Formation Tracking Errors Research Articles

Bearing-based formation control for multiple underactuated autonomous surface vehicles with flexible size scaling

Most existing formation control approaches for Autonomous surface vehicles (ASVs) focused on achieving rigid patterns with invariant inter-vehicle distance in open ocean environment. However, these methods cannot be applied to the cooperative missions on irregular inland waterway with changing width (such as rivers, canals and fjords), wherein the inter-vehicle distance should be continuously adjustable to respond to the environment dynamically. This paper proposes a bearing-based formation scaling control scheme for underactuated ASVs to achieve the desired patterns but with a flexible size scaling. By assuming that the fleet satisfies a leader–first-follower structure, the formation scaling parameters are accessible only to leaders, while each follower needs to maintain the bearing constraints to its neighboring ASVs without any knowledge of scale information. We respectively design distributed control laws for leaders and follower, and adaptive neural networks (NNs) are incorporated to approximate the dynamic uncertainties induced by parameter perturbations, external disturbances and input saturations. To improve the tracking performance, an auxiliary adaptive law is resorted to compensate the non-zero estimation error of NNs. Theoretical analysis demonstrates that the closed-loop scaling maneuver tracking and formation tracking errors converge to zero asymptotically. The comparative simulation results are presented to substantiate the effectiveness of the designed control method.

3D hybrid formation control of an underwater robot swarm: Switching topologies, unmeasurable velocities, and system constraints

This paper addresses formation control of underactuated autonomous underwater vehicles in three-dimensional space, using a hybrid protocol that combines aspects of centralized and decentralized control with constraints that are particular to underwater vehicles, including switching topologies, unmeasurable velocities, and system constraints. Using a distributed leader–follower model, the hybrid formation protocol does not require velocity sensing, access to global information, or static and connected topologies. To handle switching jointly connected networks—that is, to tolerate temporary disconnections—a distributed observer is designed for followers to cooperatively estimate leader states using local measurements and local interactions. On this basis, a compound formation control strategy is proposed to achieve geometric convergence. Firstly, cascaded extended state observers are developed to recover the unmeasurable velocities and unknown dynamic uncertainties induced by internal model uncertainty and external disturbances. Secondly, an improved three-dimensional line-of-sight guidance law at the kinematic level is used to address the underactuated configuration and the nonzero attack and sideslip angles. Thirdly, to overcome potential instability as a result of system constraints, including velocity constraints and input saturations, two adaptive compensators in the dynamic controller are used to address the negative effects of truncation. Using the proposed approach, the estimation errors and formation tracking errors are proved to be uniformly and ultimately bounded. Additionally, the numerical simulation results verify the performance of the approach and demonstrate improvement over both distributed and centralized state-of-the-art approaches.

Distributed adaptive practical formation tracking for multi‐agent systems with actuator faults

AbstractThis paper mainly studies the practical fault tolerant formation tracking for multi‐agent systems under directed topology. The objective is to achieve the desired formation in the spatial positions and track the reference signal generated by one and multiple leaders. Considering that the real state information is unavailable, the distributed observer is proposed using the relative information of neighborhood agents, where the observer gain calculation is not constrained by the number of agents. With the adaptive updating mechanism, two effective distributed fault‐tolerant formation tracking protocols are proposed and the feasible condition of time‐varying formation is introduced. Furthermore, based on the proposed control protocol, the formation tracking errors and other signals converge to bounded region around the origin. Towards the end, three simulations are considered to illustrate the effectiveness of the proposed techniques.

Terminal sliding-mode disturbance observer-based finite-time adaptive-neural formation control of autonomous surface vessels under output constraints

AbstractThis paper proposes a tracking controller for the formation construction of multiple autonomous surface vessels (ASVs) in the presence of model uncertainties and external disturbances with output constraints. To design a formation control system, the leader-following strategy is adopted for each ASV. A symmetric barrier Lyapunov function (BLF), which advances to infinity when its arguments reach a finite limit, is applied to prevent the state variables from violating constraints. An adaptive-neural technique is employed to compensate uncertain parameters and unmodeled dynamics. To overcome the explosion of differentiation term problem, a first-order filter is proposed to realize the derivative of virtual variables in the dynamic surface control (DSC). To estimate the leader velocity in finite time, a high-gain observer is effectively employed. This approach is adopted to reveal all signals of the closed-loop system which are bounded, and the formation tracking errors are semi-globally finite-time uniformly bounded. The computer simulation results demonstrate the efficacy of this newly proposed formation controller for the autonomous surface vessels.

Adaptive appointed-time formation tracking control for multiple spacecraft with collision avoidance under a dynamic event-triggered mechanism

This paper focuses on the appointed-time formation control problem for multiple spacecraft with limited communication and control resources. The control objective is to make each spacecraft move along its reference trajectory with guaranteed tracking performance while avoiding collision with each other. To this end, we attempt to propose an event-triggered formation tracking control protocol to achieve this objective. Firstly, a sliding mode manifold containing formation tracking and velocity errors is designed. Then, a group of prescribed performance constraints are imposed on the transient and steady-state behaviors of the newly defined sliding mode manifold, to derive a formation controller with performance guarantees and appointed-time convergence. By integrating the artificial potential function, a collision-free control term is devised, which is plus after the foregoing formation tracking controller to avoid the collision between the neighboring spacecraft. Furthermore, to reduce unnecessary data transmission and improve resource utilization, a dynamic event-triggered strategy is proposed to determine when the developed controller updates. In this case, the threshold parameter in triggering condition is dynamically changed over time rather than being fixed, in order to achieve a desired balance between communication frequency and system performance. Compared with the existing works, the major advantage of the proposed control protocol is that the formation tracking performance, the collision avoidance and the communication transmission preservation can be assured simultaneously. Finally, comparative simulations illustrate the effectiveness of the proposed protocol.

A novel adaptive fuzzy reinforcement learning controller for a platoon of off-axle hitching tractor-trailers with a prescribed performance and path curvature compensation

This paper addresses an artificial intelligence-based platoon control (AIPC) problem of autonomous off-axle hitching tractor-trailer wheeled mobile robots (TTWMRs) in a planar motion. Towards this end, a novel saturated nonlinear interval type-2 neuro-fuzzy reinforcement learning controller is proposed to construct a convoy-like motion of TTWMRs. To overcome the cutting-corner phenomenon in the platoon motion, the curvature of the reference trajectory is estimated and the cutting-corner behaviour is prevented. In order to deal with the situation where the velocity and acceleration signals are not measurable or corrupted by the measurement noise, a high-gain observer (HGO) is employed. The prescribed performance control (PPC) is also engaged in the control design procedure to guarantee inter-vehicular communication preservation, collision prevention between each consecutive pair in the platoon, singularity cancellation, and some prespecified desired characteristics of the convoy formation tracking errors such as maximum undershoot/overshoot, convergence rate, and final tracking precision. The Lyapunov-based stability analysis reveals semi-global uniform ultimate boundedness (SGUUB) convergence of tracking errors for the entire platoon system. With the suggested control framework, simulations and comparisons are conducted in which the control performance is considerably improved compared with the existing literature.

Distributed active disturbance rejection formation containment control for multiple autonomous underwater vehicles with prescribed performance

In this paper, a distributed formation containment control (FCC) issue is studied for multiple autonomous underwater vehicles (MAUVs) system with prescribed performance based on the active disturbance rejection control (ADRC) method in three-dimensional space. The unknown nonlinearities and external disturbances of the MAUVs system are approximated in real time by means of extended state observers (ESOs). Furthermore, tracking differentiators (TDs) are introduced for the sake of refraining from the explosion of complexity induced by the derivatives of the virtual control variables of autonomous underwater vehicles. Applying funnel variables, our designed control strategy ensures the formation tracking errors and containment errors to keep within the specified ranges, hence enhancing the control performance of the MAUVs system. Then, a FCC-ADRC scheme for MAUVs system is proposed. Compared with the traditional FCC scheme, the proposed FCC-ADRC scheme not only does not depend on the specific system configuration, but also can deal with any bounded disturbances, thus obtaining a more general, effective and robust disturbance rejection FCC strategies. Additionally, the stability of MAUVs system is verified through Lyapunov stability analysis. At last, the error curves and time-varying formation containment trajectories obtained by simulation confirm the feasibility and effectiveness of our method.

UAV formation control based on distributed Kalman model predictive control algorithm

To address the perturbation of formation of multiple unmanned aerial vehicles (UAVs) subject to external disturbances, an algorithm of distributed Kalman model predictive control is proposed in this paper to improve the accuracy of maintaining a formation in flight. A UAV two-order discrete-time system model was built before devising a Kalman prediction model based on the standard prediction model. The desired formation configuration and neighbor Kalman optimal state estimation were conducted to determine the reference state of UAVs. While taking into account the formation tracking error and input stability, a logarithmic barrier function was introduced in the design of the overall cost function to ensure flight safety. Meanwhile, information was exchanged with neighbors with the directed and time-invariant communication topological structure. With the Lyapunov stability theorem, sufficient conditions were defined for the asymptotic stability of the formation system. Simulation results revealed that the algorithm could effectively suppress the perturbation in the formation of UAVs arising from external disturbances, allowing the formation to cope with the conflicts between individual UAVs.

FSG-based divinable time-varying formation tracking of multiple Lagrangian agents with unknown disturbances and directed graphs

In this paper, a flexible shape generator (FSG) is designed to achieve the divinable transformation process of the time-varying formation, and consider the FSG-based time-varying formation tracking (TVFT) problem of multiple Lagrangian agents with unknown disturbances and directed graphs. A hierarchical control algorithm is newly designed to achieve the control goal without using the prior information of the system model and bounded disturbances, and the specific implementation of the proposed hierarchical algorithms is also provided. By using the Hurwitz criterion and adaptive system theory, the sufficient conditions are derived and the stability analysis show that the formation tracking errors of the considered system are uniform ultimate bounded. Several simulation examples are performed on five two-degree-of-freedom mechanical arms to show the effectiveness of theoretical results.

A Scalable Adaptive Approach to Multi-Vehicle Formation Control with Obstacle Avoidance

This paper deals with the problem of distributed formation tracking control and obstacle avoidance of multi-vehicle systems (MVSs) in complex obstacle-laden environments. The MVS under consideration consists of a leader vehicle with an unknown control input and a group of follower vehicles, connected via a directed interaction topology, subject to simultaneous unknown heterogeneous nonlinearities and external disturbances. The central aim is to achieve effective and collision-free formation tracking control for the nonlinear and uncertain MVS with obstacles encountered in formation maneuvering, while not demanding global information of the interaction topology. Toward this goal, a radial basis function neural network is used to model the unknown nonlinearity of vehicle dynamics in each vehicle and repulsive potentials are employed for obstacle avoidance. Furthermore, a scalable distributed adaptive formation tracking control protocol with a built-in obstacle avoidance mechanism is developed. It is proved that, with the proposed protocol, the resulting formation tracking errors are uniformly ultimately bounded and obstacle collision avoidance is guaranteed. Comprehensive simulation results are elaborated to substantiate the effectiveness and the promising collision avoidance performance of the proposed scalable adaptive formation control approach.

Nonlinear homogeneous sliding mode approach for fixed-time robust formation tracking control of networked quadrotors

A formation flight control algorithm for a multi-agent system composed of a group of perturbated quadrotors is thoroughly investigated in this paper. Both theoretical and practical aspects are addressed in detail to design and implement the control algorithm in a distributed fashion among the networked agents. By adopting the sliding mode framework: (i) A novel Nonlinear Homogeneous Nonsingular Terminal Sliding Surface (NHNTSS) is designed. To ensure Global Asymptotic Stability (GAS) as well as fixed-time convergence of the states, the sliding surface design skillfully employs the generalized weighted homogeneity theory. (ii) A novel Distributed Fixed-Time Continuous Nonsingular Control Protocol (DFCNCP) is proposed for the position-loop of each quadrotor agent by utilizing the designed NHNTSS. Moreover, the control scheme comprises a disturbance observer to compensate for the lumped disturbances affecting the position dynamics and estimate the unmeasurable linear velocities of the quadrotors. Overall, the synthesized controller can drive the formation tracking errors into close vicinity of the origin in fixed-time uniformly to the values of the Initial Conditions (ICs), i.e., initial positions of the quadrotors in the 3D state-space. The mathematical proofs based on the bi-limit approximation in the existing related works can only indicate that the system is guaranteed to be fixed-time stable without any estimation of the settling (convergence) time. In contrast, rigorous stability analyses are conducted in the present work by virtue of algebraic Lyapunov tools, i.e., Algebraic Lyapunov Equation (ALE) and Lyapunov Quadratic Function (LQF). Thus, an expression of the upper-bound on the settling-time is given explicitly. Numerical simulations and real experiments in the form of exhaustive comparative studies are carried out to validate the findings of this research work. Overall, the obtained results confirm the superiority of the proposed control strategy in terms of uniform fast fixed-time convergence, strong disturbance rejection, chattering alleviation, and control precision.

Neural-based formation control of uncertain multi-agent systems with actuator saturation

The formation control problem for a group of first-order agents with model uncertainty and actuator saturation is investigated in this manuscript. An algorithm-and-observer-based formation controller is developed to ensure the semi-global boundedness of the formation tracking error with actuator saturation. First, a fully local-error-related cooperative weight tuning procedure is proposed for the adaptive uncertainty estimation of each agent. The effect of actuator saturation on both the cooperative adaptive estimation and the controller design part is then analysed and discussed. A three-layer neural-based observer is further constructed to achieve finite-time uncertainty approximation with actuator saturation. Besides, the reverse effect led by coupled and saturated control inputs is defined and a new control input distribution algorithm is presented to attenuate the potential oscillation in system states. Finally, comparative simulations based on a multiple omnidirectional robot system are conducted to illustrate the performance of the proposed formation controllers and the new algorithm.

Distributed adaptive fault-tolerant formation control for heterogeneous multiagent systems under switching directed topologies

This paper studies the cooperative fault-tolerant formation control problem of tracking a dynamic leader for heterogeneous multiagent systems consisting of multipile unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) with actuator faults under switching directed interaction topologies. Based on local neighborhood formation information, the distributed fault-tolerant formation controllers are constructed to ensure that all follower UAVs and UGVs can accomplish the demanding formation configuration in the state space and track the dynamic leader’s trajectory. By incorporating the sliding mode control and adaptive control technique, the actuator faults and unknown parameters of follower agents can be compensated. Through the theoretical analysis, it is proved that the cooperatively semiglobally uniformly ultimately boundedness of the closed-loop system is guaranteed, and the formation tracking errors converge to a small adjustable neighborhood of the origin. A simulation example is introduced to show the validity of the proposed distributed fault-tolerant formation control algorithm.

Cooperative Learning-Based Formation Control of Autonomous Marine Surface Vessels With Prescribed Performance

This article addresses the cooperative learning formation control problem for multiple homogeneous marine surface vessels (MSVs) subject to external time-varying disturbances and modeling uncertainties under the prescribed performance constraint. The modeling uncertainties, including hydrodynamic damping terms and unmodeled dynamics are identified/learned by the localized radial basis function neural networks (NNs) in a cooperative way. Disturbance observers are incorporated into the formation control design to compensate for the external time-varying disturbances. A novel cooperative learning formation controller is proposed, which is shown to be capable not only of fulfilling the predefined formation pattern with guaranteed prescribed performance but also of identifying/learning the associated uncertain dynamics based on the cooperative deterministic learning theory. Moreover, the learned knowledge on identified uncertain dynamics is stored in NN models with converged constant NN weights. Based on the stored knowledge, an experience-based formation controller is developed, which can improve the control performance including reduction of the computational burden, while guaranteeing prescribed performance of formation tracking errors. Simulation results demonstrate the effectiveness of the proposed formation control protocol.

Distributed event-triggered fixed-time formation and trajectory tracking control for multiple stratospheric airships

In this study, an event-triggered fixed-time multiple stratospheric airship formation trajectory tracking controller is designed, and it is composed of two parts: the airship leader trajectory tracking controller (ALTTC) and the airship follower formation tracking controller (AFFTC). First, based on the framework of backstepping, the fixed-time ALTTC is designed to allow the trajectory tracking error to converge to zero within a fixed time. Subsequently, the event-triggered fixed-time AFFTC is designed to reduce the formation tracking error to zero within a fixed time. Two event-triggering conditions are designed to reduce the transmission times of control inputs and calculation times of control outputs. The fixed-time stability and the trajectory-tracking and formation-tracking performance of event-triggered closed-loop systems are theoretically shown to be ensured, and Zeno behavior is excluded in the proposed asynchronous event-triggering mechanism. Finally, simulations indicate the effectiveness of the proposed controller.

Event-based formation control of heterogeneous multiagent systems with leader agent of nonzero input

In this paper, the fully distributed event-triggered time-varying formation control of heterogeneous linear multiagent systems is studied. To make the reference trajectory controllable and flexible, the bounded input is introduced to leader agent. The intention of this paper is to decrease the unnecessary information transmission of agents via communication topology by designing the intermittent transmission control protocol. Firstly, the adaptive state compensator is designed to evaluate the state information of leader agent based on the estimation value of leader state and two kinds of event-triggered mechanisms. Then, two types of output-feedback time-varying formation controllers are presented based on different formation feasible conditions. By theoretical analysis, the estimation error of event-triggered state compensator is proved to be uniformly ultimately bounded and the event-triggered mechanisms prevent Zeno behavior, and the formation tracking errors converge to the small region of zero. Finally, some simulation experiments are provided to support the theoretical results.

Distributed event-triggered adaptive output-feedback formation tracking of uncertain underactuated underwater vehicles in three-dimensional space

We present an adaptive-observer-based event-triggered design for distributed three-dimensional output-feedback formation tracking of multiple uncertain underactuated underwater vehicles (UUVs) under a directed network. It is assumed that all nonlinear functions of the vehicle dynamics are unknown and the velocity information of vehicles is immeasurable for feedback. Compared with existing distributed tracking results for UUVs, the primary contribution of this study is the development of a state-transformation-based adaptive observer using a time-varying scaling signal to achieve the output-feedback three-dimensional formation tracking in the presence of unknown nonlinearities and the underactuation constraint. Based on the state transformation, local adaptive observers using neural network approximators and their adaptive laws are designed to estimate local unmeasured velocities of UUV followers. By designing distributed nonlinear error functions and auxiliary stabilizing signals, local output-feedback tracking laws with triggering conditions are recursively constructed to ensure preselected formation performance while solving the underactuation problem of the UUV dynamics. It is shown that the formation tracking errors remain within pre-designable time-varying bounds and finally converge to a neighborhood of the origin. Simulation results are presented to show the effectiveness of the suggested output-feedback formation tracking strategy.

A Q‐Learning‐Based Parameters Adaptive Algorithm for Formation Tracking Control of Multi‐Mobile Robot Systems

This paper proposes an adaptive formation tracking control algorithm optimized by Q‐learning scheme for multiple mobile robots. In order to handle the model uncertainties and external disturbances, a desired linear extended state observer is designed to develop an adaptive formation tracking control strategy. Then an adaptive method of sliding mode control parameters optimized by Q‐learning scheme is employed, which can avoid the complex parameter tuning process. Furthermore, the stability of the closed‐loop control system is rigorously proved by means of matrix properties of graph theory and Lyapunov theory, and the formation tracking errors can be guaranteed to be uniformly ultimately bounded. Finally, simulations are presented to show the proposed algorithm has the advantages of faster convergence rate, higher tracking accuracy, and better steady‐state performance.

Robust Collaborative Team Formation Control of Hybrid Teams of Biped Robots and Wheeled Vehicles Under External Disturbance and Communication Interactions

In this study, a collaborative team formation system of hybrid teams of biped robots and tractor-trailers is designed for some common task. The collaborative team formation system consists of a number of hybrid team formation subsystems. Each hybrid team formation subsystem is composed of a tractor-trailer as the leader and a group of biped robots as followers. For the convenience of collaborative team formation design, novel reference models are proposed to generate the desired collaborative time-varying leader-follower team formation for the cooperative tractor-trailers and biped robots in each hybrid team. Accordingly, the collaborative team formation design problem is simplified to a set of independent robust model reference tracking design problems for each agent under external disturbances and communication couplings from other agents. Subsequently, the robust <i>H</i>&#x221E; decentralized collaborative team formation tracking control strategy is proposed to achieve the independent team formation tracking control for each agent and efficiently attenuate the effect of external disturbance and communication coupling from other agents on the team formation tracking performance of each agent. In order to avoid solving the difficult Hamilton-Jacobi inequality (HJI) of the robust <i>H</i>&#x221E; decentralized collaborative team formation tracking control for each agent, the numerical linear parameter-varying (LPV) modeling method is employed to approximate the nonlinear team formation tracking error dynamic system of each agent such that the HJI can be equivalently transformed to a set of linear-matrix inequalities (LMIs) which can be efficiently solved by MATLAB LMI TOOLBOX. Since the robust <i>H</i>&#x221E; decentralized collaborative team formation tracking control scheme is employed based on local information, the collaborative team formation system can be extended to very large-scale biped robots and tractor-trailers. Finally, a simulation example of robust <i>H</i>&#x221E; decentralized collaborative team formation tracking control design of three collaborative teams, in which each hybrid team consists of one tractor-trailer as the leader and six biped robots as followers, is given to compare with the optimal <i>H</i>2 decentralized method to verify the effectiveness of the proposed scheme.

Time-varying output formation-tracking of heterogeneous multi-agent systems with time-varying delays and switching topologies

This paper focuses on the time-varying output formation (TVOF) tracking control of heterogeneous linear multi-agent systems (HL-MASs) with both delays and switching topologies, where the followers’ outputs can move along the reference trajectory generated by the leaders and maintain the desired time-varying formation. First, a distributed observer is proposed for each follower, aiming to estimate the convex combination of leaders’ state with both communication delays and switching graphs. The observer’s error for heterogeneous MASs is analyzed based on Lyapunov theory and linear matrix inequality (LMI) technique. Second, the observer is incorporated into the output formation tracking protocol. Then, an algorithm is put forward to calculate the control feedback gains and the formation tracking feasibility constraint is also provided. Furthermore, the convergence of the formation tracking error is proved. At last, the effectiveness of this proposed method is validated through a numerical simulation.