Leader-follower Formation Control Problem Research Articles

Bearing-Based Formation Tracking Control of Nonholonomic Mobile Agents With a Persistently Exciting Leader

This paper investigates the leader-following formation control problem of nonholonomic agents with a persistently exciting leader based on bearing measurements. A follower needs to maintain a desired relative position to the leader in its local coordinate frame using bearing measurements. An integrated method consisting of a bearing-based estimator and a tracking controller is proposed to achieve the leader-following control objective. The estimator is designed to estimate the relative position to the leader in the follower's local coordinate frame. Based on the estimated relative position, the controller is proposed to drive the follower to achieve the desired formation. Different from existing integrated methods, our method does not require any conditions on the relative bearing between the leader and the follower in the global frame, which are difficult to guarantee. We characterize the conditions locally on the leader only, namely, conditions on the leader's linear and angular velocities with persistently exciting steering speed, such that the overall system is asymptotically stable with our integrated method. Besides, the proposed method is extended to the multi-agent formation control problem. A reasonable solution is proposed to the multi-agent case with a minimal leader follower structure. Simulations prove the effectiveness of the proposed methods in both cases.

Distributed Leader Follower Formation Control of Mobile Robots Based on Bioinspired Neural Dynamics and Adaptive Sliding Innovation Filter

This paper investigated the distributed leader follower formation control problem for multiple differentially driven mobile robots. A distributed estimator is first introduced and it only requires the state information from each follower itself and its neighbors. Then, we propose a bioinspired neural dynamic based backstepping and sliding mode control hybrid formation control method with proof of its stability. The proposed control strategy resolves the impractical speed jump issue that exists in the conventional backstepping design. Additionally, considering the system and measurement noises, the proposed control strategy not only removes the chattering issue existing in the conventional sliding mode control but also provides smooth control input with extra robustness. After that, an adaptive sliding innovation filter is integrated with the proposed control to provide accurate state estimates that are robust to modeling uncertainties. Finally, we performed multiple simulations to demonstrate the efficiency and effectiveness of the proposed formation control strategy.

Leader–follower sliding mode formation control of fractional-order multi-agent systems: A dynamic event-triggered mechanism

This paper examines the concept of the leader–follower formation for fractional-order multi-agent systems (FO-MASs) by utilizing dynamic event-triggered sliding mode control (SMC) method. Firstly, a dynamic event-triggered mechanism (DETM) is designed relying on the combined measurement vector, in which an auxiliary variable is introduced to dynamically adjust the threshold for each fractional-order agent system. Unlike most existing event-triggered communication mechanisms, whose threshold parameters are always fixed, the threshold parameters in our designed event-triggered conditions can be dynamically adjusted according to the fractional-order dynamic rule. Numerical results show that the proposed DETM can achieve a better system performance in reducing the sampling frequency and the expected formation performance. Secondly, the leader–follower formation control problem is transformed into checking the asymptotic stability problem of the closed-loop system. In addition, due to the memorability of fractional calculus operators, a distinctive condition is established to avoid the occurrence of Zeno behaviors reported in existing dynamic event-triggered schemes. Finally, a simulation example is presented to illustrate the effectiveness and feasibility of the dynamic event-triggered SMC method proposed in this paper.

Formation Control of Networked Mobile Robots With Unknown Reference Orientation

In this article, the distributed leader-following formation control problem of networked mobile robots is investigated. The desired formation is specified by a reference trajectory generated by the leader and the followers' desired relative positions with respect to the leader. On the one hand, for any security-aware multirobot systems, the values of the leader's position and orientation are generally not allowed to be transmitted via the inter-robot communication in the case of the information leakage of formation caused by the possible eavesdropping. On the other hand, relative orientations, different from relative positions, are typically difficult for mobile robots to measure directly, which makes the reference orientation unknown to all followers. In order to track the reference trajectory and form a desired formation in the absence of the reference orientation, followers are divided into two groups according to whether they are able to directly measure the relative positions with respect to the leader. The topology of the sensing/communication network among multirobot systems is described by a directed graph containing a directed spanning tree. Then, two observer-based control laws are proposed for two groups of followers, respectively, in both of which the unknown tracking errors are properly estimated. It is rigorously proven that the resulting closed-loop multirobot system is globally uniformly asymptotically stable. Finally, the effectiveness of our approach is illustrated by an experiment conducted on networked TurtleBot3 Burger mobile robots.

Event-triggered leader-following formation control of general linear multi-agent systems with distributed infinite input time delays

By employing event-triggered control technique, this paper investigates the leaderfollowing formation control problem of general linear multi-agent systems with distributed infinite input time delays. To decrease computing costs, a novel event-triggered formation protocol taking into consideration of the distributed infinite time delays between agents is put forward. Under the designed triggering function and triggering condition, a sufficient condition on leader-following formation is obtained, and then the Zeno-behavior of triggering time sequences is excluded for the concerned closed-loop system. The continuous update of controller for each agent is avoided. Finally, the correctness and the effectiveness of these theoretical results are demonstrated by two numerical examples.

Finite-time velocity-free adaptive neural constrained cooperative control of Euler–Lagrange systems

This paper addresses a new constrained control design problem to develop the trajectory-tracking specifications of the cooperative control of Euler–Lagrange systems with respect to the convergence rate and steady-state errors by constraining the limited bounds on the trajectory-tracking errors in the leader–follower formation control problem. A control design based on an asymmetric barrier Lyapunov function is proposed for the leader–follower formation control of Euler–Lagrange systems in the presence of unknown parameters and unmodeled dynamics that progresses to the infinity when its arguments attain to the predefined bounds. These constrained output states are considered in the leader–follower formation control problem to cope with the system restrictions such as limited sensing ranges. The Lyapunov stability is pursued to assure that all the signals of the closed-loop system are bounded and the leader–follower formation errors are finite-time semi-globally uniformly ultimately bounded. Finally, computer simulation results represent the impression of the newly proposed constrained leader–follower formation control for the Euler–Lagrange systems.

Leader–follower formation control of four-legged robots with discrete-valued inputs

This paper addresses a leader–follower formation control problem for four-legged robots under discrete-valued input constraints. Four-legged robots are more suitable for rough terrain missions than wheeled robots because the tip positions of their legs can be changed depending on the terrain. However, it is difficult to control these robots through continuous-valued inputs because they are steered by switching between specific movements (i.e., discrete-valued signals). Motivated by this fact, we have proposed controllers that achieve fixed formations of four-legged robots using discrete-valued inputs, but moving formations, which are necessary for some applications, have not been considered yet. Herein, we present a solution to the above leader–follower formation control problem based on the combination of PD-like formation controllers and dynamic quantization. We further introduce a performance index to evaluate the difference between two systems whose inputs are quantized and unquantized and analyze the index for the feedback system with the presented controllers. As a result, an upper bound of the performance index is derived as a function of the system parameters. This is useful to evaluate the impact of the quantization on the behavior of the feedback system and to provide a theoretical guarantee of the stability of the system.

Secure Control Design for Networked Control Systems With Nonlinear Dynamics Under Time-Delay-Switch Attacks

A continuous controller is developed for a centralized network control system (NCS), which is composed of agents with nonlinear dynamics subject to a time-delay-switch (TDS) attack and additive disturbances. Since the state tracking error is unmeasurable during TDS attacks, controllers cannot use the state tracking error to coordinate the NCS. Therefore, a novel error signal is designed to address this unique challenge and enable the NCS to achieve a formation control objective. Furthermore, a TDS attack mitigation strategy is developed, which uses both learning- and model-based approaches to estimate an agent’s state for TDS attack detection and compensation. Lyapunov–Krasovskii functionals are used in the stability analysis to prove that the tracking errors converge to a steady-state residual, which is a function of the system uncertainty and TDS attack properties. The leader–follower formation control problem for unmanned aerial vehicles based on a pure pursuit guidance law is selected for a simulation study to validate the performance of the proposed method.

Leader-Follower Formation Learning Control of Discrete-Time Nonlinear Multiagent Systems.

This article investigates the leader-follower formation learning control (FLC) problem for discrete-time strict-feedback multiagent systems (MASs). The objective is to acquire the experience knowledge from the stable leader-follower adaptive formation control process and improve the control performance by reusing the experiential knowledge. First, a two-layer control scheme is proposed to solve the leader-follower formation control problem. In the first layer, by combining adaptive distributed observers and constructed in -step predictors, the leader's future state is predicted by the followers in a distributed manner. In the second layer, the adaptive neural network (NN) controllers are constructed for the followers to ensure that all the followers track the predicted output of the leader. In the stable formation control process, the NN weights are verified to exponentially converge to their optimal values by developing an extended stability corollary of linear time-varying (LTV) system. Second, by constructing some specific "learning rules," the NN weights with convergent sequences are synthetically acquired and stored in the followers as experience knowledge. Then, the stored knowledge is reused to construct the FLC. The proposed FLC method not only solves the leader-follower formation problem but also improves the transient control performance. Finally, the validity of the presented FLC scheme is illustrated by simulations.

Distributed prescribed-time leader–follower formation control of surface vehicles with unknowns and input saturation

In this paper, the prescribed-time leader–follower formation control problem is solved for surface vehicles (SVs) suffering from input saturation and unknowns including uncertain dynamics and external disturbances. Based on the information of neighboring vehicles, a distributed prescribed-time observer for estimating states of the leader is proposed. By virtue of input saturation, the saturation errors and system unknowns are observed by a reduced-order prescribed-time estimator. Moreover, to realize the satisfactory formation error constraints, a time scale transformation function based prescribed-time prescribed performance function is proposed, together with error transformations, the transient performance of formation errors is improved. Lyapunov stability theorem and backstepping method prove that the closed-loop system is prescribed-time stable. Simulations are given to illustrate the effectiveness of proposed theoretical results.

Distributed leader-following formation control for multiple nonholonomic mobile robots via bioinspired neurodynamic approach

This paper investigates the distributed leader-following formation control problem for multiple nonholonomic wheeled mobile robots via a bioinspired neurodynamic approach. To do this, first, we develop a distributed estimator for each follower robot which uses its own information and the information of its neighboring robots to estimate the leader’s states. Second, a formation tracking control law is proposed for each follower robot based on the estimated states of the leader using the backstepping technique. Then, a bioinspired neurodynamics-based backstepping controller is designed to solve the impractical velocity jumps problem. Furthermore, Lyapunov function-based approach is utilized to derive sufficient conditions which guarantee asymptotic stability of the multiple mobile robot system. Finally, simulation results are presented to illustrate the effectiveness of the proposed controllers.

Leader-Follower Formation of Second-Order Nonlinear Multi-Agent Systems by Adaptive Neural Networks with Novel Kernel

In this research work, a novel kernel is conceptualized with the cosine of the distances for radial basis function neural networks (RBFNNs’) for leader-follower formation control problem of second-order nonlinear systems. The adaptive RBFNNs’ acts as a function approximator and also generates the control signal. A weight tuning rule gives the estimated weights. The desired formation for a nonlinear second-order system is achieved. Switching topology is applied between the leader and followers. The results are compared with a purely Gaussian kernel based on Euclidean distances and a mixture of cosine and Gaussian kernels. The overall stability of the system is proved by the Lyapunov function. Numerical simulations show the superior performance of the novel cosine kernel.

Leader–follower formation with reduction of the off-tracking and velocity estimation under visibility constraints

This article addresses the time-varying leader–follower formation control problem for nonholonomic mobile robots, under communication and visibility constraints. Although the leader–follower formation control under visibility constraints has been studied, the elimination of the off-tracking effect has not been widely addressed yet. In this work, a new method to eliminate the off-tracking effect, considering the time-invariant formation as a tractor–trailer system, for unknown and circular tractor paths, taking into account the visibility constraints, is proposed. For a time-varying formation with not circular tractor’s path, the proposed method significantly reduces the off-tracking. Only the relative position and the relative orientation, provided by the on board monocular camera, are required. Thus, both the leader robot’s absolute position and the leader robot’s velocities are not needed. Furthermore, to avoid explicit communication among the robots, an extended state observer is implemented to estimate both the translational and the rotational leader’s velocity. In this way, the desired tasks are executed and achieved in a decentralized manner. For a time-varying formation, with constant leader robot’s velocities, the proposed control strategy, based on the kinematic model, guarantees that the formation errors asymptotically converge to the origin. Based on the Lyapunov theory, the stability proof of the formation errors dynamics is shown. Simulation results, considering time-varying leader robot’s velocities, show the efficiency of the proposed scheme.

Robust tracking control of bearing-constrained leader–follower formation

This paper studies a leader–follower formation control problem where the leaders move with constant velocity, the followers know the desired bearing vectors in the target formation and can sense either the displacement vectors or the bearing vectors with regard to several neighboring agents. For both cases, distributed control laws are proposed so that the desired formation is achieved under the presence of unknown bounded uniformly continuous uncertainties in the followers’ model. Except for the assumption that the local reference frames of all agents are aligned, the proposed control laws do not require any relative velocity, bearing rate or information exchange between the agents. The convergence of the target formation is established based on Barbalat’s lemma. Simulation results are also given to support the analysis.

Adaptive neural formation control for underactuated unmanned surface vehicles with collision and connectivity constraints

The aim of this paper is to address the leader–follower formation control problem for a group of underactuated unmanned surface vehicles (USVs) with non-diagonal inertia matrix subject to modeling uncertainties and limited sensing capabilities. No communication is required among the USVs, but every USV is only equipped with on-board sensors to measure the line-of-sight (LOS) range and the relative bearing angle. The connectivity preserving constraint arisen from the limited sensing capability and the collision avoidance constraint resulting from the safety requirement are imposed on the LOS range and the relative bearing angle between every follower and its leader. These constraints are subsequently incorporated into the tan-type barrier Lyapunov function-based formation control design. Every USV reconstructs the velocity of its leader using the high-gain observer based solely on the available LOS range and relative bearing angle. Based on coordinate transformation, backstepping procedure, dynamic surface control (DSC) technique, and neural network approximation, a singularity-free formation controller is then developed, which guarantees the boundedness of all the closed-loop system signals and achieves satisfaction of prescribed performance specifications on the formation errors. Simulations are performed to verify the effectiveness of the formation control strategy.

Heterogeneous formation control of multiple rotorcrafts with unknown dynamics by reinforcement learning

In this paper, a distributed model-free solution based on reinforcement learning is proposed for the leader–follower formation control problem of heterogeneous multi-agent systems. The multi-agent system consists of multiple rotorcrafts involving a virtual leader and multiple followers, where the dynamics of leaders and followers is unknown. The formation control problem is firstly formulated as an optimal output regulation problem. A discounted performance function is then introduced to guarantee that the tracking error asymptotically converges to zero, and an online off-policy reinforcement learning algorithm is proposed to solve the optimal output problem online using the data generated along the trajectories of the agents. A simulation example is provided to validate the effectiveness of the proposed control method.

Adaptive leader–follower formation control for swarms of unmanned aerial vehicles with motion constraints and unknown disturbances

In this paper, the 3D leader–follower formation control problem, which focuses on swarms of fixed-wing Unmanned Aerial Vehicles (UAVs) with motion constraints and disturbances, has been investigated. Original formation errors of the follower UAVs have been transformed into the Frenet-Serret frame. Formation control laws satisfying five motion constraints (i.e., linear velocity, linear acceleration, heading rate, climb rate and climb angle) have been designed. The convergence of the control laws has been discussed via the Lyapunov stability tool. In addition, to address the unknown disturbances, an adaptive disturbance observer is exploited. Furthermore, formation control laws involving estimated disturbances are presented as well. The collision avoidance between UAVs is achieved with the artificial potential method. Simulation results obtained using four scenarios verify the effectiveness of the proposed method in situations with constant disturbances and varying disturbances, as well as without disturbances.

Bounded neural adaptive formation control of multiple underactuated AUVs under uncertain dynamics

This paper studies the leader-following formation control problem of multiple underactuated autonomous underwater vehicles (AUVs) under uncertain dynamics and limited control torques. A multi-layer neural network-based estimation model is designed to handle the unknown follower dynamics. The backstepping approach, a neural estimation model, as well as a saturation function, are employed to propose a bounded formation control law. Then, a Lyapunov-based stability analysis ensures a maximum bound for all the closed-loop system variables and guarantees that the formation errors between vehicles ultimately converge to a bounded compact set. The outstanding properties of the designed controller are highlighted as follows. First, only the leader position and given formation are required without any leader velocity information requirement. Second, update laws of the neural network weight are extracted using the estimation errors instead of tracking ones, which can effectively enhance the transient characteristics of the control system. Third, the control torques are bounded within predefined bounds. At the end, extensive simulations are given for a number of AUVs to verify the efficiency of the presented formation control scheme.

Adaptive Image-Based Leader–Follower Formation Control of Mobile Robots With Visibility Constraints

This article addresses the problem of leader-follower formation control of mobile robots using only onboard monocular cameras that subjected to visibility constraints. An adaptive image-based visual servoing control strategy was proposed following the prescribed performance control methodology. First, the leader-follower visual kinematics in the image plane and an error transformation with predefined performance specifications are presented. Then, an adaptive control law with online estimating the inverse height between the optical center of camera and the single feature point attached to leader is designed to ensure the global stability of the closed-loop system. Finally, the applicability and performance of the proposed control scheme are demonstrated by the numerical simulations and hardware experiments. Compared with other formation control schemes, our solution relies only on onboard visual sensors without communication, since it does not need the relative angle/distance between the robots, or the velocity of the leader. Moreover, it guarantees the prescribed transient and the steady-state performance besides the visibility constraints.

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.