is then introduced to address the case where the reference velocity is time-varying. Both control laws are based on the complex Laplacian approach and do not require agents' velocity information. The convergence of these algorithms are proved and their performance are examined via numerical examples. Simulation results verify the outperformance of the proposed control laws compared to the rival control schemes in the literature.

Distributed Active Disturbance Rejection Formation Tracking Control for Quadrotor UAVs.

In this article, a distributed active disturbance rejection formation tracking control strategy is developed for a quadrotor unmanned aerial vehicle (UAV) swarm system with switching communication topologies. The proposed control strategy consists of two parts: 1) attitude-loop control and 2) position-loop control. First, a distributed cascade active disturbance rejection control (CADRC) method is designed for the attitude subsystem. With this attitude control method, the stability of the attitude subsystem can be achieved even in the presence of unknown time-varying disturbances. Second, a distributed formation tracking control method is designed for the position subsystem. This position control method ensures that the quadrotor UAV swarm maintains dynamic formation flying and accurately tracks a predetermined trajectory. Through stability analysis, it can be proved that the proposed control strategy can ensure the stability of the whole swarm system. Finally, the proposed control strategy is applied to a quadrotor UAV swarm system to verify its effectiveness and the ability to suppress the influence of unknown time-varying disturbances.

Disturbance-Observer-Based Adaptive Prescribed Performance Formation Tracking Control for Multiple Underactuated Surface Vehicles

This study proposes a new disturbance-observer-based adaptive distributed formation control scheme for multiple underactuated surface vehicles (USVs) subject to unknown synthesized disturbances under prescribed performance constraints. A modified sliding mode differentiator (MSMD) is applied as a nonlinear disturbance observer to estimate unknown synthesized disturbances, which contain unknown environmental disturbances and system modelling uncertainties, thus enhancing the robustness of the system. Based on this, we impose the time-varying performance constraints on the position tracking error between the neighboring USVs. A novel differentiable error transformation equation is embedded in the prescribed performance control, and an adaptive prescribed performance controller is constructed by employing the backstepping method to ensure that the position tracking error remains within the prescribed transient and steady performance, and each USV realizes collision-free formation motion. Furthermore, a novel second-order nonlinear differentiator is introduced to extract the derivative information of the virtual control law. Finally, the numerical simulation results verify the effectiveness of the proposed control scheme.

Formation Planning for Tethered Multirotor UAV Cooperative Transportation With Unknown Payload and Cable Length

This study investigates the formation planning problem of tethered multirotor unmanned aerial vehicle (UAV) cooperative transportation with unknown payload and cable length. Normally, the transportation formation and trajectory are given in advance or designed based on the coupled system model. It is challenging to dynamically generate flexible formations in response to changing environments when the payload and cable length are unknown. This paper proposes an online formation planning method for multirotor UAVs. First, by analyzing the tension on cables, we propose some formation criteria and further construct a corresponding performance function of optimization. Then, desired trajectories/formations that can reduce the cost functions are generated by using the admittance model. Next, an estimation-based formation tracking control is designed, which ensures that multirotor UAVs follow the desired trajectories/formations. Finally, numerical simulations and experiments are conducted to demonstrate the effectiveness of the proposed method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper is motivated by the formation planning problem of tethered multirotor UAV cooperative transportation. In industry and production applications, a team of multirotor UAVs has a larger load capacity than a single one. Nevertheless, the formation planning of the tethered cooperative transportation is challenging, especially when the payload and cable length are unknown. Rather than give a predefined formation or trajectory, this paper suggests an online formation planning method for multirotor UAVs in case of unknown payload and cable length. The method is implemented through the following three parts: 1) By analyzing the tension on cables, we propose some formation criteria and further construct a corresponding performance function of optimization. 2) By using the admittance model, we generate desired trajectories/formations that can minimize the proposed cost function. 3) By estimating cable tension, we design formation tracking control laws for multirotor UAVs to follow the desired trajectories/formations. The proposed formation planning method does not rely on the knowledge of the payload and length of cables, which makes it can be easily applied to extensive industry, production, and military practice. Finally, numerical simulations and experiments are conducted to demonstrate the feasibility of the proposed method.

Predefined-Time Bipartite Time-Varying Formation Tracking Control of Networked Autonomous Surface Vehicles via Hierarchical Control Approach

Predefined-Time Bipartite Time-Varying Formation Tracking Control of Networked Autonomous Surface Vehicles via Hierarchical Control Approach

Time-Varying Formation Tracking Control of Multi-Leader Multiagent Systems With Sampled-Data

In this paper, the time-varying formation tracking (TVFT) problem of multi-leader multi-agent systems (MASs) under sampled-data control is studied. First, an improved TVFT criterion is derived by employing a general looped-functional and a zero integral functional. Then a new TVFT controller is designed based on our proposed method. Unlike the existing works, the TVFT controller can allow for bigger sampling intervals of multi-leader MASs. The results demonstrate that the states of the followers can form the designated formation and rotate around the convex combination formed by the multiple leaders. In addition, we generalize the results of TVFT to the sampled-data consensus for MASs, a sampled-data consensus controller which can reduce communication consumption is designed. Meanwhile, the values of the allowable maximum sampling intervals (AMSIs) are calculated. Finally, the superiority and availability of the theoretical results are verified by two simulation experiments. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The motivation of this paper is to address the problem of TVFT for MAS with multiple leaders. It has been applied to several practical engineering systems, e.g., satellite formation control and unmanned air vehicles (UAVs) formation control. Note that information exchange is a prerequisite to ensure safe and stable control of multi-UAV formation. However, continuous-time communication is difficult to be realized in the actual environment, and it will inevitably consume a lot of energy. In addition, sampled-data controller for MAS with a small sampling interval may cause network congestion. Therefore, a sampled-data controller which allows for a bigger sampling interval for MAS is designed to save network resources in this paper. Through simulation experiments, it can be proved that the followers not only track the leaders, but also form the designated formation.

Formation tracking control in open multiagent systems with general linear dynamics

This paper studies the formation tracking problem of the so-called open multiagent systems. In these systems, agents can freely join or leave at any time, i.e. the system sizes are changeable. To achieve formation tracking control in these systems, we propose a general theoretical analysis framework that consists of a formation adjustment strategy and a formation tracking protocol. Therein, the former is used to adjust the predefined task-oriented formation shape to the varying size of the system. This strategy is built on the existing scalable self-healing idea and then modified by a size estimation method. The latter is used to drive the present followers to form the adjusted formation and track a leader. To accommodate undirected and directed graphs, two distributed formation tracking protocols are designed respectively. Due to possible agent migration, the designed tracking protocols are endowed with self-adaptive ability, i.e. without depending on global topology information. Then, their convergence properties are analysed using the Lyapunov theory. Finally, two simulations are presented to verify the effectiveness of the proposed framework.

Adaptive Formation Tracking Control of Multiple Vertical Takeoff and Landing UAVs With Bearing-Only Measurements.

This article studies the leader-following formation tracking control problem of multiple vertical takeoff and landing (VTOL) unmanned aerial vehicles (UAVs) subject to uncertain parameters, in which the target formation configuration is defined by using the interneighbors' bearing vectors. An adaptive formation control algorithm with bearing-only measurements is proposed under a hierarchical control framework. More specifically, a saturated adaptive distributed control force is developed in the position loop with bearing-only measurements. Since the bearing vectors with respect to the neighbors can be directly measured by low-cost onboard cameras, the proposed formation algorithm can be implemented without interagent communication. Subsequently, in the attitude loop, an adaptive hybrid control scheme via two modified Rodrigues parameters (MRPs) sets is proposed, which achieves the command attitude tracking globally and also avoids the unwinding problem of MRPs. Based on the Lyapunov stability analysis and hybrid theory, we prove that the overall closed-loop error system is globally asymptotically stable. Finally, we provide a numerical example to demonstrate the effectiveness of the proposed control algorithm.

Formation tracking control with disturbance rejection in leader-follower multi-agent systems under dynamic event-triggered mechanism

This paper investigates the problem of time-varying formation tracking (TVFT) in a linear multi-agent systems (MASs) with external disturbance in a type of directed network topology, and proposes a formation control strategy in a leader-follower control framework with disturbance rejection under a dynamic event-triggering mechanism (DETM). Firstly, in order to improve the overall performance of the system, an extended state observer is used to estimate the status of the follower and the presence of external disturbance in real time. Secondly, a DETM is designed to avoid continuous communication between adjacent intelligent agents. And the formation tracking error between adjacent multi-agents is used to formulate a distributed TVFT control strategy. Furthermore, a compensation function is designed to actively offset the impact of time-varying disturbances on system. A Lyapunov function is then established for stability analysis, verifying the absence of Zeno behavior with this DETM. Finally, a comparative numerical simulation was conducted using an unmanned aerial vehicle (UAV) cluster case to verify that the proposed method can save communication resources to a greater extent and has good control performance.

Edge-Based Communication-Triggered Formation Tracking Control With Application to Multiple Mobile Robots

Edge-Based Communication-Triggered Formation Tracking Control With Application to Multiple Mobile Robots

Fully Data-Driven Robust Output Formation Tracking Control for Heterogeneous Multiagent System With Multiple Leaders and Actuator Faults.

This article investigates a fully data-driven method to solve the robust output formation tracking control problem for the multiagent system (MAS) under actuator faults. The outputs of the followers are controlled to track those of multiple leaders with respect to a convex point while achieving an expected time-varying formation. To obviate the requirement of various system prior knowledge in typical MAS control, a hierarchical frame is developed with three learning and control stages using the online measured data. First, a distributed adaptive observer is designed to coordinate the state convex of multiple leaders while estimating unknown dynamics. The adaptive mechanism relaxes the demand for global topology. Second, by collecting and reusing the online system data, an off-policy reinforcement learning (RL) method is proposed in a continuous form to acquire nominal feedback gains from partial observations of the followers. Essential system models are learned along with the RL process, while solutions to the output regulation equations are implicitly obtained. Third, a comprehensive robust controller is further presented based on the previous learning results. To address the actuator faults with efficiency loss and bias, the adaptive neural networks and robust compensations are utilized in a model-free manner. The output formation tracking is achieved under a derived feasibility condition while stabilities of the learning and control methods are analyzed. Finally, simulation results demonstrate the validity of this fully data-driven control frame.

Distributed prescribed-time cooperative formation tracking control of networked unmanned surface vessels under directed graph

To investigate the formation tracking control problem of networked unmanned surface vessels (USVs) under a directed graph, this article provides a prescribed-time distributed cooperative formation tracking control scheme that specifies tracking error convergence time in advance. Firstly, aiming at the unknown state of the leading USV, a distributed prescribed-time state observer is designed for the following USVs, which can quickly and accurately estimate the position and speed of the leading USV in a prescribed time. Then, based on the state observer, the prescribed-time sliding surface is designed, and the prescribed-time cooperative formation tracking controller is constructed using the prescribed-time sliding mode surface. In addition, a fast adaptive compensation law is developed to mitigate the issue of input saturation. The analysis based on Lyapunov theory displays that the upper bounds of the convergence time of the observer, the sliding mode surface, and the controller proposed in this study explicitly exist in the controller parameters, so they can be easily adjusted in the control design process and are not restricted by the initial state. Finally, the simulation results demonstrate that the proposed approach exhibits high reliability and effectiveness.