To overcome nonlinear and 6-DOF(degrees of freedom)under-actuated problems for the attitude and position of quadrotor UAVs,an adaptive backstepping sliding mode method for flight attitude of quadrotor UAVs is proposed...To overcome nonlinear and 6-DOF(degrees of freedom)under-actuated problems for the attitude and position of quadrotor UAVs,an adaptive backstepping sliding mode method for flight attitude of quadrotor UAVs is proposed,in which an adaptive law is designed to online estimate the parameter variations and the upper bound of external disturbances and the assessments is utilized to compensate the backstepping sliding mode control.In addition,the tracking error of the design method is shown to asymptotically converge to zero by using Lyapunov theory.Finally,based on the numerical simulation of quadrotor UAVs using the setting parameters,the results show that the proposed control approach can stabilize the attitude and has hover flight capabilities under the parameter perturbations and external disturbances.展开更多
In this paper,a novel robust composite sliding mode controller(RCSMC)is proposed to accommodate actuator faults for a quadrotor UAV subject to unknown disturbances.The closed-loop system is divided into two parts:the ...In this paper,a novel robust composite sliding mode controller(RCSMC)is proposed to accommodate actuator faults for a quadrotor UAV subject to unknown disturbances.The closed-loop system is divided into two parts:the nominal system without disturbances which is controlled by the designed baseline controller,and the equivalent total disturbances including parameter uncertainties and actuator faults,which is estimated by the developed adaptive finite-time extended state observer(AFTESO).The estimated total disturbances are rejected by RCSMC and the asymptotic stability of flight control system is guaranteed.The proposed method is verified through numerical simulations.展开更多
Quadrotor unmanned aerial vehicles(UAVs)are widely used in inspection,agriculture,express delivery,and other fields owing to their low cost and high flexibility.However,the current UAV control system has shortcomings ...Quadrotor unmanned aerial vehicles(UAVs)are widely used in inspection,agriculture,express delivery,and other fields owing to their low cost and high flexibility.However,the current UAV control system has shortcomings such as poor control accuracy and weak anti-interference ability to a certain extent.To address the control problem of a four-rotor UAV,we propose a method to enhance the controller’s accuracy by considering underactuated dynamics,nonlinearities,and external disturbances.A mathematical model is constructed based on the flight principles of the quadrotor UAV.We develop a control algorithm that combines humanoid intelligence with a cascade Proportional-Integral-Derivative(PID)approach.This algorithm incorporates the rate of change of the error into the inputs of the cascade PID controller,uses both the error and its rate of change as characteristic variables of the UAV’s control system,and employs a hyperbolic tangent function to improve the outer-loop control.The result is a double closed-loop intelligent PID(DCLIPID)control algorithm.Through MATLAB numerical simulation tests,it is found that the DCLIPID algorithm reduces the rise time by 0.5 s and the number of oscillations by 2 times compared to the string PID algorithm when a unit step signal is used as input.A UAV flight test was designed for comparison with the serial PID algorithm,and it was found that when the UAV planned the trajectory autonomously,the errors in the X-,Y-,and Z-directions were reduced by 0.22,0.21,and 0.31 m,respectively.Under the interference environment of artificial wind about 3.6 m·s-1,the UAV hovering error in X-,Y-,and Z-directions are 0.24,0.42,and 0.27 m,respectively.The simulation and experimental results show that the control method of humanoid intelligence and cascade PID can improve the real-time,control accuracy and anti-interference ability of the UAV,and the method has a certain reference value for the research in the field of UAV control.展开更多
In order to speed up and simplify the design of the quadrotor unmanned aerial vehicle(UAV)and carry out experimental simulation and verification of relevant control algorithms,this paper analyzed the system dynamics m...In order to speed up and simplify the design of the quadrotor unmanned aerial vehicle(UAV)and carry out experimental simulation and verification of relevant control algorithms,this paper analyzed the system dynamics model of the mechanical structure and flight principle of the quadrotor aircraft,and used the Newton-Euler method to derive the non-linear dynamic equations.Aiming at improving the modeling accuracy and system integrity of the quadrotor,the physical system modeling was combined with the CAD software and the Matlab/Simscape toolbox.The three-dimensional quadrotor solid model built by CAD software was imported into the Simscape simulation platform to construct the body and power system model of the quadrotor.Based on this,the control algorithm designed by Simulink was added to the simulation platform to facilitate the experiment verification and parameter tuning.The simulation results show that the designed aircraft can achieve hover and tracking well and meet the control performance requirements of the system.展开更多
In this article,a fixed-time tracking control strategy is proposed for a quadrotor UAV(QUAV)with external disturbance and asymmetric output error constraints.Firstly,a dynamic model of the QUAV is transformed into a s...In this article,a fixed-time tracking control strategy is proposed for a quadrotor UAV(QUAV)with external disturbance and asymmetric output error constraints.Firstly,a dynamic model of the QUAV is transformed into a strict feedback system with external disturbance,and it is decoupled into attitude subsystem and position subsystem for simplifying controller design.Secondly,an asymmetric tangent barrier Lyapunov function(ATBLF)is applied to solve the tracking error constraints problem,and a fixed-time control law is designed.Meanwhile,a fixed-time disturbance observer(FTDO)is designed to cope with external disturbance.Then,it is proved that the designed controller guarantees the tracking error remains within the constraint ranges and converges to zero in fixed-time by Lyapunov stability theory.Finally,the effectiveness of the proposed control scheme is verified by numerical simulations.展开更多
Different from the traditional controller system for quadrotor tasks, the vision-based strategiesare more practical and powerful to execute more complex tasks, becoming more attractive toresearchers. In this paper, an...Different from the traditional controller system for quadrotor tasks, the vision-based strategiesare more practical and powerful to execute more complex tasks, becoming more attractive toresearchers. In this paper, an image-feature-based controller with states extracted in imagesdirectly is proposed for the quadrotor to track a moving underground target, in which suitableimage features are defined and a coupling problem between position and attitude loop is solvedby a decoupling algorithm. Moreover, the external disturbances caused by visual noise, wind, orother problems are eliminated by a robust observer with low-pass filters. A Lyapunov-based stabilitymethod is presented to prove the convergent properties of the system. Finally, a simulationusing python3.6 with realistic images is established to verify that the system is stable and withhigh performance, the results of which show the data of unmanned aerial vehicle in movingtarget tracking.展开更多
In this paper,the flight formation control problem of a group of quadrotor unmanned aerial vehicles(UAVs) with parametric uncertainties and external disturbances is studied.Unitquaternions are used to represent the ...In this paper,the flight formation control problem of a group of quadrotor unmanned aerial vehicles(UAVs) with parametric uncertainties and external disturbances is studied.Unitquaternions are used to represent the attitudes of the quadrotor UAVs.Separating the model into a translational subsystem and a rotational subsystem,an intermediary control input is introduced to track a desired velocity and extract desired orientations.Then considering the internal parametric uncertainties and external disturbances of the quadrotor UAVs,the priori-bounded intermediary adaptive control input is designed for velocity tracking and formation keeping,by which the bounded control thrust and the desired orientation can be extracted.Thereafter,an adaptive control torque input is designed for the rotational subsystem to track the desired orientation.With the proposed control scheme,the desired velocity is tracked and a desired formation shape is built up.Global stability of the closed-loop system is proven via Lyapunov-based stability analysis.Numerical simulation results are presented to illustrate the effectiveness of the proposed control scheme.展开更多
In this paper,a composite adaptive fault-tolerant control strategy is proposed for a quadrotor unmanned aerial vehicle(UAV)to simultaneously compensate actuator faults,model uncertainties and external disturbances.By ...In this paper,a composite adaptive fault-tolerant control strategy is proposed for a quadrotor unmanned aerial vehicle(UAV)to simultaneously compensate actuator faults,model uncertainties and external disturbances.By assuming knowledge of the bounds on external disturbances,a baseline sliding mode control is first designed to achieve the desired system tracking performance and retain insensitive to disturbances.Then,regarding actuator faults and model uncertainties of the quadrotor UAV,neural adaptive control schemes are constructed and incorporated into the baseline sliding mode control to deal with them.Moreover,in terms of unknown external disturbances,a disturbance observer is designed and synthesized with the control law to further improve the robustness of the proposed control strategy.Finally,a series of comparative simulation tests are conducted to validate the effectiveness of the proposed control strategy where a quadrotor UAV is subject to inertial moment variations and different level of actuator faults.The capabilities and advantages of the proposed control strategy are confirmed and verified by simulation results.展开更多
At present,the attitude control method of plant protection UAV is the classical PID control,but there are some imperfections in the PID control,such as the contradiction between speediness and overshoot,the weak anti-...At present,the attitude control method of plant protection UAV is the classical PID control,but there are some imperfections in the PID control,such as the contradiction between speediness and overshoot,the weak anti-jamming ability and adaptability.The physical parameters of plant protection UAV are time-varying,and the airflow also interferes with it.The control ability of classical PID is limited,and its control parameters are fixed,and its anti-jamming ability and adaptability are not strong.Therefore,a fuzzy adaptive PID controller is proposed in this paper.Fuzzy logic control is used to optimize the control parameters of PID in order to improve the dynamic and static performance and adaptability of attitude control of plant protection UAV.In the process of research,the mathematical model of UAV is established firstly,then the fuzzy adaptive PID is designed,and then the simulation is carried out in Simulink.The simulation results show that the fuzzy adaptive PID controller has better dynamic and static control performance and adaptability than the traditional PID controller.Therefore,the proposed control method has excellent application value in the attitude of plant protection UAV.展开更多
This paper proposes a fast adaptive fault estimator-based active fault-tolerant control strategy for a quadrotor UAV against multiple actuator faults.A fast adaptive fault estimation algorithm is designed to estimate ...This paper proposes a fast adaptive fault estimator-based active fault-tolerant control strategy for a quadrotor UAV against multiple actuator faults.A fast adaptive fault estimation algorithm is designed to estimate the unknown actuator fault parameters.By synthesizing the fast adaptive fault estimator with the embedded control law,an active fault-tolerant control mechanism is established to compensate the adverse e®ects of multiple actuator faults.The e®ectiveness of the proposed strategy is validated through both numerical simulations and experimental tests.展开更多
This paper studies a novel trajectory tracking guidance law for a quadrotor unmanned aerial vehicle(UAV)with obstacle avoidance based on nonlinear model predictive control(NMPC)scheme.By augmenting a reference positio...This paper studies a novel trajectory tracking guidance law for a quadrotor unmanned aerial vehicle(UAV)with obstacle avoidance based on nonlinear model predictive control(NMPC)scheme.By augmenting a reference position trajectory to a reference dynamical system,the authors formulate the tracking problem as a standard NMPC design problem to generate constrained reference velocity commands for autopilots.However,concerning the closed-loop stability,it is difficult to find a local static state feedback to construct the terminal constraint in the design of NMPC-based guidance law.In order to circumvent this issue,the authors introduce a contraction constraint as a stability constraint,which borrows the ideas from the Lyapunov’s direct method and the backstepping technique.To achieve the obstacle avoidance extension,the authors impose a well-designed potential field function-based penalty term on the performance index.Considering the practical application,the heavy computational burden caused by solving the NMPC optimization problem online is alleviated by using the dynamical adjustment of the prediction horizon for the real-time control.Finally,extensive simulations and the real experiment are given to demonstrate the effectiveness of the proposed NMPC scheme.展开更多
Purpose-The purpose of this paper is to enhance the quadrotor’s capability of short-distance delivery to satisfy the large demand for quadrotor,which is used for goods distribution in huge warehouses,under time-varyi...Purpose-The purpose of this paper is to enhance the quadrotor’s capability of short-distance delivery to satisfy the large demand for quadrotor,which is used for goods distribution in huge warehouses,under time-varying payload and external wind disturbance.Design/methodology/approach-A trajectory tracking controller design based on the combination of an adaptive sliding mode control(ASMC)method and the active disturbance rejection control(ADRC)technique is proposed.Besides,an inner-outer loop control system structure is adopted.Findings–Simulation results of different trajectory tracking verify the effectiveness and robustness of the proposed tracking control method under various conditions,including parameter uncertainty and external wind disturbance.The proposed control strategy ensures that quadrotor UAV is capable of tracking linear and spiral trajectory well whether it loads or unloads goods in the presence of the external wind disturbance.Originality/value-The proposed method of designing a trajectory tracking controller is based on an integral ADRC and ASMC scheme so as to deal with the trajectory tracking problem for a quadrotor with payload variation.展开更多
基金Project(61203021)supported by the National Natural Science Foundation of ChinaProject(2011216011)supported by the Scientific and Technological Project of Liaoning Province,China+1 种基金Project(2013020024)supported by the Natural Science Foundation of Liaoning Province,ChinaProjects(LJQ2015061,LR2015034)supported by the Program for Liaoning Excellent Talents in University,China
文摘To overcome nonlinear and 6-DOF(degrees of freedom)under-actuated problems for the attitude and position of quadrotor UAVs,an adaptive backstepping sliding mode method for flight attitude of quadrotor UAVs is proposed,in which an adaptive law is designed to online estimate the parameter variations and the upper bound of external disturbances and the assessments is utilized to compensate the backstepping sliding mode control.In addition,the tracking error of the design method is shown to asymptotically converge to zero by using Lyapunov theory.Finally,based on the numerical simulation of quadrotor UAVs using the setting parameters,the results show that the proposed control approach can stabilize the attitude and has hover flight capabilities under the parameter perturbations and external disturbances.
基金supported by the Innovation Fund of Key Laboratory of High-Altitude Simulating Technology,AECC Sichuan Turbine Research Institute(18zd9101).
文摘In this paper,a novel robust composite sliding mode controller(RCSMC)is proposed to accommodate actuator faults for a quadrotor UAV subject to unknown disturbances.The closed-loop system is divided into two parts:the nominal system without disturbances which is controlled by the designed baseline controller,and the equivalent total disturbances including parameter uncertainties and actuator faults,which is estimated by the developed adaptive finite-time extended state observer(AFTESO).The estimated total disturbances are rejected by RCSMC and the asymptotic stability of flight control system is guaranteed.The proposed method is verified through numerical simulations.
基金supported by the Scientific Research Projects of Higher Education Institutions in Hebei Province(Grant No.QN2023188)the project of Hebei University of Science and Technology(Grant No.1200752).
文摘Quadrotor unmanned aerial vehicles(UAVs)are widely used in inspection,agriculture,express delivery,and other fields owing to their low cost and high flexibility.However,the current UAV control system has shortcomings such as poor control accuracy and weak anti-interference ability to a certain extent.To address the control problem of a four-rotor UAV,we propose a method to enhance the controller’s accuracy by considering underactuated dynamics,nonlinearities,and external disturbances.A mathematical model is constructed based on the flight principles of the quadrotor UAV.We develop a control algorithm that combines humanoid intelligence with a cascade Proportional-Integral-Derivative(PID)approach.This algorithm incorporates the rate of change of the error into the inputs of the cascade PID controller,uses both the error and its rate of change as characteristic variables of the UAV’s control system,and employs a hyperbolic tangent function to improve the outer-loop control.The result is a double closed-loop intelligent PID(DCLIPID)control algorithm.Through MATLAB numerical simulation tests,it is found that the DCLIPID algorithm reduces the rise time by 0.5 s and the number of oscillations by 2 times compared to the string PID algorithm when a unit step signal is used as input.A UAV flight test was designed for comparison with the serial PID algorithm,and it was found that when the UAV planned the trajectory autonomously,the errors in the X-,Y-,and Z-directions were reduced by 0.22,0.21,and 0.31 m,respectively.Under the interference environment of artificial wind about 3.6 m·s-1,the UAV hovering error in X-,Y-,and Z-directions are 0.24,0.42,and 0.27 m,respectively.The simulation and experimental results show that the control method of humanoid intelligence and cascade PID can improve the real-time,control accuracy and anti-interference ability of the UAV,and the method has a certain reference value for the research in the field of UAV control.
文摘In order to speed up and simplify the design of the quadrotor unmanned aerial vehicle(UAV)and carry out experimental simulation and verification of relevant control algorithms,this paper analyzed the system dynamics model of the mechanical structure and flight principle of the quadrotor aircraft,and used the Newton-Euler method to derive the non-linear dynamic equations.Aiming at improving the modeling accuracy and system integrity of the quadrotor,the physical system modeling was combined with the CAD software and the Matlab/Simscape toolbox.The three-dimensional quadrotor solid model built by CAD software was imported into the Simscape simulation platform to construct the body and power system model of the quadrotor.Based on this,the control algorithm designed by Simulink was added to the simulation platform to facilitate the experiment verification and parameter tuning.The simulation results show that the designed aircraft can achieve hover and tracking well and meet the control performance requirements of the system.
基金supported by Science and Technology Project of Hebei Education Department under Grant No.ZD2022012the Natural Science Foundation of Hebei Province under Grant Nos.F2020203105 and F2022203085+1 种基金the National Natural Science Foundation of China under Grant No.62073234Central Government Guided Local Science and Technology Development Fund Project under Grant No.236Z1601G。
文摘In this article,a fixed-time tracking control strategy is proposed for a quadrotor UAV(QUAV)with external disturbance and asymmetric output error constraints.Firstly,a dynamic model of the QUAV is transformed into a strict feedback system with external disturbance,and it is decoupled into attitude subsystem and position subsystem for simplifying controller design.Secondly,an asymmetric tangent barrier Lyapunov function(ATBLF)is applied to solve the tracking error constraints problem,and a fixed-time control law is designed.Meanwhile,a fixed-time disturbance observer(FTDO)is designed to cope with external disturbance.Then,it is proved that the designed controller guarantees the tracking error remains within the constraint ranges and converges to zero in fixed-time by Lyapunov stability theory.Finally,the effectiveness of the proposed control scheme is verified by numerical simulations.
基金National Natural Science Foundation of China[61931020,62033010].
文摘Different from the traditional controller system for quadrotor tasks, the vision-based strategiesare more practical and powerful to execute more complex tasks, becoming more attractive toresearchers. In this paper, an image-feature-based controller with states extracted in imagesdirectly is proposed for the quadrotor to track a moving underground target, in which suitableimage features are defined and a coupling problem between position and attitude loop is solvedby a decoupling algorithm. Moreover, the external disturbances caused by visual noise, wind, orother problems are eliminated by a robust observer with low-pass filters. A Lyapunov-based stabilitymethod is presented to prove the convergent properties of the system. Finally, a simulationusing python3.6 with realistic images is established to verify that the system is stable and withhigh performance, the results of which show the data of unmanned aerial vehicle in movingtarget tracking.
基金supported by the National Natural Science Foundation of China(No.61374048)
文摘In this paper,the flight formation control problem of a group of quadrotor unmanned aerial vehicles(UAVs) with parametric uncertainties and external disturbances is studied.Unitquaternions are used to represent the attitudes of the quadrotor UAVs.Separating the model into a translational subsystem and a rotational subsystem,an intermediary control input is introduced to track a desired velocity and extract desired orientations.Then considering the internal parametric uncertainties and external disturbances of the quadrotor UAVs,the priori-bounded intermediary adaptive control input is designed for velocity tracking and formation keeping,by which the bounded control thrust and the desired orientation can be extracted.Thereafter,an adaptive control torque input is designed for the rotational subsystem to track the desired orientation.With the proposed control scheme,the desired velocity is tracked and a desired formation shape is built up.Global stability of the closed-loop system is proven via Lyapunov-based stability analysis.Numerical simulation results are presented to illustrate the effectiveness of the proposed control scheme.
基金partially supported by the National Natural Science Foundation of China under Grant Nos.62003266 and 61833013the Fundamental Research Funds for the Central Universities under Grant No.G2019KY05103the Natural Sciences and Engineering Research Council of Canada。
文摘In this paper,a composite adaptive fault-tolerant control strategy is proposed for a quadrotor unmanned aerial vehicle(UAV)to simultaneously compensate actuator faults,model uncertainties and external disturbances.By assuming knowledge of the bounds on external disturbances,a baseline sliding mode control is first designed to achieve the desired system tracking performance and retain insensitive to disturbances.Then,regarding actuator faults and model uncertainties of the quadrotor UAV,neural adaptive control schemes are constructed and incorporated into the baseline sliding mode control to deal with them.Moreover,in terms of unknown external disturbances,a disturbance observer is designed and synthesized with the control law to further improve the robustness of the proposed control strategy.Finally,a series of comparative simulation tests are conducted to validate the effectiveness of the proposed control strategy where a quadrotor UAV is subject to inertial moment variations and different level of actuator faults.The capabilities and advantages of the proposed control strategy are confirmed and verified by simulation results.
基金This research work was supported by Project of Scientific Operating Expenses from Ministry of Education of China(2017PT19)National Natural Science Foundation of China(31761133019).
文摘At present,the attitude control method of plant protection UAV is the classical PID control,but there are some imperfections in the PID control,such as the contradiction between speediness and overshoot,the weak anti-jamming ability and adaptability.The physical parameters of plant protection UAV are time-varying,and the airflow also interferes with it.The control ability of classical PID is limited,and its control parameters are fixed,and its anti-jamming ability and adaptability are not strong.Therefore,a fuzzy adaptive PID controller is proposed in this paper.Fuzzy logic control is used to optimize the control parameters of PID in order to improve the dynamic and static performance and adaptability of attitude control of plant protection UAV.In the process of research,the mathematical model of UAV is established firstly,then the fuzzy adaptive PID is designed,and then the simulation is carried out in Simulink.The simulation results show that the fuzzy adaptive PID controller has better dynamic and static control performance and adaptability than the traditional PID controller.Therefore,the proposed control method has excellent application value in the attitude of plant protection UAV.
基金National Key Research and Development Program of China(Grant No.2020YFA0711200)National Natural Science Foundation of China(Grant Nos.61833013 and 61973012)+2 种基金Defense Industrial Technology Development Program(Grant No.JCKY2020601C016)Key Research and Development Program of Zhejiang(Grant No.2021C03158)Science and Technology Key Innovative Project of Hangzhou(Grant No.20182014B06).
文摘This paper proposes a fast adaptive fault estimator-based active fault-tolerant control strategy for a quadrotor UAV against multiple actuator faults.A fast adaptive fault estimation algorithm is designed to estimate the unknown actuator fault parameters.By synthesizing the fast adaptive fault estimator with the embedded control law,an active fault-tolerant control mechanism is established to compensate the adverse e®ects of multiple actuator faults.The e®ectiveness of the proposed strategy is validated through both numerical simulations and experimental tests.
基金supported by the National Natural Science Foundation of China under Grant No.62073264in part by Key Research and Development Project of Shaanxi Province under Grant Nos.S2021-YF-ZDCXLZDLGY-0027,2020ZDLGY06-02+3 种基金Fundamental Research Funds for the Central Universities under Grant No.3102019ZDHKY02in part by Aeronautical Science Foundation of China under Grant No.2019ZA053008in part by Natural Science Foundation for Young Scholars of China under Grant No.61803309Science Foundation for Post Doctorate Research Grant No.2018M633574。
文摘This paper studies a novel trajectory tracking guidance law for a quadrotor unmanned aerial vehicle(UAV)with obstacle avoidance based on nonlinear model predictive control(NMPC)scheme.By augmenting a reference position trajectory to a reference dynamical system,the authors formulate the tracking problem as a standard NMPC design problem to generate constrained reference velocity commands for autopilots.However,concerning the closed-loop stability,it is difficult to find a local static state feedback to construct the terminal constraint in the design of NMPC-based guidance law.In order to circumvent this issue,the authors introduce a contraction constraint as a stability constraint,which borrows the ideas from the Lyapunov’s direct method and the backstepping technique.To achieve the obstacle avoidance extension,the authors impose a well-designed potential field function-based penalty term on the performance index.Considering the practical application,the heavy computational burden caused by solving the NMPC optimization problem online is alleviated by using the dynamical adjustment of the prediction horizon for the real-time control.Finally,extensive simulations and the real experiment are given to demonstrate the effectiveness of the proposed NMPC scheme.
基金This work was partially supported by the National Natural Science Foundation of China(Grant No.61273050).496。
文摘Purpose-The purpose of this paper is to enhance the quadrotor’s capability of short-distance delivery to satisfy the large demand for quadrotor,which is used for goods distribution in huge warehouses,under time-varying payload and external wind disturbance.Design/methodology/approach-A trajectory tracking controller design based on the combination of an adaptive sliding mode control(ASMC)method and the active disturbance rejection control(ADRC)technique is proposed.Besides,an inner-outer loop control system structure is adopted.Findings–Simulation results of different trajectory tracking verify the effectiveness and robustness of the proposed tracking control method under various conditions,including parameter uncertainty and external wind disturbance.The proposed control strategy ensures that quadrotor UAV is capable of tracking linear and spiral trajectory well whether it loads or unloads goods in the presence of the external wind disturbance.Originality/value-The proposed method of designing a trajectory tracking controller is based on an integral ADRC and ASMC scheme so as to deal with the trajectory tracking problem for a quadrotor with payload variation.