Leader-follower Formation Research Articles

Network-based leader-following formation control of second-order autonomous unmanned systems

This article investigates two kinds of leader-following formation control problems of second-order autonomous unmanned systems under directed topology, that are, the cases with constant velocity and time-varying velocity for the leader. First, the kinematical equation of autonomous unmanned systems is established according to some real scenarios. Second, by assuming the velocity of the leader is constant, a sufficient condition ensuring the formation control of autonomous unmanned systems is derived and some control parameters are suitably designed. Third, it is assumed that the velocity of leader is time-varying, and the formation controller with two parts is designed. The first part is intended to form the desired formation of all followers and the second part aims to reach the consensus of velocity. Some simulation examples are finally presented to verify the effectiveness of the obtained theoretical results.

Leader–Follower Formation Control With Prescribed Performance Guarantees

This article addresses the problem of achieving relative position-based formation control for leader-follower multiagent systems in a distributed manner using a prescribed performance strategy. Both the first- and second-order cases are treated and a leader-follower framework is introduced in the sense that a group of agents with external inputs is selected as leaders in order to drive the group of followers in a way that the entire system achieves a target formation within certain prescribed performance transient bounds. Under the assumption of tree graphs, a distributed control law is proposed for the first-order case when the decay rate of the performance functions is within a sufficient bound. Then, two classes of tree graphs that can have additional followers are investigated. For the second-order case, we propose a distributed control law based on a backstepping approach for the group of leaders to steer the entire system achieving the target formation within the prescribed performance bounds. Finally, several simulation examples are given to illustrate the results.

Adaptive Leader–Follower Formation for Unmanned Surface Vehicles Subject to Output Constraints

This paper addresses the leader–follower formation control strategy for unmanned surface vehicles with model uncertainties. First, to achieve the desired formation configuration, the line-of-sight (LOS) scheme is incorporated in the guidance design. The constraints of LOS range and angle are required to meet the connectivity maintenance and collision avoidance. Tan-type time-varying Barrier Lyapunov function (BLF) is applied to address the output constraints. Next, in the formation control design, bioinspired models are combined with backstepping techniques to achieve less calculation. Adaptive fuzzy control approach is developed to deal with the uncertainties of marine vessels due to their superior approximation capability. Finally, the uniform ultimate boundedness of all signals can be guaranteed via stability analysis. Simulation examples are carried out to demonstrate the feasibility of the theoretical results.

A Distributed Model Predictive Control Strategy for Constrained Multi-Vehicle Systems Moving in Unknown Environments

In this paper, we propose a distributed model predictive control strategy for a team of vehicles moving in an unknown obstacle scenario. In particular, we combine receding horizon control arguments with leader-follower formations in order to design a flexible architecture where the vehicle topology, if needed, can be rearranged to better cope with the presence of obstacles. Each vehicle is equipped with an ad-hoc dual-mode controller in charge of tracking along the leader-follower chain the predecessor vehicle (namely the target for the leader) and ensuring absence of collisions. Moreover, whenever the leader recognizes that the obstacle scenario obstructs its navigation, the current formation is properly reconfigured by preserving recursive feasibility and obstacle avoidance properties. Final numerical results on a team of seven point mobile robots are instrumental to show the main features of the proposed distributed model predictive control algorithm.

Multi-autonomous underwater vehicle formation control and cluster search using a fusion control strategy at complex underwater environment

We introduce a multiple autonomous underwater vehicle (multi-AUV) control strategy to improve the cooperative operation ability in formation control and cluster search operations and to minimize the likelihood of collisions and interference with teammates and obstacles under various complex working conditions. Our approach uses a fusion control strategy with a redistribution mechanism (RM) based on virtual structure and leader–follower formation characteristics to improve the rapidity, stability, and accuracy of the multi-AUVs. The RM improved the rapidity and uniqueness of the random distribution formation by addressing over- and under-allocation. The combination of two (26-point and 8-point) path updating methods based on a hybrid bio-inspired self-organizing map algorithm considerably enhanced the performance of the multi-AUV system. Simulation tests and performance analyses indicated that the 8-point path updating method performed better in terms of rapidity; however, the 26-point path updating method was superior in integrity. The hunting performance of the fusion-controlled multi-AUV formation, was then analyzed to verify the feasibility of real-time formations under dynamic and static mixing of multi-obstacles by considering shape irregularities and the random distribution of multi-obstacles in three-dimensional underwater environments.

Proximity Operations and Three Degree-of-Freedom Maneuvers Using the Smartphone Video Guidance Sensor

This paper presents the first demonstration of NASA’s Smartphone Video Guidance Sensor (SVGS) as real-time position and attitude estimator for proximity and formation maneuvers. An optimal linear quadratic Gaussian controller was used, combining a linear quadratic regulator and a Kalman filter. The system was demonstrated controlling the 3-degree of freedom planar motion of the RINGS ground units (Resonant Inductive Near-field Generation Systems). A state-space model of the system’s 3-DOF motion dynamics was derived, and model parameters extracted using a system identification technique. The system’s motion control performance is experimentally demonstrated in both tracking and formation maneuvers. The results highlight the capabilities and performance of the Smartphone Video Guidance Sensor (SVGS) as a vision-based real-time position and attitude sensor for motion control, formation flight and proximity operations. A leader-follower formation maneuver approach is demonstrated, as well as position hold and path following.

Formation keeping method of weakly driven multi robot in time-varying flow field

In order to solve the problem that group formation control and optimal path cannot be considered simultaneously for weakly driven multi robot under the influence of environmental flow field, a method combining time-optimal path planning and leader-follower formation control is proposed in this paper. The time-optimal path of the leader is obtained by level set method, and the formation keeping is based on this path. According to the position of the leader and the reachable set of the follower at a certain time, the position of the follower is determined by solving the formation optimization function, and the complete path is completed by solving the formation optimization problem iteratively. While the formation optimization function maintains the group formation, the reachable set generated by the level set method ensures the feasibility of the path obtained in the time-varying strong flow.

Distributed Control Algorithm for Leader–Follower Formation Tracking of Multiple Quadrotors: Theory and Experiment

This article studies the leader-follower formation tracking problem of multiple quadrotors. In particular, the quadrotors are steered to track a reference trajectory while maintaining a desired configuration. The reference trajectory is partially available to a subset of quadrotors, and each quadrotor just interacts locally with its neighbors. A distributed control algorithm is proposed under a hierarchical framework. First, by introducing a distributed saturation control strategy, a command force is synthesized for the position to track the reference trajectory with a desired displacement. Second, a bounded applied force and a nonsingular command attitude are extracted from the synthesized command force based on a proper choice criterion of control parameters. Last but not the least, an applied torque is designed for the attitude to track the command one. In terms of Lyapunov theory, it is shown that the overall closed-loop error system is asymptotically stable. This indicates the accomplishment of the concerned leader-follower formation tracking control objective of multiple quadrotors. Finally, the effectiveness of the proposed distributed control algorithm is verified through both simulations and experiments.

Observer-based Time-varying Formation Tracking for One-sided Lipschitz Nonlinear Systems via Adaptive Protocol

In this paper, we investigate the problem of observer-based time-varying leader-following formation tracking for multi-agent systems with the one-sided Lipschitz and quadratic inner-boundedness nonlinear dynamics. An idea of the observer-based protocol with an edge-based adaptive law is designed for nonlinear systems, which enable agents to achieve a desired formation tracking when it cannot obtain the full state of the nonlinear system. In contrast to the previous nonlinear formation systems, the advantage of the developed method is that it is less conservative and more general for the nonlinear system with large Lipschitz constants. Besides, under the proposed adaptive law, the design of the protocol does not rely on the known communication topology. Finally, the simulation results for one leader and six followers are proposed to show the feasibility and effectiveness of the proposed method in the nonlinear time-varying formation system.

Distributed Formation Navigation of Constrained Second-Order Multiagent Systems With Collision Avoidance and Connectivity Maintenance.

In this article, we consider the distributed formation navigation problem of second-order multiagent systems subject to both velocity and input constraints. Both collision avoidance and connectivity maintenance of the network are considered in the controller design. A control barrier function method is employed to achieve multiple control objectives simultaneously while satisfying the velocity and input constraints. First, a nominal distributed leader-following formation controller is proposed which satisfies the velocity and input constraints uniformly and handles switching communication graphs. A nonsmooth analysis is employed to prove the global convergence of the controller. Then, a topology-based connectivity maintenance strategy using a new notion of the formation-guided minimum cost spanning tree is proposed and the corresponding barrier function-based constraints are derived. The barrier function-based collision-avoidance conditions are also developed. All barrier function-based constraints are then combined to formulate a quadratic programming problem which modifies the nominal controller when necessary to achieve both collision avoidance and connectivity maintenance. Simulation results demonstrate the effectiveness of the proposed control strategy.

Velocity and Input Constrained Coordination of Second-Order Multi-Agent Systems With Relative Output Information

In this work, we consider the coordination control of second-order multi-agent systems subject to both velocity and input constraints with only relative output information. First, the leaderless consensus problem is considered where a nonlinear distributed controller is proposed which achieves asymptotic consensus of the agents using only local velocity and relative output information. Then, generalization to the leader-following formation control with known leader's input is studied. For the case of unknown leader's input, a finite-time observer-based controller is proposed using sliding mode control ideas. Finally, the collision avoidance requirement for the leader-following formation control is handled by employing control barrier functions. Necessary modifications to the nominal formation controllers are obtained by properly formulating some quadratic problems and the velocity and input constraints are met during the entire operation. Several simulation examples are provided to illustrate the developed controllers and the effectiveness of the collision avoidance strategy.

Distributed Coordination of Heterogeneous Multi-agent Systems with Dynamic Quantization and L2 − L∞ Control

This paper studies the dynamic output feedback consensus control problem of linear heterogeneous multi-agent systems under the leader-follower formation with a dynamic quantizer. In the practical engineering, the status information of the unmanned aircraft vehicle (UAV) and the unmanned underground vehicle (UGV) is normally unmeasurable, which is difficult to design the state feedback controller for the UAV-UGV formation. Besides, in the communication topology of the leader-follower formation based on UAVs and UGVs, the signals should be quantized in each follower. However, the traditional static quantizer has quantization error, which affects the formation stability. Therefore, the control objective is to guarantee the UAV-UGV formation tracking consensus while improve the precision of the quantization. First, the followers and leader systems are based on the discrete-time model, and the output trajectory of the leader is time-varying. Then, a dynamic output feedback controller is provided with a dynamic quantizer to guarantee the tracking performance of the heterogeneous multi-agent systems with a leader. The followers can asymptotically track the leader system with L2 − L∞ control gains by solving a set of linear matrix inequalities (LMIs). Finally, simulation results demonstrate the effectiveness of the designed control strategies.

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.

Charge-product control approach to electrostatic leader-follower formations in LEO plasma wakes

The feasibility of using electrostatic forces to stabilize a close-proximity leader-follower formation is investigated. The leader craft is equipped with a set of affixed spheres whose charge is modulated to hold the charged follower craft along a proscribed trajectory to its nominal leader-relative position. This charge structure and the follower craft are constrained to remain in the plasma wake generated behind all LEO craft because the more-dense ambient plasma outside the wake prevents object charging and electric field propagation. Once the formation is achieved, a controlled electric field is generated by the leader to counter relative accelerations from perturbations like differential drag and solar radiation pressure, holding the follow near its nominal position. Two controllers are derived for the system described, incorporating Coulomb accelerations and linearized gravity and drag accelerations. Simulations are run under unmodeled perturbations and sensor noise for different scenarios, demonstrating the challenges and benefits associated with electrostatic actuation.

Leader–follower formation control of surface vehicles: A fixed-time control approach

In this paper, a novel fixed-time controller (FTC) strategy based on leader–follower mechanism and finite-time disturbance observer (FDO) is proposed for surface vehicles (SVs) formation suffering from complex unknowns. The excellent features of designed strategy are shown below: (1) A fixed-time tracking control (FTTC) approach combining with integral sliding mode (ISM) technology is devised for a nominal leader SV such that fixed-time stability can be ensured; (2) To achieve formation efficiently, a fixed-time formation controller (FTFC) strategy incorporating with backstepping technology is proposed for coordinating follower SVs; (3) Considering complex disturbances in the entire formation system, finite-time disturbance observers (FDOs) are injected into the FTFC framework which in turn contributes to accurate formation control with fixed-time convergence. Finally, simulation results demonstrate remarkable performance of the proposed FDO-FTFC scheme.

Leader–follower formation source seeking control of multiple ships using sliding mode active disturbance rejection observer

In this paper, the control of multiple ships for unknown scalar field source seeking problem with unknown external disturbances is considered. The sliding mode active disturbance rejection observers are designed first to converge to fixed multiple of the unknown external disturbances in finite time, respectively, and a least square method is adopted to estimate the gradient of the unknown scalar field at the position of the leading ship. Second, the surge, sway and angle velocity of the leading ship can converge to the virtual kinematic controllers through the input control of the dynamic controllers using force and torque in finite time. Third, the virtual controllers and dynamic controllers of the following ships are developed to urge the following ships to accomplish the source seeking problem from the perspective of dynamics. Finally, theoretical proofs and simulations are provided to prove the effectiveness of the strategy proposed.

Discrete-Time Distributed Observers Over Jointly Connected Switching Networks and an Application

In this article, we first establish an exponential stability result for a class of linear switched systems and then apply this result to show the existence of the distributed observer for a discrete-time leader system over jointly connected switching networks. Then, we further develop the adaptive distributed observer for the discrete-time leader system over jointly connected switching networks, which has the advantage over the distributed observer in that, it does not require that every follower subsystem know the system matrix of the leader system. As an application of the discrete-time distributed observer, we solve the cooperative output regulation problem of a discrete-time linear multiagent system over jointly connected switching networks. A leader-following formation problem of mobile robots is used to illustrate our design.

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.

From Trajectory Tracking Control to Leader–Follower Formation Control

This work investigates the leader–follower formation control of multiple nonholonomic mobile robots. First, the formation control problem is converted into a trajectory tracking problem and a tracking controller based on the dynamic feedback linearization technique drives each follower robot toward its corresponding reference trajectory in order to achieve the formation. The desired orientation for each follower is selected such that the nonholonomic constraint of the robot is respected, and thus the tracking of the reference trajectory for each follower is feasible. An adaptive dynamic controller that considers the actuators dynamics in the design procedure is proposed. The dynamic model of the robots includes the actuators dynamics in order to obtain the velocities as control inputs instead of torques or voltages. Using Lyapunov control theory, the tracking errors are proven to be asymptotically stable and the formation is achieved despite the uncertainty of the dynamic model parameters. In order to assess the proposed control laws, a ROS-framework is developed to conduct real experiments using four ROS-enabled mobile robots TURTLEBOTs. Moreover, the leader fault problem, which is considered as the main drawback of the leader–follower approach, is solved under ROS. An experiment is conducted where in order to overcome this problem, the desired formation and the leader role are modified dynamically during the experiment.