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Keywords = leader-following tracking

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34 pages, 37899 KB  
Article
Research on a Tracking Control Method Assisted by Visual Targets in the Autonomous Navigation Task of a Split Drilling Robot
by Shaoze You, Chaoquan Tang, Menggang Li and Yufeng Duan
Appl. Sci. 2026, 16(12), 5929; https://doi.org/10.3390/app16125929 - 11 Jun 2026
Viewed by 158
Abstract
Split-type robots are increasingly deployed in unstructured confined environments such as underground coal mines, where autonomous navigation and cooperative tracking control remain critical challenges. This paper presents a visual target-assisted tracking control scheme for a split-type drilling robot, adopting an active leader–passive follower [...] Read more.
Split-type robots are increasingly deployed in unstructured confined environments such as underground coal mines, where autonomous navigation and cooperative tracking control remain critical challenges. This paper presents a visual target-assisted tracking control scheme for a split-type drilling robot, adopting an active leader–passive follower architecture. The leader robot performs autonomous mobility and obstacle avoidance using 3D LiDAR-based offline path generation and online optimal search. The follower robot uses AprilTag visual fiducial markers to estimate the six-degree-of-freedom relative pose via the Perspective-N-Point algorithm, and it tracks the leader using a two-dimensional fuzzy PID controller that adaptively tunes PID parameters. Extensive experiments are conducted in simulation, simulated tunnels, a large-scale robot platform, and a real drilling robot prototype. Results demonstrate that the leader achieves an average navigation error below 0.175 m, while the follower maintains an average relative tracking error within 0.06 m. The proposed method enables stable, comparable accuracy with smoother, less oscillatory response, and high-precision cooperative navigation for heavy-duty split-type robots, offering a practical solution for intelligent drilling operations in underground confined spaces. Full article
(This article belongs to the Topic Fuzzy Optimization and Decision Making)
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24 pages, 4438 KB  
Article
Dynamic Self-Organization and Safe Navigation for Hierarchical Embodied Swarms
by Lanbo Wu and Chen Wei
Drones 2026, 10(6), 453; https://doi.org/10.3390/drones10060453 - 10 Jun 2026
Viewed by 318
Abstract
This paper is concerned with cooperative multi-UAV navigation in a planar obstacle environment. A hierarchical embodied swarm framework with leader, subleader, and follower roles is proposed. At the high level, a passable-corridor-driven decision layer is developed to perform split–merge reconfiguration and navigate/encircle mode [...] Read more.
This paper is concerned with cooperative multi-UAV navigation in a planar obstacle environment. A hierarchical embodied swarm framework with leader, subleader, and follower roles is proposed. At the high level, a passable-corridor-driven decision layer is developed to perform split–merge reconfiguration and navigate/encircle mode switching. At the low level, a multi-term force synthesis controller is constructed for formation maintenance, inter-agent collision avoidance, obstacle avoidance, and sub-swarm cohesion. To accommodate both rule-based and local large language model (LLM) decisions, a feasibility projection operator is introduced so that only kinematically admissible structural actions are executed. In addition, a LiDAR-based obstacle-repulsion term and an occlusion-attenuated attraction mechanism are incorporated to improve navigation safety in cluttered environments. A Lyapunov analysis of the smooth controller core further certifies that, for a known (possibly time-varying) cruise velocity compensated by feedforward, the formation tracking error is uniformly bounded by the initial energy. Finally, multi-seed numerical simulations verify the proposed framework in standard, ablated, and complex scenarios. In the hardest alternating-gate scenario, the LLM-assisted variant raises mission success from 0.000 to 0.100, increases the goal-reaching ratio from 0.025 to 0.125, and reduces the mean terminal error from 44.738m to 39.851m, showing the value of semantic high-level reconfiguration under tight passage constraints. Full article
(This article belongs to the Special Issue UAV Swarm Intelligent Control and Decision-Making)
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31 pages, 21714 KB  
Article
Distributed Formation Control Method with Hierarchical Leader–Follower Architecture and Repulsive Function-Based Obstacle Avoidance for UAV Formation Flight
by Jaewan Choi and Younghoon Choi
Aerospace 2026, 13(6), 526; https://doi.org/10.3390/aerospace13060526 - 4 Jun 2026
Viewed by 180
Abstract
In modern battlefields, the rapid advancement of Counter-UAV (C-UAV) technologies has made single-UAV missions increasingly difficult. This highlights the need for distributed swarm systems that can operate reliably under such threats. Among various swarm coordination methods, hierarchical leader–follower structures have been actively studied [...] Read more.
In modern battlefields, the rapid advancement of Counter-UAV (C-UAV) technologies has made single-UAV missions increasingly difficult. This highlights the need for distributed swarm systems that can operate reliably under such threats. Among various swarm coordination methods, hierarchical leader–follower structures have been actively studied for battlefield environments with high risk of agent loss and limited communication. The Virtual Leader-based Formation System (VLFS), which follows this structure, enables formation through a virtual leader. It also introduces a novel collision avoidance approach that allows followers to avoid obstacles during formation flight. However, the conventional VLFS suffers from long convergence time with severe oscillations. In addition, it does not consider inter-UAV collisions and has demonstrated avoidance only in simple obstacle environments. To address these limitations, this paper proposes the VLFS-RF method, which directly integrates a repulsive function into the VLFS. The proposed method consists of four control modes that perform formation tracking, inter-UAV collision avoidance, and obstacle avoidance simultaneously according to the situation. Software-In-The-Loop (SITL) simulations were conducted in a ROS-Gazebo environment using V-shaped and hexagonal formations. The results show that the formation tracking error is reduced by approximately 59% compared to the conventional VLFS. In addition, inter-UAV collisions are prevented during initial convergence, and obstacles are successfully avoided in narrow passages and gaps between two obstacles. These results demonstrate that VLFS-RF is a practical formation control method for UAV swarms in complex environments. Full article
(This article belongs to the Section Aeronautics)
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30 pages, 2291 KB  
Article
Cluster Target Tracking Based on Multi-Sensor Adaptive GLMB Filter
by Zheng Zhang, Daozhi Wei and Xirui Xue
Sensors 2026, 26(11), 3559; https://doi.org/10.3390/s26113559 - 3 Jun 2026
Viewed by 276
Abstract
In complex detection environments, unknown detection probability and clutter rate hinder accurate tracking of cluster targets. To address this issue, this paper proposes a novel multi-sensor adaptive generalized labeled multi-Bernoulli (MS-AGLMB) filter. Specifically, we consider interactions among cluster members and adopt a virtual [...] Read more.
In complex detection environments, unknown detection probability and clutter rate hinder accurate tracking of cluster targets. To address this issue, this paper proposes a novel multi-sensor adaptive generalized labeled multi-Bernoulli (MS-AGLMB) filter. Specifically, we consider interactions among cluster members and adopt a virtual leader–follower model to describe cluster kinematics. Given unknown environmental parameters, we employ an adaptive cardinalized probability hypothesis density (CPHD) filter to estimate the detection probability and clutter rate in real time. Furthermore, we use Gibbs sampling to efficiently truncate GLMB association hypotheses, obtaining the posterior density and solving the multi-sensor measurement partitioning problem. A joint prediction and update strategy enables simultaneous estimation of target trajectories, detection probability, clutter rate, and cluster structure. Simulation results demonstrate that the proposed algorithm achieves greater robustness in scenarios with time-varying detection probability and clutter rate, outperforming comparison filters in cluster target tracking. Full article
(This article belongs to the Section Physical Sensors)
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28 pages, 7955 KB  
Article
Task-Heterogeneous Formation Planning and Control for Unmanned Surface Vehicles Based on Hybrid Deep Reinforcement Learning
by Yawen Zhang, Wenkui Li, Chenyang Shan, Haoyu Bu and Bing Han
J. Mar. Sci. Eng. 2026, 14(10), 959; https://doi.org/10.3390/jmse14100959 - 21 May 2026
Viewed by 190
Abstract
To address the control coupling challenges arising from task heterogeneity of unmanned surface vehicle (USV) formation, a distributed hybrid deep reinforcement learning (HDRL) framework is proposed. The framework decomposes the formation task into two subtasks: leader path planning using the single-agent deep reinforcement [...] Read more.
To address the control coupling challenges arising from task heterogeneity of unmanned surface vehicle (USV) formation, a distributed hybrid deep reinforcement learning (HDRL) framework is proposed. The framework decomposes the formation task into two subtasks: leader path planning using the single-agent deep reinforcement learning (SADRL) algorithm and follower formation tracking using the multi-agent deep reinforcement learning (MADRL) algorithm. By embedding the physical constraints of the real Otter USV into the training loop, the policy network outputs are mapped to propeller revolutions that conform to its dynamic characteristics. To optimize control performance, a dynamic gating mechanism triggered by formation position error is developed to mitigate multi-objective interference through temporal task scheduling. Concurrently, a mirror mapping mechanism leveraging the physical symmetry of the formation is designed to achieve policy sharing and data augmentation. Furthermore, the desired velocity calculated based on rigid-body kinematics is used to achieve kinematic-compensated formation tracking. The simulation results indicate that, compared to the SADRL algorithm, the planning success rate of HDRL is improved by 44.59%. Furthermore, compared to the MADRL algorithm, the integrated tracking performance is enhanced by 21.79–39.64%. Full article
(This article belongs to the Section Ocean Engineering)
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39 pages, 10477 KB  
Article
A Multilayer Decision-Making Method for UAV Formation Cooperative Flight in Complex Urban Environments
by Junjie Wang, Dongyu Yan, Yongping Hao and Han Miao
Sensors 2026, 26(10), 3245; https://doi.org/10.3390/s26103245 - 20 May 2026
Viewed by 377
Abstract
To address the challenges of dynamic obstacles, limited perception, and multi-UAV coordination constraints in complex urban environments, a hierarchical control framework based on a virtual leader-follower architecture is proposed, covering global planning, local obstacle avoidance, and formation coordination. In the global planning layer, [...] Read more.
To address the challenges of dynamic obstacles, limited perception, and multi-UAV coordination constraints in complex urban environments, a hierarchical control framework based on a virtual leader-follower architecture is proposed, covering global planning, local obstacle avoidance, and formation coordination. In the global planning layer, a dynamic adaptive strategy rapidly exploring random tree star (DASRRT*) algorithm is proposed. To address the low sampling efficiency and limited path extension in dense environments that affect traditional RRT*, a hybrid guided sampling strategy, inefficient node optimization strategy, and perception-based adaptive step size strategy are designed. Additionally, a multi-objective cost function is introduced to provide smoother trajectories that better comply with dynamic constraints for trajectory tracking. In the local obstacle-avoidance layer, a distributed controller is constructed based on an improved artificial potential field method, integrating collision avoidance control laws derived from a spring-damper model, dynamic obstacle-avoidance laws that account for obstacle velocities, and formation coordination control laws grounded in consensus theory. In the coordination control layer, a real-time local target selection strategy is established to guide the virtual leader to precisely track the global path, and a dual-mode switching mechanism based on environmental complexity is constructed to dynamically adjust the priority between formation maintenance and autonomous obstacle-avoidance tasks. Comparative experimental results show that the proposed DASRRT* algorithm reduces path planning time by an average of 34.78% and shortens path length by 1.15%. Simulation results for formation flight demonstrate that the proposed hierarchical control framework can adaptively adjust control modes in response to changes in environmental complexity, exhibiting strong adaptability to complex environments and a good ability to generalize to various scenes. Full article
(This article belongs to the Section Navigation and Positioning)
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23 pages, 4346 KB  
Article
Rapid Optimization Method for Grid-Forming Energy Storage Systems Frequency Control Based on Leader–Follower Game Strategy
by Yingjun Guo, Yu Qi, Chunxiao Mei, Yanxun Guo, Erhui Zhang, Shuo Zhang and Hexu Sun
Energies 2026, 19(10), 2414; https://doi.org/10.3390/en19102414 - 17 May 2026
Viewed by 311
Abstract
The integration of grid-forming energy storage systems (GFM-ESSs) provides essential support for the stable operation of grid-connected converters in renewable energy systems. However, GFM-ESSs may exhibit low-frequency oscillations in response to grid state variations, posing a threat to power system stability. To address [...] Read more.
The integration of grid-forming energy storage systems (GFM-ESSs) provides essential support for the stable operation of grid-connected converters in renewable energy systems. However, GFM-ESSs may exhibit low-frequency oscillations in response to grid state variations, posing a threat to power system stability. To address this challenge, this paper proposes a fast continuous optimization method for the active power–frequency control loop of multi-VSG-based GFM-ESSs. First, a parameter coupling model for multiple VSGs is established, and an internal parameter decoupling control strategy is proposed. Subsequently, an iterative optimization model based on a gradient-based master–slave game is developed, in which the minimization of converter frequency deviation serves as the leader’s objective, while the minimization of system frequency deviation acts as the follower’s objective. Frequency fluctuations are further mitigated through tracking differentiator-based active power compensation. The effectiveness of the proposed method is validated through simulation with six GFM-ESS units integrated into a modified IEEE 33-node system featuring six renewable energy stations. Simulation results demonstrate that the proposed approach significantly suppresses frequency fluctuations while also reducing the response time and the rate of frequency change under grid disturbance conditions. Full article
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18 pages, 1654 KB  
Article
Predefined-Time Neural Adaptive Control for Distributed Formation Control of Nonlinear Multiagent Systems with Full-State Constraints
by Yuehua Fang, Xuan Yu, Jianhua Zhang, Yichen Jiang and Cheng Siong Chin
Mathematics 2026, 14(10), 1658; https://doi.org/10.3390/math14101658 - 13 May 2026
Viewed by 236
Abstract
This paper investigates the distributed formation control problem for nonlinear multiagent systems subject to full-state constraints and proposes a predefined-time neural adaptive control scheme based on a nonlinear mapping technique. To handle the time-varying asymmetric constraints on system states, a smooth and invertible [...] Read more.
This paper investigates the distributed formation control problem for nonlinear multiagent systems subject to full-state constraints and proposes a predefined-time neural adaptive control scheme based on a nonlinear mapping technique. To handle the time-varying asymmetric constraints on system states, a smooth and invertible nonlinear mapping function is introduced to transform the original constrained states into unconstrained variables, thereby eliminating the dependence on initial conditions typically required by traditional barrier Lyapunov functions. Within this transformed framework, a predefined-time distributed formation control law is developed, which guarantees that all followers converge to the desired formation configuration and track the leader’s trajectory within a user-specified time upper bound, independent of the initial states. Radial basis function neural networks are employed to approximate the unknown nonlinear dynamics of each agent, and adaptive laws are designed to update the network weights online. Theoretical analysis shows that all closed-loop signals remain bounded, the original system states strictly stay within their prescribed constraint boundaries at all times, and the formation tracking errors converge to a small neighborhood of the origin within the predefined time. Numerical simulations validate the effectiveness of the proposed method, demonstrating faster convergence, higher steady-state accuracy, and improved robustness to initial conditions compared to existing control approaches. Full article
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24 pages, 11740 KB  
Article
Hierarchical Target Tracking for Unmanned Aerial Vehicle Swarms with Distributed Optimization and Affine Control
by Han Wang, Xiaolong Liang, Jiaqiang Zhang, Yueqi Hou and Aiwu Yang
Drones 2026, 10(5), 366; https://doi.org/10.3390/drones10050366 - 11 May 2026
Viewed by 514
Abstract
Target tracking of unmanned aerial vehicle (UAV) swarms remains a significant challenge due to highly maneuverable target swarms and complex environments. To address these challenges, a hierarchical target tracking architecture is proposed, comprising a leader layer and a follower layer. This design reduces [...] Read more.
Target tracking of unmanned aerial vehicle (UAV) swarms remains a significant challenge due to highly maneuverable target swarms and complex environments. To address these challenges, a hierarchical target tracking architecture is proposed, comprising a leader layer and a follower layer. This design reduces task complexity while improving formation adaptability and system scalability. In the leader layer, a distributed time-varying optimization model and a distributed protocol are developed to enable the UAV swarm to track highly maneuverable target swarms in real time. In the follower layer, a control protocol based on an affine transformation is employed to enable adaptive formation control under complex environmental constraints (e.g., threat avoidance). Moreover, the convergence performance of the proposed method is rigorously demonstrated through theoretical analysis. Finally, simulation results validate the convergence, feasibility, and scalability of the proposed method. Comparative simulations further demonstrate the superiority of the proposed method. Full article
(This article belongs to the Special Issue UAV Swarm Intelligent Control and Decision-Making)
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32 pages, 2777 KB  
Article
Resilient Leader–Follower Consensus of Fractional-Order Nonlinear Multi-Agent Systems Under Sybil and DoS Attacks via Event-Triggered Adaptive Control
by Muhammad Jabir Khan, Waqar Ul Hassan, Kanikar Muangchoo and Sakulbuth Ekvittayaniphon
Fractal Fract. 2026, 10(5), 315; https://doi.org/10.3390/fractalfract10050315 - 7 May 2026
Viewed by 558
Abstract
This paper investigates the leader–follower consensus problem for fractional-order nonlinear multi-agent systems operating under simultaneous Sybil and Denial-of-Service (DoS) attacks. The communication topology is modeled as a time-varying directed graph with intermittent link failures due to DoS disruptions, while malicious data injection induced [...] Read more.
This paper investigates the leader–follower consensus problem for fractional-order nonlinear multi-agent systems operating under simultaneous Sybil and Denial-of-Service (DoS) attacks. The communication topology is modeled as a time-varying directed graph with intermittent link failures due to DoS disruptions, while malicious data injection induced by Sybil attacks is incorporated into the agent dynamics. In addition, bounded disturbances and time-varying input delays are explicitly considered. To counter these challenges, an event-triggered distributed control framework was developed to reduce communication load while preserving agents’ tracking performance. Furthermore, an adaptive compensation mechanism is introduced to estimate and attenuate the combined effects of cyber attacks and external disturbances. A novel Wirtinger-type fractional integral inequality is established, providing a less conservative tool for constructing Lyapunov–Krasovskii functionals in fractional-order systems. Sufficient conditions for asymptotic leader–follower consensus are obtained in terms of linear matrix inequalities using fractional Lyapunov stability theory. The proposed scheme guarantees the convergence of tracking errors, excludes Zeno behavior through a decaying triggering threshold, and ensures robustness against malicious signal injection and communication interruptions. The results demonstrate that the developed event-triggered adaptive strategy achieves resilient consensus in fractional-order multi-agent systems despite simultaneous cyber attacks at both the network and information layers. Full article
(This article belongs to the Special Issue Advances in Dynamics and Control of Fractional-Order Systems)
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34 pages, 12471 KB  
Article
Neural Network-Augmented Actuation Control System Designed for Path Tracking of Autonomous Underwater-Transportation Systems Under Sensor and Process Noise
by Faheem Ur Rehman, Syed Muhammad Tayyab, Hammad Khan, Aijun Li and Paolo Pennacchi
Actuators 2026, 15(5), 246; https://doi.org/10.3390/act15050246 - 30 Apr 2026
Viewed by 330
Abstract
Underwater-transportation systems have significant potential for both military and commercial applications. Neural Network (NN)-based control offers enhanced robustness for actuators to manage the states of autonomous underwater-transportation systems which include Rigid-Connection Transportation Systems (RCTSs), Flexible-Connection Transportation Systems (FCTSs) and Leader–Follower-Formation Control Transportation Systems [...] Read more.
Underwater-transportation systems have significant potential for both military and commercial applications. Neural Network (NN)-based control offers enhanced robustness for actuators to manage the states of autonomous underwater-transportation systems which include Rigid-Connection Transportation Systems (RCTSs), Flexible-Connection Transportation Systems (FCTSs) and Leader–Follower-Formation Control Transportation Systems (LFFCTSs). In this study, NN-Augmented Control (NNAC) is applied to the aforementioned three transportation systems to enable accurate path tracking by the actuators installed onboard these systems under both ideal operating conditions and in the presence of sensor and process noise. The Extended Kalman Filter (EKF) is employed to estimate the system states under noisy conditions. The results demonstrate that NNAC provides robust and adaptive control of actuators, achieving efficient trajectory tracking via the transportation systems despite the influence of sensor and process noise disturbances. NNAC predominance was also observed in comparison with the conventional PID controller. Among the transportation configurations under the NNAC strategy, the RCTS exhibited the highest tracking accuracy with the lowest power consumption by the actuators. The power consumption of actuators installed on the LFFCTS was marginally higher than that of the RCTS. However, the translational motion accuracy of the follower vehicle in the LFFCTS was the lowest due to indirect actuation control through the formation controller. In contrast, actuators in the FCTS showed the highest power consumption while motion accuracy was comparatively lowest, attributed to the increased complexity of its dynamic positioning requirements. Full article
(This article belongs to the Special Issue Fault Diagnosis and Prognosis in Actuators)
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25 pages, 86452 KB  
Article
Research on Real-Time Trajectory Planning and Tracking Control for Multi-ROV Shipwreck Search
by Wenyang Gan, Haozhe Liang and Caixia Cai
J. Mar. Sci. Eng. 2026, 14(9), 802; https://doi.org/10.3390/jmse14090802 - 28 Apr 2026
Viewed by 392
Abstract
Multi-robot collaboration and marine robotics constitute key research directions in intelligent autonomous systems. In this context, multi-ROV cooperative operations are increasingly deployed for sunken ship search missions. A central technical challenge in such applications is to ensure efficient, non-redundant coverage while maintaining accurate [...] Read more.
Multi-robot collaboration and marine robotics constitute key research directions in intelligent autonomous systems. In this context, multi-ROV cooperative operations are increasingly deployed for sunken ship search missions. A central technical challenge in such applications is to ensure efficient, non-redundant coverage while maintaining accurate formation tracking. This scenario confronts two principal difficulties. First, overlapping operational regions among multiple ROVs tend to produce both redundant coverage and search blind zones. Second, trajectory tracking accuracy is significantly degraded by the combined effects of hydrodynamic disturbances and inherent actuator constraints in ROVs. To address these challenges, an improved dynamic window approach (DWA), incorporating a search distance penalty mechanism, is proposed for multi-ROV trajectory planning. Concurrently, a cascaded tracking control architecture is constructed, wherein a model predictive kinematic controller generates constrained velocity references, while an adaptive sliding mode dynamic controller augmented with an extended state observer provides robust disturbance rejection. Collaborative search is conducted using a three-ROV leader–follower formation. Simulation results indicate that regional search coverage is effectively improved and areas of repeated detection are significantly reduced by the proposed planning algorithm. Real-time trajectory tracking is achieved by the designed controller under two typical extreme strong disturbance conditions, namely, time-varying disturbances and abrupt disturbances, on the premise of satisfying thruster thrust constraints. The proposed scheme enables all three ROVs to successfully complete the tracking task under time-varying disturbances while reducing the frequency of thrust saturation events by up to seven times. In contrast, under the conventional MPC–ASMC controller, one ROV deviates from the formation and fails to complete the tracking task. Under abrupt disturbances, the proposed approach reduces the trajectory tracking error by up to six times and decreases the frequency of thrust saturation events by up to four times. Full article
(This article belongs to the Section Ocean Engineering)
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25 pages, 3920 KB  
Article
Research on Multi-UAV Cooperative Formation Control Method Considering Coupling and Communication Delay
by Zequn Liu, Zhuxin Guo, Jianing Wei, Yunfei Zhang, Wanlin Fan and Yanfang Fu
Appl. Sci. 2026, 16(8), 4049; https://doi.org/10.3390/app16084049 - 21 Apr 2026
Viewed by 366
Abstract
Coupling effects and communication delays present major challenges for distributed formation control of multi-UAV formations. This work characterizes coupling effects and integrates them into cooperative control synthesis under delay conditions. A leader state observer is introduced to reconstruct the leader’s state via neighboring [...] Read more.
Coupling effects and communication delays present major challenges for distributed formation control of multi-UAV formations. This work characterizes coupling effects and integrates them into cooperative control synthesis under delay conditions. A leader state observer is introduced to reconstruct the leader’s state via neighboring information, reducing reliance on direct links and improving communication robustness. A delay aware cooperative control law with coupling effects is then developed, and Lyapunov–Krasovskii analysis establishes matrix inequality conditions to ensure stability. The key innovation lies in actively exploiting communication coupling to accelerate the error convergence rate and ensure formation tracking under communication delays. Theoretical analysis, grounded in the Lyapunov stability theorem, elucidates the mechanism by which coupling effects accelerate the error convergence rate. The effectiveness of the proposed method is validated through simulations of leader–follower formations. Full article
(This article belongs to the Section Aerospace Science and Engineering)
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21 pages, 2215 KB  
Article
Optimal Consensus Tracking Control for Nonlinear Multi-Agent Systems via Actor–Critic Reinforcement Learning
by Yi Mo, Xinsuo Li, Kunyu Xiang and Dengguo Xu
Symmetry 2026, 18(4), 691; https://doi.org/10.3390/sym18040691 - 21 Apr 2026
Viewed by 446
Abstract
This paper presents an adaptive optimal consensus tracking control scheme for canonical nonlinear multi-agent systems (MASs) with unknown dynamics, employing an actor–critic reinforcement learning (RL) framework. The scheme integrates a sliding mode mechanism to suppress tracking errors and ensure consensus tracking between the [...] Read more.
This paper presents an adaptive optimal consensus tracking control scheme for canonical nonlinear multi-agent systems (MASs) with unknown dynamics, employing an actor–critic reinforcement learning (RL) framework. The scheme integrates a sliding mode mechanism to suppress tracking errors and ensure consensus tracking between the followers and the leader. Additionally, optimal control is designed to find a Nash equilibrium in a graphical game. To address the intractability of obtaining an analytical solution for the coupled Hamilton–Jacobi–Bellman (HJB) equation, a policy iteration algorithm is utilized. Within this algorithm, a critic neural network (NN) approximates the gradient of the optimal value function, while an actor NN approximates the optimal control policy. Together, these networks form a compact actor–critic (AC) architecture that achieves optimal consensus tracking. Furthermore, the proposed method guarantees the boundedness of all closed-loop signals while ensuring consensus tracking. Finally, two simulations are conducted to verify the effectiveness and advantages of the proposed method. Full article
(This article belongs to the Special Issue Symmetry in Control Systems: Theory, Design, and Application)
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19 pages, 2350 KB  
Article
A Dual Approach to the A* Algorithm to Generate Consistent Trajectories for the Leader–Follower Scheme
by Griselda Stephany Abarca-Jiménez, Manuel Vladimir Vega-Blanco, Jesús Mares-Carreño, Juan Cruz-Castro and Yunuén López-Grijalba
Appl. Syst. Innov. 2026, 9(4), 78; https://doi.org/10.3390/asi9040078 - 16 Apr 2026
Viewed by 786
Abstract
Path planning and formation control in leader–follower robotic systems are active areas of research, as both are highly relevant to the proper execution of the assigned task. In this work, a dual approach to the A* algorithm is applied to generate consistent trajectories [...] Read more.
Path planning and formation control in leader–follower robotic systems are active areas of research, as both are highly relevant to the proper execution of the assigned task. In this work, a dual approach to the A* algorithm is applied to generate consistent trajectories for a multi-agent robotic system with a leader–follower scheme. The conventional A* algorithm aims to minimize the cost of finding the best path by minimizing distances. In this case, a modified A* algorithm is used because, although decision-making also involves choosing among eight options or cells, the goal is not to minimize distance; instead, the focus is on analyzing the direction of acceleration. The proposed algorithm is robust regarding the initial and relative pose of the leader with respect to the followers. The leader is tracked using a digital accelerometer. The algorithm is tested by simulating various patterns and implemented in two experimental test scenarios: the first with differential mobile robots, and the second with an Ackerman-type mobile robot. In both scenarios, the trajectories were achieved with deviations in x and y between the follower’s path and the leader’s path of less than 0.03, and the leader’s pose independence was maintained. Full article
(This article belongs to the Topic Collection Series on Applied System Innovation)
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