Coordinated transportation of tethered multi-rotor UAVs based on differential graphical games

Time-varying formation tracking (TVFT) control problem for multiple Euler–Lagrange (EL) systems with an uncertain leader is investigated in this article. The objective of this problem is for the followers' states to track the uncertain leader's output and achieve the desired formation. One of the major challenges in solving such a problem lies in estimating the information of the leader. In this article, an observer-based TVFT control framework is presented in this article, which does not require all or part of the follower agents to know the system dynamic knowledge of the leader agent directly in advance. First, two fully distributed adaptive observers are presented for estimating the uncertain leader's state, output, and the unknown system matrices under an IE condition, which relaxes the existing restrictive persistently exciting or cooperative finite-time excitation condition. Then, on the basis of the constructed adaptive observers, state and output variables of the leader, a fully distributed TVFT for EL systems with an uncertain leader is developed, which means the proposed formation tracking controller operates independently of the system dynamic knowledge of the leader agent; with the help of the Lyapunov stability theory, the TVFT criterion for the considered system is derived. Finally, in order to demonstrate the theoretical results derived in this article, a practical air–ground formation tracking platform, which consists of an unmanned aerial vehicle and four unmanned ground vehicles, is introduced, and physical experimental results are obtained.

This paper introduces novel Integral Reinforcement Learning solution to a class of differential games known as differential graphical games. The agents' error dynamics are coupled dynamical systems driven by the control input of each agent and the control inputs of its neighbors. A new class of control policies is developed to solve the differential graphical games with innovative performance index which is used to measure the system performance. The graphical game Integral Reinforcement Learning Bellman equations are shown to be equivalent to certain graphical game coupled Hamilton-Jacobi-Bellman equations developed herein. Online Policy Iteration algorithm is proposed to solve the differential graphical game in real-time. Convergence of the policy iteration algorithm is shown under mild assumptions about the inter-connectivity properties of the graph. Novel coupled Riccati formulation is developed to solve the differential graphical games.

This paper seeks to combine differential game theory with the actor-critic-identifier architecture to determine forward-in-time, approximate optimal controllers for formation tracking in multi-agent systems, where the agents have uncertain heterogeneous nonlinear dynamics. A continuous control strategy is proposed, using communication feedback from extended neighbors on a communication topology that has a spanning tree. A model-based reinforcement learning technique is developed to cooperatively control a group of agents to track a trajectory in a desired formation. Simulation results are presented to demonstrate the performance of the developed technique.

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.

Time-varying formation tracking problem for single-integrator multi-agent system with one leader and several followers on directed graphs are investigated. The followers need to achieve predefined time-varying formation while tracking the leader with unknown control input. Firstly, a time-varying formation tracking control protocol is designed by using neighbor information. Then based on the Lyapunov theory, a proof that the multi-agent systems can achieve the desired time-varying formation tracking is given. Furthermore, a simulation example of formation tracking motion of multi-agent systems composed of three followers and one leader under designed protocol is given. Finally, the protocol is applied to a unmanned ground vehicle(UGV) systems composed of one leader and three followers to demonstrate the effectiveness of the theoretical results.

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.

This paper investigates the single-evader and multi-pursuer (SEMP) reach-avoid differential graphical (RADG) games of nonlinear heterogeneous players subject to saturated input and limited communication channels. The evader’s objective is to reach a designated target area while avoiding the pursuers, whose aim is to intercept the evader. First, we reformulate the SEMP RADG game as an optimal control problem within a weighted communication topology graph by incorporating the interception and control errors. Then, optimal control strategies that account for input saturation are derived by solving the coupled Hamilton-Jacobi (HJ) equations. These strategies are shown to constitute the Nash Equilibrium (NE) of the game. In addition, four types of pursuers, namely, isolated, passive, invisible, and regular pursuers, are defined based on the communication topology, and the conditions for achieving an Interactive Nash Equilibrium (INE), which is proposed for SEMP RADG games, are analyzed. Moreover, a single-network approximate dynamic programming (ADP) algorithm using concurrent learning (CL) is proposed to provide the near-optimal solutions to the coupled HJ equations. Asymptotic capture conditions are established through an examination of equilibrium points, and extensions to general pursuit-evasion (PE) games and half-space targets are further discussed. Our results are validated through numerical simulations.

The study focuses on the analysis and optimization of energy supply systems for unmanned aerial vehicles (UAVs), specifically FPV drones equipped with 10-inch propellers, to increase flight duration and operational efficiency under various civilian application scenarios. With the rapid expansion of drone usage in fields such as agriculture, environmental monitoring, logistics, and technical inspection, the issue of selecting the most efficient power source has become particularly relevant. The research aims to determine the optimal type of battery in terms of weight, energy density, endurance, and cost-effectiveness, ensuring reliable operation and sufficient energy reserve for different mission profiles. The article presents a comparative analysis between a lithium-polymer (LiPo) battery pack (6S, 10Ah) and three lithium-ion (Li-Ion) battery assemblies based on Molicel P42A cells with different configurations: 6S2P, 6S3P, and 6S4P. The analysis includes both theoretical calculations and practical considerations derived from known empirical data. Each configuration was evaluated based on three main criteria – flight time, maximum range, and overall economic viability. Additionally, the influence of payload mass (0–3 kg) on flight duration and efficiency was modeled for six key mission scenarios: observation and video surveillance, light and medium cargo delivery, heavy cargo delivery, one-way missions, and high-speed flight operations. Methodologically, the work takes into account motor efficiency (0.8–0.85), aerodynamic drag, and the voltage behavior of both LiPo and Li-Ion systems under load. The results demonstrate that Li-Ion batteries offer a higher specific energy density (up to 180 Wh/kg) and lower cost per watt-hour compared to LiPo alternatives, though their discharge characteristics limit maximum current output. Among the tested configurations, the Li-Ion 6S3P assembly showed the most balanced performance, providing a flight time of up to 45 minutes without payload and maintaining stable voltage throughout the discharge cycle. The LiPo 6S 10Ah pack remains advantageous for high-current, short-duration missions such as racing or rapid-response operations due to its superior instantaneous power output. The study concludes that no single battery configuration is universally optimal for all use cases. However, the Li-Ion 6S3P pack can be considered the most versatile and practical solution for multi-purpose civilian FPV platforms, combining reasonable cost, low weight, and extended endurance. The article also provides recommendations for selecting power systems depending on the mission profile and discusses the practical aspects of battery assembly, including the use of bi-metal copper and nickel-plated steel strips (0.15×10 mm) to ensure low resistance and reliable current transfer during high-load operation. The findings highlight the need for further experimental validation under real-world flight conditions, as well as future research focused on optimizing propeller geometry, assessing temperature impacts, and integrating hybrid power systems for small UAVs. The proposed analytical framework and results can serve as a methodological foundation for engineers, drone developers, and energy system designers seeking to enhance the performance and energy efficiency of modern FPV drones

In this paper, a novel formation and path tracking control method is proposed for multiple unmanned ships. In this method, an individual unmanned ship is used to be the leader that tracks the desired path; other unmanned ships are used to be the followers which track the leader only by using its position to keep the formation. Simulation results show that this method could achieve the formation and path tracking control of multiple unmanned ships effectively.

This paper studies the formation tracking control problem in the agents’ local co-ordinate frame without any special assumption, such as positive definiteness, on the initial orientation matrix. When follower agents do not have knowledge of their absolute orientation with respect to a global reference frame, formation control is difficult and special assumptions on initial orientation matrix are generally imposed for orientation synchronization. To address this, a distributed fixed time orientation synchronization law is first presented, using only relative orientation measurements, which aligns the co-ordinate frames of agents almost globally in finite time and locally in fixed time. This law is then used in cascade with an acceleration command for formation tracking control in a leader-follower set-up. Global asymptotic convergence of formation tracking error is proved for displacement based formation. For bearing-only formation control, semi-global uniformly asymptotic stability is established. Simulations illustrate the applicability of the results.

Stability and robustness analysis of minmax solutions for differential graphical games

This paper investigates the formation tracking control strategy for nonholonomic mobile robots, ensuring convergence within a predefined time. To begin with, the control system is designed by leveraging the robot’s kinematic model to create two distinct control loops for position and attitude, culminating in an integrated dual closed-loop architecture. Then, based on the Lyapunov stability theory, the position subsystem and the attitude subsystem of the system have been verified to maintain stability within a predefined time. Finally, through MATLAB numerical simulation examples, the feasibility of the proposed mobile robots formation control scheme is demonstrated, further confirming the effectiveness of the algorithm and achieving control within the predefined time.

With the rapid development of intelligent information technology, human–computer interaction for unmanned aerial vehicle (UAV) systems has gradually developed from single-mode interaction to multi-modal interaction. Due to the problems of information ambiguity and operational redundancy in multi-modal interaction, and the inability to effectively realize the coupling of human–computer interaction of different modalities, a priority strategy for multi-modal interaction for UAV systems is proposed. Living cells or tissues, whether in a static or active state, will produce regular electrical phenomena called bioelectricity. Human–computer interaction intention recognition technology based on bioelectrical signals can significantly enhance the real-time performance and flexibility of human–computer interaction and has great development potential. The characteristics of human–computer interaction intention recognition methods based on bioelectrical signals, such as electroencephalograms (EEGs), electromyograms (EMGs), electrooculograms (EOGs), and other conventional methods are introduced and analyzed, and then the basic characteristics of single-mode interaction and multi-modal interaction are compared. Furthermore, the priority strategies for UAV systems under different interaction modes are studied based on the analysis of task value evaluation parameters. The cumulative value, urgency, and task complexity are comprehensively analyzed and evaluated, and a set of priority strategies for multi-modal interaction is integrated. Through the simulation and verification of the multi-modal human–computer interaction software of the UAV system, it is determined that the proposed priority strategy conforms to the operation intention of the user, which improves the interaction efficiency and the reliability. In noisy environments, the UAV system control can be combined with the complementary information of various interaction methods to achieve precise control, which has obvious advantages.

In this paper, the distributed formation tracking control problem of quadrotor unmanned aerial vehicles is considered. Adaptive backstepping inherently accommodates model uncertainties and external disturbances, making it a robust choice for the dynamic and unpredictable environments in which unmanned aerial vehicles operate. This paper designs a formation flight control scheme for quadrotor unmanned aerial vehicles based on adaptive backstepping technology. The proposed control scheme is divided into two parts. For the position subsystem, a distributed robust formation tracking control scheme is developed to achieve formation flight of quadrotor unmanned aerial vehicles and track the desired flight trajectory. For the attitude subsystem, an adaptive disturbance rejection control scheme is proposed to achieve attitude stabilization during unmanned aerial vehicle flight under uncertain disturbances. Compared to existing results, the novelty of this paper lies in presenting a disturbance rejection flight control scheme for actual quadrotor unmanned aerial vehicle formations, without the need to know the model parameters of each unmanned aerial vehicle. Finally, a quadrotor unmanned aerial vehicle swarm system is used to verify the effectiveness of the proposed control scheme.

Considering deferred time-varying tracking error constraint and external disturbance, a disturbance observer based-practical fixed-time formation tracking controller is designed for multiple quadrotor UAVs(QUAVs). To begin with, a shifting function is proposed to ensure that the tracking error of a class of MIMO nonlinear systems can quickly return to the constraint from the outside of constraint. At the same time, the shifting function sets the initial value to an arbitrarily small constant, which can avoid the singular problem. Then, nonlinear transformation is established to transfer the constrained problem into an unconstrained problem. Furthermore, an adaptive gain fixed-time disturbance observer (AGFXDO) is proposed to tackle the external disturbance with relaxed assumption condition. The fixed-time stability of the estimate error is proven. Based on those, a practical fixed-time distributed formation tracking control strategy is designed for the multiple QUAVs. The practical fixed-time stability of the transformed error is rigorously proven and the tracking error is guaranteed to yield the constraint and converges to an arbitrarily small vicinity of zero after prespecified time for arbitrarily given bounded initial values. At the end, the effectiveness of the developed control scheme is illustrated by the compared simulations. Through the comparative analysis of metrics integral of absolute magnitude of error (TAE), integral of time-multiplied absolute magnitude of the error (ITAE), integral of square value of controller signal (ISV), the tracking errors enter the constraint boundaries within 3 seconds and rapidly achieve convergence. Compared with the existing FXDO-based method, the proposed AGFXDO based control approach reduces 21.7% of TAE and 76.9% of ITAE, simultaneously, it maintains lower controller value as reflected in ISV.