Robust Formation Control Research Articles

Robust time-varying formation control for underactuated autonomous underwater vehicles with disturbances under input saturation

In this paper, a robust control scheme is developed for time-varying formation of multiple underactuated autonomous underwater vehicles (AUVs) with disturbances under input saturation. Firstly, the reference trajectory of the follower is defined using a body-fixed coordinate transformation based on the leader position and predetermined time-varying formation. Next, three new additional control terms are proposed to handle the input saturation and underactuation problems of AUVs, respectively. On the basis of the above, the robust formation control law is designed incorporating a disturbance observer into the dynamic surface control (DSC) method, where the disturbance observer is constructed to online estimate unknown time-varying disturbances. The designed formation control law does not depend on the leader's acceleration due to using DSC and the mass matrix in the dynamic model of AUVs is non-diagonal, which is more realistic. Strict stability analysis indicates that the designed robust formation control law can make AUVs achieve the predefined time-varying formation, while guaranteeing uniform ultimate boundedness of all signals of the AUV formation closed-loop control systems. Simulation results on three AUVs demonstrate the effectiveness of the proposed formation control scheme.

Robust formation control in [formula omitted] for tree-graph structures with prescribed transient and steady state performance

This paper presents a novel control protocol for distance and orientation formation control of rigid bodies, whose sensing graph is a static and undirected tree, in the special Euclidean group SE(3). The proposed control laws are decentralized, in the sense that each agent uses only local relative information from its neighbors to calculate its control signal, as well as robust with respect to modeling (parametric and structural) uncertainties and external disturbances. The proposed methodology guarantees the satisfaction of inter-agent distance constraints that resemble collision avoidance and connectivity maintenance properties. Moreover, certain predefined functions characterize the transient and steady state performance of the closed loop system. Finally, simulation results verify the validity and efficiency of the proposed approach.

Robust time‐varying formation control for multiple underwater vehicles subject to nonlinearities and uncertainties

SummaryThis paper addresses the robust formation control problem for multiple autonomous underwater vehicles (AUVs) to achieve the desired formation trajectory and time‐varying formation pattern and to align the vehicle attitudes. The dynamics of each AUV system involves parameter variations, nonlinear dynamics, and external disturbances. A robust distributed formation control protocol is developed based on the graph theory and the robust compensation theory. It is proven that the tracking errors of the global uncertain system can converge into a given neighborhood of the origin in a finite time. Simulation results substantiate the effectiveness of the developed formation control method for multiple AUVs subject to nonlinearities and uncertainties.

Distributed Formation Control: Asymptotic Stabilization Results Under Local Noisy Information.

This paper studies the relative-position-based reference-frame-free formation control in the plane for discrete-time multiagent systems under both measurement and communication noises. To achieve the desired formation, a robust distributed orientation estimate algorithm and a robust distributed formation control law are designed. The main idea of our method is to use the historical measurement information to get unbiased estimates and use the stochastic approximation method to inhibit the noise. Under mild assumptions on the measurement/communication noises and agents' initial orientation angles, we show that a common reference frame can be asymptotically shared by all agents and the desired formation can be asymptotically stabilized almost surely under the designed distributed control law, if and only if the magnitude of the bearing measurement noise is less than ( π / 4) , the communication and distance sensing topology is rooted and the corresponding bearing sensing topology is connected. Simulations are conducted to verify the correctness and effectiveness of our orientation estimate algorithm and formation control law.

Robust Formation Control for Uncertain Multiagent Systems With an Unknown Control Direction and Disturbances

This paper proposes robust formation control laws for uncertain multiagent systems subjected to an unknown control direction and disturbances under the assumption that information about the reference trajectory is only available to some of the agents. Different from the existing results, the proposed control algorithms can enable the agents to converge to the specified points utilizing only local relative measurements, in which no control direction information and upper bounds of external uncertainties are required. To simplify and facilitate the analysis, external disturbances are roughly divided into structured and unstructured uncertainties. To attenuate the errors caused by the structured uncertainties, an adaptive control technique is applied to obtain the estimates of the unknown constant coefficients, and compensating functions with learning ability are developed to eliminate the errors caused by the unstructured uncertainties. A Nussbaum-type function is employed to settle the formation control problem in the presence of unknown signs of the control direction. Formation stability analysis for uncertain nonlinear multiagent systems is performed according to the Lyapunov stability theory. It is proved that the formation errors are bounded within a small desired accuracy by implementing the proposed robust control laws, and the desired formation is then achieved. Finally, two illustrative examples are presented to support the obtained theoretical results.

Autonomous leader-follower formation control of non-holonomic wheeled mobile robots by incremental path planning and sliding mode augmented tracking control

This paper presents a novel robust and autonomous formation control scheme for wheeled mobile robots in the leader-follower formation control framework considering their non-holonomic constraints. In the proposed formation control scheme, the leader robot of the group plans its path of navigation autonomously in a cluttered environment by employing incremental path planning by modified artificial potential field. Then, the follower robots in the group plan their path in order to follow the leader robot by maintaining a particular formation using the separation-bearing (l − Ψ) control. Then the formation control problem has been transformed into a trajectory tracking control problem. The kinematic control component of the tracking controller provides the necessary velocity input for eliminating the non-holonomic constraints, whereas, the sliding mode augmented robust trajectory tracking control component minimises the effects of nonlinearities, model uncertainties, parameter variations, and disturbances. The effectiveness of the proposed control law has been established by simulation studies.

Event-Triggered Control for Nonlinear Uncertain Second-Order Multi-Agent Formation With Collision Avoidance

In this paper, we investigate the robust formation control of nonlinear uncertain second-order multi-agent systems with guaranteed collision avoidance. A novel event-triggered control algorithm together with event-triggered mechanism is designed to significantly reduce the control updating and eliminate continuous communication between agents. The model uncertainties and external disturbances are estimated in finite time by the continuous robust integral of sign of the error (RISE)-based observer. Moreover, inter-agent collisions and obstacles are avoided through incorporating artificial potential function approach into the formation control scheme. Based on the Lyapunov method and graph theory, sufficient conditions on multi-agent formation stability, robustness against perturbations, collision avoidance, and Zeno behavior elimination are derived. The simulation results finally are given to validate the performance of our approach.

UDE-Based Robust Command Filtered Backstepping Control for Close Formation Flight

This paper presents an uncertainty and disturbance estimator (UDE)-based nonlinear robust controller for close formation flight in light of the command filtered backstepping technique. To maximize the formation aerodynamic benefits at different flight maneuvers, the formation geometry is described in the wind frame of the leader aircraft. A novel nonlinear robust close formation control algorithm with a two-degree-of-freedom nature is developed. The command filtered backstepping technique is employed to design the baseline formation controller, whereas the UDE is introduced to enhance the robustness of the baseline formation control. The proposed control law can lead to desired tracking performance for the close formation flight under different maneuvers without using the acceleration information of the leader aircraft, asymptotical stability for the close formation flight at a level and straight flight with constant speeds, and enough robustness against the formation aerodynamic effects by purely observing system states and inputs. Numerical simulations are performed to show the feasibility and efficiency of the proposed controller.

Robust Formation Control for Multiple Quadrotors With Nonlinearities and Disturbances

In this paper, the robust formation control problem is investigated for a group of quadrotors. Each quadrotor dynamics exhibits the features of underactuation, high nonlinearities and couplings, and disturbances in both the translational and rotational motions. A distributed robust controller is developed, which consists of a position controller to govern the translational motion for the desired formation and an attitude controller to control the rotational motion of each quadrotor. Theoretical analysis and simulation studies of a formation of multiple uncertain quadrotors are presented to validate the effectiveness of the proposed formation control scheme.

Quad-Rotor robust time-varying formation control: a Continuous Sliding-Mode Control approach

ABSTRACT This paper deals with the robust tracking problem for a group of Quad-Rotors forming a time-varying geometric pattern, i.e. formation control, in the presence of external disturbances. Such a robust control strategy is able to deal with any formation scheme such that there exists a directed spanning tree from the leader agent to all other agents. The proposed output-control strategy is based on a Continuous Sliding-Mode Control (Continuous-SMC) approach which is composed of a Finite-Time Sliding-Mode Observer (FT-SMO) and hierarchical cascade Continuous-SMCs. It is assumed that only the positions and angles of each Quad-Rotor are available to measure. Despite the disturbances acting on all the Quad-Rotor dynamics, this control strategy provides uniform finite-time stability for the altitude and yaw angle tracking and formation errors, and uniform exponential stability for the forward and lateral tracking and formation errors. Moreover, four different types of Continuous-SMCs can be used in the proposed strategy. Numerical simulations illustrate the performance of the proposed strategy.

Adaptive cooperative formation control of autonomous surface vessels with uncertain dynamics and external disturbances

This paper investigates the leader-follower cooperative formation control problem of autonomous surface vessels (ASVs) with uncertain dynamics and external disturbances. Especially, ASVs can communicate with each other under a directed interaction topology. Based on directed graph theories, backstepping and the minimal learning parameter (MLP) algorithm, a novel distributed robust formation controller with two different adaptive laws is developed for each ASV. Dynamic surface control (DSC) is utilized to eliminate repeated derivative of virtual control laws, which is important to generate real-time control signals. Neural networks (NNs) approximation combined with an MLP-based adaptive law is incorporated into the proposed controller to enhance the robustness against model uncertainties. Then only one learning parameter instead of the enormous weights matrix is estimated for each ASV. An auxiliary adaptive law is designed to obtain a continuous controller when compensating approximation errors and disturbances. It is shown that desired formation shapes can be achieved with the proposed controller if the interaction topology has a directed spanning tree, and formation errors are guaranteed to be semi-global uniformly ultimately bounded (SGUUB). Simulations and comparison results are provided to illustrate the effectiveness of theoretical results.

Robust and adaptive chatter free formation control of wheeled mobile robots with uncertainties

This paper addresses the robust formation control of non-holonomic mobile robots with homogeneous system architecture and decentralized control structure. Therefore, it was necessary the mathematical modeling of mobile robots, from which, the Separation-Bearing variant of Leader-Following control strategy was implemented. The stability proof were based on the Lyapunov theory. The sliding mode control (SMC) strategy was used in the controller design to make the control robust to the incidence of uncertainties and disturbances. The Fuzzy Adaptive Formation Control is designed to eliminate the previous bounding knowledge of these uncertainties and disturbances. The proposed control effectiveness is demonstrated by results obtained with simulations in Matlab/Simulink. The pure kinematic and kinematic with disturbances is also analyzed. The results shows the controllers effectiveness to formation of multi-robots systems to the eight-shaped trajectory.

Robust adaptive formation control of underactuated autonomous surface vessels based on MLP and DOB

This paper investigates the leader–follower formation problem of multiple underactuated autonomous surface vessels in the presence of model uncertainties and environmental disturbances. Specially, the formation is defined in the body-fixed coordinates of the leader vessel and velocities of the leader are unavailable to followers. A novel robust adaptive formation control scheme based on the minimal learning parameter (MLP) algorithm and the disturbance observer (DOB) is presented. To address related formation configurations and unknown velocities of the leader, adaptive programming of the virtual vessel is introduced. By the neural networks (NNs) technique, the DOB is constructed and the formation controller is developed with different MLP-based adaptive laws. Under the proposed controller, it is shown that the desired formation can be achieved only with the position and yaw angle of the leader. And formation errors are guaranteed to be semiglobal uniformly ultimately bounded. Compared with existing results, the NNs-based DOB can compensate disturbances effectively with less model information. Meanwhile, the formation controller and the DOB can share the same set of NNs with smaller computational effort, where only two parameters need to be learned online for each of them. Simulations and comparison results are provided to illustrate the effectiveness of theoretical results.

Cluster formation for multi‐agent systems under disturbances and unmodelled uncertainties

The cluster formation problem of the multi-agent system in the presence of disturbances and unmodelled uncertainties has been studied. Agents in the system are partitioned into multiple clusters and each cluster is required to maintain a predefined time-varying sub-formation, where the sub-formations can be different from each other. An identifier-based robust control algorithm using the neighbouring relative information has been proposed to accomplish the time-varying cluster formation. Some sufficient conditions for the second-order multi-agent system to achieve the control objective have been proposed based on the graph theory and the Lyapunov method. Numerical simulations are provided to testify the validity of the algorithm. Compared to the previous work on cluster formation control, the novel feature of this study is that disturbances and unmodelled uncertainties are taken into consideration and the authors propose a robust cluster formation control algorithm based on a non-linear identifier to eliminate the adverse effects of disturbances and unmodelled uncertainties.

Robust Distance-Based Formation Control of Multiple Rigid Bodies with Orientation Alignment

This paper addresses the problem of distance- and orientation-based formation control of a class of second-order nonlinear multi-agent systems in 3D space, under static and undirected communication topologies. More specifically, we design a decentralized model-free control protocol in the sense that each agent uses only local information from its neighbors to calculate its own control signal, without incorporating any knowledge of the model nonlinearities and exogenous disturbances. Moreover, the transient and steady state response is solely determined by certain designer-specified performance functions and is fully decoupled by the agents’ dynamic model, the control gain selection, the underlying graph topology as well as the initial conditions. Additionally, by introducing certain inter-agent distance constraints, we guarantee collision avoidance and connectivity maintenance between neighboring agents. Finally, simulation results verify the performance of the proposed controllers.

Distributed Sliding-Mode Formation Controller Design for Multirobot Dynamic Systems

This paper presents a distributed formation control for multirobot dynamic systems with external disturbances and system uncertainties. First from the Lagrangian analysis, the dynamic model of a wheeled mobile robot can be derived. Then, the robust distributed formation controller is proposed based on sliding-mode control, consensus algorithm, and graph theory. In this study, the robust stability of the closed-loop system is guaranteed by the Lyapunov stability theorem. From the simulation results, the proposed approach provides better formation responses compared to consensus algorithm.

Leader-following control of perturbed second-order integrator systems with binary relative information

ABSTRACTIn this paper, we study the leader-following control problem for second-order integrator systems with bounded input disturbances using only binary relative position and velocity information. The leader is allowed to be dynamically evolving with a bounded acceleration which is unknown to any of the followers. With the proposed distributed controller, we prove that despite the fact that only very coarse relative information is available, robust finite-time leader-following control can be achieved by properly choosing the control gains. As an extension, robust finite-time formation control can also be achieved with the proposed control strategy using only binary relative information. Two simulation examples are provided to illustrate the results.

Observer‐based controller design with disturbance feedforward framework for formation control of satellites

In this study, a bespoke sliding mode non-linear observer and a linear controller framework is proposed for achieving robust formation control of a cluster of satellites in the case of a circular reference orbit. Exploiting the structure of the satellite dynamics, a non-linear observer is proposed based on super-twist sliding mode ideas. The observer estimates the states and any unknown bounded disturbances in ‘finite time’. The stability properties of the observers are demonstrated using Lyapunov techniques. A distributed controller, based on the estimated states and the relative position output information, depending on the underlying communication topology, is proposed. A polytopic representation of the collective dynamics which depends on the eigenvalues of the Laplacian matrix associated with the communication topology is used to synthesise the gains of the proposed control laws. A simulation example is used to demonstrate the efficacy of the proposed approach.

Distributed Consensus-Based Robust Adaptive Formation Control for Nonholonomic Mobile Robots with Partial Known Dynamics

This paper investigates the distributed consensus-based robust adaptive formation control for nonholonomic mobile robots with partially known dynamics. Firstly, multirobot formation control problem has been converted into a state consensus problem. Secondly, the practical control strategies, which incorporate the distributed kinematic controllers and the robust adaptive torque controllers, are designed for solving the formation control problem. Thirdly, the specified reference trajectory for the geometric centroid of the formation is assumed as the trajectory of a virtual leader, whose information is available to only a subset of the followers. Finally, numerical results are provided to illustrate the effectiveness of the proposed control approaches.

Robust formation control without velocity measurement of the leader robot

In this paper a control problem of leader–follower motion coordination of multiple nonholonomic mobile robots is addressed and subsequently in the proposed scheme, a reference trajectory generated based on the information from the leader is tracked by the follower robots. To alleviate demanded information on the leader, specifically to eliminate the measurement requirement or estimation of the leader's velocity and dynamics, a virtual vehicle is constructed whereby its trajectory converges to the reference trajectory of the follower. Trajectory tracking controller is then designed to allow the follower robot to track the virtual vehicle using neural network approximation, in combination with the backstepping and Lyapunov direct design technique and finally the performance and effectiveness of the controller is verified throughout the experiments.