Formation Control Law Research Articles

Distributed fixed‐time sliding mode formation control for unmanned aerial‐ground vehicle (UAV‐UGV) heterogeneous system

AbstractThis study proposes a distributed fixed‐time sliding mode formation control (FTSMFC) method to address formation control problem for unmanned aerial‐ground vehicle (UAV‐UGV) heterogeneous system under the directed topology and subject to external disturbances. First, a distributed fixed‐time state observer (FTSO) is introduced to provide state estimation of the leader UAV, which overcomes the limitation of partial information availability among followers. Then, a novel fixed‐time disturbance observer (FTDO) is presented to enhance the system's anti‐disturbance ability by estimating and compensating external disturbances within a fixed time. Furthermore, by integrating sliding mode techniques and the information from the FTSO and FTDO, a distributed FTSMFC is developed to enforce the system to achieve predefined formation configuration within a fixed time independent of initial states of the system. Finally, a simulation comparison with the other controllers is carried out to show the validity and superiority of the proposed formation control law.

Neurodynamics-based formation tracking control of leader-follower nonholonomic multiagent systems

This paper uses a bioinspired neurodynamic (BIN) approach to investigate the formation control problem of leader-follower nonholonomic multiagent systems. In scenarios where not all followers can receive the leader's state, a distributed adaptive estimator is presented to estimate the leader's state. The distributed formation controller, designed using the backstepping technique, utilizes the estimated leader states and neighboring formation tracking error. To address the issue of impractical velocity jumps, a BIN-based approach is integrated into the backstepping controller. Furthermore, considering the practical applications of nonholonomic multiagent systems, a backstepping controller with a saturation velocity constraint is proposed. Rigorous proofs are provided. Finally, the effectiveness of the presented formation control law is illustrated through numerical simulations.

Relational Maneuvering of Leader-Follower Unmanned Aerial Vehicles for Flexible Formation.

In this article, we propose a new formation scheme for a leader-follower unmanned aerial vehicle (UAV) system inspired by a human pilot's behavior wherein the formation geometry does not necessarily remain fixed as the vehicles maneuver. In other words, the position and the orientation of the follower with respect to the leader are subject to change as they maneuver while satisfying some constraints. Our strategy ensures that the follower UAV maintains a desired fixed relative distance with respect to the leader UAV, whereas its orientation with respect to the leader UAV may change to reduce its control effort and provide it with a tactical advantage. We call this new relational maneuvering scheme flexible since the set of feasible positions for the follower UAV is not fixed, as is common in close proximity two-ship formations in air-to-air combat. By assigning the follower UAV's linear and angular velocities as its control inputs, our approach tries to emulate a human pilot's behavior in UAVs by taking anticipatory maneuvers when the leader UAV makes aggressive turns. The proposed flexible-geometry formation scheme is robust to the leader's maneuver changes since the follower UAV's control law does not need the information of the leader's angular speed control and only uses relative measurements. This makes the design lucrative even when the vehicles are heterogeneous, global measurements are unavailable, or if the leader UAV is noncooperative. Finally, we present multiple simulations to highlight the merits of the flexible formation control laws.

Output-feedback formation tracking control of autonomous surface vessels with collision avoidance

In this paper, a formation control problem with collision avoidance is investigated for underactuated surface vessels with position–heading measurements. Each vessels is subject to actuator magnitude and rate saturations. At first, an anti-saturation nonlinear extended state observer is developed to recover the linear velocity and yaw rate as well as unknown uncertainty and disturbances. Then, observer-based formation control laws are designed based on an artificial potential functions, obstacle avoidance yaw references and a backstepping technique. The stability of closed-loop formation control system is proved. The salient features of this paper are as follows. First, formation control with the capability of collision avoidance is achieved by using artificial potential functions and obstacle avoidance yaw references, which is more aggressive. Second, the proposed controller is able to deal with the magnitude and rate constraints of the actuator. Third, the proposed anti-saturation nonlinear extended state observer can achieve better estimation results for rapidly changing signals. Simulation results are given to substantiate the proposed formation control laws.

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.

Realization of Robust Formation for Multi-UAV Systems Using Control Barrier Functions

Network robustness is a necessary prerequisite for the effective execution of resilient control in distributed multiple unmanned aerial vehicles (UAVs). However, it remains a challenging task to construct a communication graph that satisfies specific network robustness properties. This paper investigates robust formation control of multi-UAV systems using control barrier functions (CBFs). We first propose a novel formation law to drive groups of UAVs into formations with communication graphs that satisfy the [Formula: see text]-robustness. With such a law, all the normal UAVs in the formation are capable of executing a given resilient consensus protocol, and achieving convergence in the presence of malicious attackers. Then, we present a control law that facilitates the establishment of UAV formations, in which the communication graphs satisfy p-fraction robustness. Finally, simulation examples are given to verify the effectiveness of the proposed formation control laws.

Maintaining and steering a formation in an unknown dynamic environment via a consistent distributed dynamic map

AbstractIn this paper, we study the problem of maintaining a stable mobile robot formation, steering and localizing all robots in an unknown dynamic environment consisting of multiple periodically moving objects, without the presence of a global positioning system or a robot tracking system. We propose a distributed observer such that each agent can estimate global positions of all mobile robots and that of moving landmarks in an unknown environment. By combining the proposed distributed observer with the distributed formation control and centroid tracking control law, we show that the formation shape can be maintained by utilizing its available relative measurements and the estimated relative measurements to its neighbors, and the group's centroid follows a desired trajectory. We present stability analysis of the closed‐loop system. Finally, we validate the proposed methods in a simulation result where a group of mobile robots can maintain a robust formation and maneuver in an unknown dynamic environment.

Multi-USV cooperative oil spill source seeking via extremum seeking combined with information fusion

This paper addresses the issue of cooperative source seeking for oil spill pollution by multiple unmanned surface vehicles (USVs), where the oil spill plume propagation is modeled by a linear advection–diffusion equation in two-dimensional space. The main objective is to construct a cooperative source seeking scheme for a group of USVs in the framework of extremum seeking combined with information fusion to solve such cooperative source seeking problem. To do this, both a gradient-based control law and a formation control law are included in the cooperative source seeking scheme. The gradient-based control law that is constructed by extremum-seeking control combined with information fusion drives the multiple USVs to approach the oil spill source, where the gradient is estimated online via the extremum-seeking control and the fused concentration value that is derived via a linear H∞ filter from the local concentration measurements at the USV’s current position. In the source seeking process, the USVs driven by the formation control law based on the virtual structure method maintain a preset circular formation. The convergence performance of the cooperative source seeking scheme is analyzed rigorously by the Lyapunov method. Finally, extensive numerical simulations are included to validate the theoretical algorithm.

Fixed-time event-triggered sliding mode time-varying formation control for multiple surface vessels with fast convergence

ABSTRACT This paper proposes a new fixed-time sliding mode time-varying formation control strategy for multiple surface vessels (MSVs) to improve control performance and ensure navigation safety. First, a fixed-time extended state observer (FxESO) is designed to provide estimations of velocities and lumped disturbances. Then, the event-triggered fixed-time distributed time-varying formation control law is designed based on prescribed performance function (PPF) and fixed-time nonsingular terminal sliding mode (FxNTSM) manifold. Finally, system stability is analyzed based on Lyapunov theory. The salient features of the proposed scheme are as follows. First, a novel hyperbolic cosecant PPF is incorporated into the control scheme to enhance control performance. Then, the proposed scheme is combined with relative threshold event-triggered strategy to reduce unnecessary updates of actuators. Finally, a uniform exact differentiator is introduced to avoid the formation control law including the acceleration of adjacent vessel. Comparative results are given to demonstrate the superiority of the proposed scheme.

Energy-Efficient Distributed Formation Control of Sampled-Data Multiagent Systems With Packet Losses.

This article investigates an energy-efficient formation control problem for multiagent systems with sampled data and random packet losses. A Bernoulli stochastic variable is used to describe packet losses, which is defined relative to the transmission energy consumed by antennas. A distributed sampled-data formation control law is designed and some analytic sufficient conditions on the formation control are derived. It is revealed that the sampling period, control parameters, network topology, as well as the transmission energy used by sensors impose inherent limitations in achieving the formation. Also, a method for searching the minimum allowable transmission energy is presented. Finally, numerical simulations are shown for illustration and verification.

Time-varying formation for MSVs with input and prescribed performance constraints by fixed-time event-triggered sliding mode control

This work develops a new fixed-time sliding mode time-varying formation control strategy for multiple surface vessels (MSVs) to improve the control performance, ensure the navigation safety and reduce the communication burden. At first, a fixed-time adaptive radial basis function neural network (FxRBFNN) observer is designed to provide the estimations for external environmental disturbances and model parameters uncertainties. Then, observer-based fixed-time distributed time-varying formation event-triggered control law is proposed based on the novel fixed-time auxiliary dynamic system (FxADS), the proposed prescribed performance function, the designed fixed-time nonsingular terminal sliding mode (FxNTSM) manifold and the proposed uniform exact differentiator. Finally, the system stability is proved by Lyapunov theory. The salient features as follows. First, to enhance the convergence performance for time-varying formation control method, a novel hyperbolic cosecant prescribed performance function (PPF) is introduced. Second, a novel FxADS is proposed to confront input constraints. Third, the proposed scheme is combined with a relative threshold event-triggered strategy to reduce the unnecessary updates of actuators under the premise of ensuring the control performance. Fourth, to avoid the proposed formation control law including adjacent vessel accelerations, this work proposed an improved uniform exact differentiator to identify them. Numerical simulations confirm that the proposed scheme has superior control performance.

Affine Formation Maneuver Control for Multi-Agent Based on Optimal Flight System

The use of affine maneuver control to maintain the desired configuration of unmanned aerial vehicle (UAV) swarms has been widely practiced. Nevertheless, the lack of capability to interact with obstacles and navigate autonomously could potentially limit its extension. To address this problem, we present an innovative formation flight system featuring a virtual leader that seamlessly integrates global control and local control, effectively addressing the limitations of existing methods that rely on fixed configuration changes to accommodate real-world constraints. To enhance the elasticity of an algorithm for configuration change in an obstacle-laden environment, this paper introduces a second-order differentiable virtual force-based metric for planning local trajectories. The virtual field comprises several artificial potential field (APF) forces that adaptively adjust the formation compared to the existing following control. Then, a distributed and decoupled trajectory optimization framework that considers obstacle avoidance and dynamic feasibility is designed. This novel multi-agent agreement strategy can efficiently coordinate the global planning and local trajectory optimizations of the formation compared to a single method. Finally, an affine-based maneuver approach is employed to validate an optimal formation control law for ensuring closed-loop system stability. The simulation results demonstrate that the proposed scheme improves track accuracy by 32.92% compared to the traditional method, while also preserving formation and avoiding obstacles simultaneously.

Self-Organized Polygon Formation Control Based on Distributed Estimation

This paper studies the problem of controlling a multi-robot system to achieve a polygon formation in a self-organized manner. Different from the typical formation control strategies where robots are steered to satisfy the predefined control variables, such as pair-wise distances, relative positions and bearings, the foremost idea of this paper is to achieve polygon formations by injecting control inputs randomly to a few robots (say, vertex robots) of the group, and the rest follow the simple principles of moving towards the midpoint of their two nearest neighbors in the ring graph without any external inputs. In our problem, a fleet of robots is initially distributed in the plane. The so-called vertex robots take the responsibility of determining the geometric shape of the entire formation and its overall size, while the others move so as to minimize the differences with two direct neighbors. In the first step, each vertex robot estimates the number of robots in its associated chain. Two types of control inputs that serve for the estimation are designed using the measurements from the latest and the last two time instants respectively. In the second step, the self-organized formation control law is proposed where only vertex robots receive external information. Comparisons between the two estimation strategies are carried out in terms of the convergence speed and robustness. The effectiveness of the whole control framework is further validated in both simulation and physical experiments.

Formation control for linear multi-agent systems with asynchronously sampled outputs

The focus of this paper is to investigate the problem of formation control for linear multi-agent systems through output feedback, utilizing the asynchronous sampled-data mechanism. Each agent matches one state observer to estimate its own state by only using the asynchronously sampled outputs. Based on the asynchronously sampled estimates of states, we develop a formation control law that operates in a distributed manner. The establishment of auxiliary time sequences plays a significant role in coping with the difficulty of asynchronous sampling. Through the study, an explicit upper bound of sampling periods and admissible formation condition, which guarantee that the predefined geometric shape is asymptotically formed, are given. Two examples are eventually carried out to show that formation is achieved successfully.

Formation control scheme with reinforcement learning strategy for a group of multiple surface vehicles

AbstractThis article presents a comprehensive approach to integrate formation tracking control and optimal control for a fleet of multiple surface vehicles (SVs), accounting for both kinematic and dynamic models of each SV agent. The proposed control framework comprises two core components: a high‐level displacement‐based formation controller and a low‐level reinforcement learning (RL)‐based optimal control strategy for individual SV agents. The high‐level formation control law, employing a modified gradient method, is introduced to guide the SVs in achieving desired formations. Meanwhile, the low‐level control structure, featuring time‐varying references, incorporates the RL algorithm by transforming the time‐varying closed agent system into an equivalent autonomous system. The application of Lyapunov's direct approach, along with the existence of the Bellman function, guarantees the stability and optimality of the proposed design. Through extensive numerical simulations, encompassing various comparisons and scenarios, this study demonstrates the efficacy of the novel formation control strategy for multiple SV agent systems, showcasing its potential for real‐world applications.

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

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

Homogeneous Finite-Time Pose Tracking of Leader–Following Spacecraft Formation Using a Twistor-Based Model

For integrated pose control of six-degree-of-freedom (6-DOF) leader–following spacecraft formations, the coupled relative pose between two spacecraft is described by a unified model in the framework of twistors, based on which a finite-time control law is devised for the 6-DOF dynamic system. Firstly, some necessary coordinate frames are defined, and then, relative 6-DOF dynamics of the follower spacecraft with respect to the desired frame are modeled by using twistors. Secondly, an integrated pose controller is designed for the 6-DOF formation that takes full advantage of homogeneous theory to guarantee finite-time stability. Finally, numerical simulations are carried out to validate the effectiveness of the proposed controller. Developing integrated 6-DOF formation control law based on twistors is more straightforward than conventional methods, and the finite-time algorithm achieves stronger robustness than asymptotic ones.

Cooperative Formation Control for Multiple AUVs With Intermittent Underwater Acoustic Communication in IoUT

Autonomous Underwater Vehicle (AUV) system has played an important role in complex Internet of Underwater Things (IoUT). As we know, single AUV is inefficient in collecting data in large-scale IoUT. In order to improve the timeliness of data, this paper uses multiple AUVs with specific formation shape to collect sensory data. However, the intermittent and unreliable characteristics of underwater acoustic communication between AUVs seriously affects the performance of formation control. To solve this issue, this paper mainly investigates formation control problem of leader-follower structured AUVs with state prediction estimation under the condition of unreliable underwater acoustic channel. Firstly, a novel formation control law derived from backstepping sliding mode method is proposed, and then a suitable Lyapunov functional is constructed to prove sufficient stability conditions. Secondly, Gaussian prediction model considering time delay and packet dropout has been designed to estimate the intermittent communication channel. Moreover, a new metric named formation uniform degree (FUD) is proposed to measure the degree of queue uniformity in a quantitative manner. Finally, extensive simulation results compared with traditional methods based on ideal channel model demonstrate the effectiveness of proposed formation control method.

Bearing‐based formation control of second‐order multiagent systems with bounded disturbances

AbstractThis article investigates the bearing‐based formation control problem for second‐order multiagent systems (SMS) in the presence of the bounded disturbances in their models. The main contributions of this article are listed as follows: (1) We extend the bearing formation control to SMS. (2) We propose two novel robust distributed bearing formation control laws. In the first control law, the bearing measurement in the global inertial frame is required. This control law guarantees that the inter‐agent bearings converge to the desired bearings. The second control law requires obtaining the local bearing measurements and relative orientation measurements. This control law guarantees that the inter‐agent bearings converge to the desired bearings and the orientation of each agent converges to a common orientation. Some simulations are conducted, and simulation results verify the effectiveness of the proposed control laws.

Fixed-time velocity-free safe formation control of AUVs with actuator saturation and unknown disturbances

This paper designs a fixed-time formation control law for multiple autonomous underwater vehicle (AUV) system (MAS) subjected to unmeasurable velocities, actuator saturation and time-varying disturbances. To address these challenges, the actuator saturation and time-varying disturbances are initially integrated into lumped disturbances, the initial step is to integrate actuator saturation and time-varying disturbances into lumped disturbances, followed by designing a fixed-time extended state observer (FTESO) to estimate the unavailable velocities and the lumped disturbances in fixed time. Moreover, a nonlinear filter is also utilized to eliminate the problem of computational explosion that arises due to derivatives in the controller design process. Additionally, a tan-type barrier Lyapunov function (TT-BLF) is presented to constrain the tracking errors within a predetermined time-varying constraint function. Then, a novel fixed-time formation control algorithm based on FTESO and TT-BLF is further designed to ensure that the formation tracking errors converge to a small neighborhood near origin in fixed time, and the fast formation task can be completed within a fixed time. Finally, the simulation experiments verify the effectiveness of the proposed controller.