Leader-follower Formation Control Research Articles

Bioinspired neurodynamics based formation control for unmanned surface vehicles with line-of-sight range and angle constraints

In this work, a leader–follower formation control for a group of waterjet unmanned marine surface vehicles (USV) is proposed under the consideration of formation tracking errors constraints. To guarantee line-of-sight (LOS) range and angle tracking errors constraints, a time-varying tan-type barrier Lyapunov function (BLF) is used. In addition, the bioinspired neurodynamics is introduced to solve the traditional differential explosion problem which can not only avoid the differential of the virtual control but can limit the output in a certain range. Further, an observer is involved to overcome the leader’s velocity unavailable problem and decrease the communication burden. Simulation results verify that under the proposed method, the LOS range and angle errors can converge into an arbitrary small neighborhood around 0, while the requirements of the constraints are never violated during the maneuver.

Leader-Following Formation Control and Collision Avoidance of Second-Order Multi-Agent Systems With Time Delay

In this article, the formation control problem has been considered for second-order multi-agent system with time delay. The involved controller is divided into two parts. The first part is to design the leader-following and adaptive control strategies that are utilized to achieve the specified formation shape. Based on a potential field function, the second part is applied to realizing the collision avoidance of the agents communicating with each other. By using the Lyapunov theory, some sufficient criteria are derived to ensure the specified formation shape of all agents and collision avoidance of any pair of agents. The derived criteria are formulated in terms of algebraic conditions, in which the control gains play an important role. Finally, a numerical simulation is given to illustrate the effectiveness of the derived results.

Adaptive Neural Network Leader-Follower Formation Control for a Class of Second-Order Nonlinear Multi-Agent Systems With Unknown Dynamics

In this article, an adaptive leader-follower formation control on the basis of neural network (NN) is developed for a class of second-order nonlinear multi-agent systems with unknown dynamics. Unlike the first-order formation control that only needs to govern the position states, the second-order formation control needs to govern both the position and velocity variables. Hence the second-order formation is more challenging and interesting than the first-order case. In the control design, the adaptive NN approximator is employed to compensate the nonlinear uncertainties, so that the control design difficulty coming from the unknown dynamics is effectively overcome. Through Lyapunov stability analysis, it is demonstrated that the proposed control method can complete the control tasks. To further demonstrate the effectiveness, the formation method is implemented to a numerical simulation, and it shows the desired results.

Leader-follower formation suboptimal control for quadrotors

In this work, a leader-follower formation control problem of quadrotors is investigated. The quadrotor dynamic model is represented by unit quaternion with the consideration of external disturbance. Nonlinear H∞ design approach is introduced and robust controllers for both leader and follower robots are derived by solving a Hamilton-Jacobi inequality following from a result for general nonlinear affine systems. Then some robustness conditions of the proposed controllers are obtained by selecting appropriate parametrised Lyapunov functions. The resultant state feedback controllers establish the asymptotically stability of the closed-loop nonlinear system. In addition, integral backstepping (IB) controllers are also derived for the leader-follower formation control problem. The purpose of designing IB controllers is to evaluate the robustness of H∞ controllers by comparison. The simulation results from both types of controllers are compared and robustness performance of the H∞ controllers over the IB controllers are demonstrated.

Leader-Follower Formation Suboptimal Control for Quadrotors

In this work, a leader-follower formation control problem of quadrotors is investigated. The quadrotor dynamic model is represented by unit quaternion with the consideration of external disturbance. Nonlinear H∞ design approach is introduced and robust controllers for both leader and follower robots are derived by solving a Hamilton-Jacobi inequality following from a result for general nonlinear affine systems. Then some robustness conditions of the proposed controllers are obtained by selecting appropriate parametrised Lyapunov functions. The resultant state feedback controllers establish the asymptotically stability of the closed-loop nonlinear system. In addition, integral backstepping (IB) controllers are also derived for the leader-follower formation control problem. The purpose of designing IB controllers is to evaluate the robustness of H∞ controllers by comparison. The simulation results from both types of controllers are compared and robustness performance of the H∞ controllers over the IB controllers are demonstrated.

Bearing Leader-Follower Formation Control under Persistence of Excitation

This paper addresses the problem of formation control with a leader-follower structure in three dimensional space by exploring persistence of excitation (PE) of the desired bearing reference, which is provided by a possibly moving or time-varying desired formation. Using only bearing measurements, control laws are proposed for a group of agents with single-integrator dynamics. By defining a desired formation such that the corresponding inter-vehicle bearing measurements are persistently exciting, relaxed conditions on the interaction topology (which do not require bearing rigidity nor constraint consistence) can be used to derive distributed control laws that guarantee exponential stabilization of the desired formation in terms of relative position. A key outcome of this approach is that even if there is only one connection originated from each follower, exponential stability of the formation can be achieved as long as the excitation conditions are met on the desired formation. The approach generalizes stability results provided in prior work for leader-first follower (LFF) structure, based on bearing rigidity and constraint consistence that required at least two connections for each follower except for the first one. Simulations results are provided to illustrate the performance of the proposed control method.

Leader-follower formation control of nonholonomic mobile robots with bearing-only measurements

This paper investigates the leader-follower formation control problem of nonholonomic vehicles. An estimator is first developed to estimate the relative position in its local coordinate system with bearing measurements, to avoid directly using positions or relative positions in the global reference frame. A control law is then proposed for the follower vehicle to follow the leader based on the estimated relative position. It is shown that the estimation error converges to zero, if some conditions on the relative angular velocity between the leader and the follower are satisfied. It is also shown that the stability of the closed loop system involving both the estimator and the controller is guaranteed if some mild conditions on the trajectory of the leader are satisfied. Extension to the case of multiple followers is also considered. Simulation results of numerical examples verify the effectiveness of the proposed control scheme.

Sliding mode based neural adaptive formation control of underactuated AUVs with leader-follower strategy

In this brief, the leader-follower formation control of underactuated autonomous underwater vehicles subject to uncertain dynamics and ocean disturbances is addressed. A robust sliding mode formation control strategy is presented by utilizing backstepping method, adaptive neural network and dynamic surface control technique. The stability of the formation control system is proved based on the Lyapunov's direct method where all the signals are guaranteed to be uniformly ultimately bounded. The main advantages of this control strategy are summarized as: (i) the presented controller only depends on the position measurements of the leader, which is more convenient to implement in practice. (ii) the proposed controller does not require any prior knowledge about the hydrodynamic damping and disturbances from the environment. (iii) a continuous PI function is designed to avoid the effect of inherent chattering in standard sliding mode control. (iv) the computational explosion of the standard backstepping method is avoided by the command filter based on the dynamic surface control technique. At last, the comparative simulations are provided to verify the effectiveness of the presented control strategy.

On Composite Leader–follower Formation Control for Wheeled Mobile Robots with Adaptive Disturbance Rejection

ABSTRACTThis paper proposes a composite control strategy for the formation control of a group of wheeled mobile robots (WMRs) by taking full advantages of model predictive control (MPC) and adaptive terminal sliding mode control (ATSMC) techniques. To begin with, in order to confirm the formulation stability of leader-follow system, a formation controller based on MPC scheme is proposed to assure the desired formation and the position consistency of followers. Afterward, a dynamic controller based on ATSMC scheme is developed for the leader to observe and then compensate the external disturbance as soon as possible. With the presented composite control strategy, not only the desired formation but also trajectory tracking can be simultaneously achieved, in addition to offering the leader to be robust and adaptive to overcome the uncertain disturbances. At last, the simulation results illustrate the feasibility and effectiveness of the proposed control strategy.

Optimized Formation Control Using Simplified Reinforcement Learning for a Class of Multiagent Systems With Unknown Dynamics

The article proposes an optimized leader-follower formation control using a simplified reinforcement learning (RL) of identifier-critic-actor architecture for a class of nonlinear multiagent systems. In general, optimal control is expected to be obtained by solving Hamilton-Jacobi-Bellman (HJB) equation, but the equation associated with a nonlinear system is difficult to solve by analytical method. Although the difficulty can be effectively overcome by the RL strategy, the existing RL algorithms are very complex because their updating laws are obtained by carrying out gradient descent algorithm to square of the approximated HJB equation (Bellman residual error). For a multiagent system, due to the state coupling problem, these methods will become difficult implementation. In the proposed optimized scheme, the RL updating laws are derived from negative gradient of a simple positive function, which is the equivalence to HJB equation; therefore, the control algorithm is significantly simple. Furthermore, in order to solve the problem of unknown system dynamics, an adaptive identifier is integrated into the control. Finally, the theory and simulation demonstrate that the optimized formation scheme can guarantee the desired control performance.

A 3-D Trailer Approach to Leader-Following Formation Control

A real-time 3-D trajectory planner for the leader-following formation control of autonomous vehicles is proposed. The planner relies on the definition of a trailer body whose hinge point is rigidly attached to the leader and assigns each follower to a distinct point of such a trailer. Convergence results for the trailer body reference frame are presented based on Lyapunov analysis, which guarantee that the planning can be independently implemented by $n$ followers, with a common leader, as they asymptotically behave as $n$ points of a unique trailer body. As such, the need for communication among followers is dispensable. The proposed strategy is divided into trajectory planning and trajectory tracking, the first problem being vehicle-independent. Experimental results obtained with quadrotor vehicles are presented, which demonstrate the richness and suitability of the planned trajectories.

Neuroadaptive Sliding Mode Formation Control of Autonomous Underwater Vehicles With Uncertain Dynamics

This article investigates the leader–follower formation control problem for the multiple underactuated autonomous underwater vehicles with model uncertainties and external disturbances. Sliding mode control, multilayer neural network, and adaptive robust techniques are employed to design a formation controller for underwater vehicles. After that, a Lyapunov-based stability analysis is proposed to guarantee that all variables are uniformly ultimately bounded in the closed-loop control system. The following advantages of this approach are highlighted: 1) the proposed control strategy only depends on the measurements of line-of-sight and angle sensors; no other information about the leader vehicle is required; 2) a continuous function is designed to replace the signum term in the control system, which greatly reduces the inherent chattering of sliding mode controller; 3) the proposed controller does not rely on any prior knowledge about hydrodynamic damping and external disturbances, which is easily implemented in practice. Finally, the numerical simulations are provided to demonstrate the effectiveness of the proposed controller.

Adaptive Leader-Follower Formation Control of Under-actuated Surface Vessels with Model Uncertainties and Input Constraints

This paper deals with the leader-follower formation control of underactuated autonomous surface vehicles in the presence of model uncertainties and input constraints. In a leader-follower formation, an autonomous surface vehicle (ASV) called leader tracks a pre-described trajectory and other ASVs called followers that are controlled to follow the leader with a desired distance and desired relative bearing. To this end, some adaptive robust techniques are adopted to guarantee the robustness of the closed-loop system against model uncertainties, external disturbances, and input saturation constraints. Based on the Lyapunov synthesis, it is proven that with the developed formation controllers, the closed-loop system is stable and all the formation errors converge to a small neighborhood of zero. Simulation results demonstrate the effectiveness of the proposed method.

Adaptive Leader–Follower Formation Control of Nonholonomic Mobile Robots With Prescribed Transient and Steady-State Performance

In this article, we study the formation tracking control problem for a group of nonholonomic mobile robots under communication constraints. We use a simple leader–follower formation tracking control strategy, in which only the leading robot of the robotic group obtains the given trajectory's information, and each robot only receives information from its immediate leader. Thus, the communication graph forms a static and simple directed spanning tree. We assume that the information exchange among the robots is limited by some given communication radius. Under the limited communication range, the leader–follower distance and bearing angle constraints are considered in the formation control design. To provide the given specifications on the transient and steady-state performances of formation tracking errors, the boundaries of the predefined constraints are enforced by designer-specified performance requirements, which are functions of time. Consequently, we incorporate the barrier Lyapunov function into formation control design to mathematically prove that the formation tracking errors evolve always within the predefined regions and converge asymptotically to zero. The proposed formation control strategy can also guarantee the connectivity maintenance and collision avoidance between the leader and the follower. Simulation results show the performance of the proposed formation tracking control.

A leader–follower formation control approach for target hunting by multiple autonomous underwater vehicle in three-dimensional underwater environments

As one of the challenging tasks of multiple autonomous underwater vehicles systems, the realization of target hunting is the great significance. The multiple autonomous underwater vehicle target hunting is studied in this article. In some research, because the hunting members cannot reach the hunting point at the same time, the hunting time is long or the target escapes. To improve the efficiency of the target hunting, the leader–follower formation algorithm is introduced. Firstly, the task is assigned based on the distance between the autonomous underwater vehicle and the target. Then, the autonomous underwater vehicles with the same task are formed based on leader–follower mode, and the formation is kept to track the target. In the final capture phase, multiple autonomous underwater vehicle system use angle matching algorithm to round up target. The simulation results show that the proposed algorithm can effectively accomplish the target hunting task, save the hunting time, and avoid the target escape. Compared with the bioinspired neural network algorithm, the proposed algorithm shows better performance.

Flatness-based finite-time leader–follower formation control of multiple quadrotors with external disturbances

This study considers the leader–follower formation control problem for multiple quadrotors in the presence of external disturbances. Based on the differential flatness theory, the underactuated quadrotor system is transformed into a fully actuated one with four degrees of freedom and four control inputs. Based on this model, a distributed finite-time observer is developed to reconstruct the leader's states for each follower. Then, an observer-based finite-time controller is proposed based on an adaptive disturbance rejection approach, which is independent of the upper bounds of the disturbances, to address the formation control problem for multiple quadrotors. The stability analysis indicates that the closed-loop system theoretically achieves the finite-time stability and robustness against the disturbances. Finally, a numerical simulation is provided to verify the performance of the proposed formation control scheme.

Event-Based Adaptive Power Control in Vehicular Networked Systems With State-Dependent Bursty Fading Channels

This brief considers both safety and efficiency issues for vehicular networked systems (VNSs) where vehicles exchange information over vehicle to vehicle (V2V) wireless communication channels. One of the challenges to ensure system safety and efficiency lies in unreliable V2V fading channel conditions, which stochastically change as a function of the vehicle states and are subject to severe data rate drops. By adopting a bursty state-dependent fading model, this brief presents a novel event-based adaptive power control scheme. Under this scheme, the VNS assures efficient use of communication resources while preserving almost sure asymptotic stability. The benefits of the proposed scheme over other power policies are shown in a leader-follower formation control example.

Leader–follower formation control of two quadrotor UAVs

This paper reports the design and implementation of a leader–follower (L–F) formation control of two Parrot AR Drone 2.0 quadrotor UAVs (drones). In order to implement such control, three control elements were developed. These were the flight-dynamic characteristics, the position tracking and L–F formation control, and the data communication system between drones and ground-control station. The dynamic characteristics were identified as the first-order process with time delay models, which were asymmetrical to x−, x+, x− and x+ directions. Accordingly, dedicated Proportional-Derivative (PD) controllers were designed for the respective models. A Pole-Placement strategy was applied to design the PD controllers in order to achieve a non-oscillatory position tracking. These controllers were combined with five operating modes to form an F–L formation control. The controls were implemented on two-drones and one-ground-control station. The ground-control station dictated a prescribed path for the leader drone. Subsequently, the leader position became follower set-point. During the implementation test, these drones completed their L–F formation. The follower drone tracked the y-axis coordinate of the leader’s drone and maintained a safe distance to the respective x-axis coordinate. The accuracy of the controls was measured in terms of the root mean squares errors, and these were within 50–115 cm.

Vision-Based Leader–Follower Formation Control of Multiagents With Visibility Constraints

In this brief, a vision-based tracking scheme is studied for the leader–follower formation control of multiagent system under visibility constraints without communication among agents. A kinect is the sole sensor installed on each agent to estimate the pose, including relative orientations and relative positions of the local leader. A dipolar vector field is established to generate and maintain a desired formation given the desired displacement on positions among agents. The visibility constraints of kinect are converted into input constrains given the pose of the local leader, and an auxiliary system is designed to analyze the effect of visibility constraints. Combining the state of the auxiliary system with the vector filed, the proposed control protocol is able to achieve the formation tracking without global or local communication among agents. Simulation studies on the robot operating system using the Gazebo simulator and experimental results on Turtlebot2 are presented to illustrate the performance of the proposed approaches.

Lyapunov and Sliding Mode Based Leader-follower Formation Control for Multiple Mobile Robots with an Augmented Distance-angle Strategy

In this paper, a new two-layer control strategy which combines Kinematic Controller based on Lyapunov Theory (KCLT) with Dynamic Controller based on Sliding Mode (DCSM) is proposed to solve the problem of leader-follower formation control for multiple wheeled mobile robots (M-WMR). An augmented distance-angle leader-follower formation kinematic is constructed to describe the formation states, and a 2D LiDAR sensor is utilized to measure the states instead of using camera and image processing on each follower. Instead of transferring the measured formation states into reference position command for each follower, KCLT is designed to generate follower’s velocity command. By taking the velocity command of followers as reference signals, DCSM is implemented to realize formation control. Lyapunov stability theory verifies that with the designed controller all the error signals can converge to 0 theoretically, which implies formation control of M-WMR under the proposed method can be realized. Real experiments with one leader and two followers are carried out to demonstrate the effectiveness of the proposed control schema. In order to verify the robustness of the proposed method, the reference rotational velocity of the leader robot is designed to change between +0:2 rad/s and -0:2 rad/s at some specified position. And the experimental results are compared with that of traditional proportional-integral-derivative (PID) method.