| With the proposal of industry 4.0 and the promulgation of the National Intelligent Manufacturing 2025 development plan,the compound growth rate of cooperative robot sales in China has exceeded 50 %.Robot technology has been more applied to intelligent production line,home life,medical treatment,service,scientific research and education,aid and other fields,and collaborative robot has become the key direction of the future development of the robot industry.The modular joint of human-machine collaboration manipulator is usually composed of harmonic reducer with large transmission ratio and torque sensor,which has the characteristics of high flexibility,safety,perception,lightweight and modularization.Harmonic reducer uses flexible wheel deformation to transfer torque,and has the characteristics of large deformation under load and flexible joints.It is also called flexible joint manipulator.The complex nonlinear and strong coupling dynamics of flexible joints affect the stability and trajectory tracking accuracy of manipulator control.The control strategy is the key to the high precision development of flexible joint manipulator.In this paper,a dynamic model considering joint flexibility is established.The manifold of multi-channel uncertain flexible joint generalized system is derived.Based on the error state space control framework,the tracking control of flexible joint manipulator is studied.Finally,the tracking accuracy of the flexible joint manipulator is improved and the steady-state error is reduced.Firstly,the dynamic model of the flexible joint is established.By analyzing the structure of joint,the source of joint flexibility was determined.The permanent magnet synchronous motor model is built based on FOC technology.The transmission error source was analyzed and the model of assembly error was determined.For the continuity of controller design,a continuous nonlinear friction model is constructed.The nonlinear stiffness and hysteresis of harmonic reducer are modeled based on the flexibility model.The required dynamic parameters were obtained through identification experiments.The dynamic surface control method is used to simulate the flexible joint control.The results show that the nonlinear and uncertainty of the flexible joint can not be compensated in time,and the tracking error fluctuates.Based on the single-joint dynamics model established above,the dynamics model of flexible joint manipulator is established.The robot arm coordinate system is established to derive the homogeneous transformation matrix of end-effector.The eight closed solutions of inverse kinematics of manipulator are solved by analytical method.A cascade system is adopted to treat the whole manipulator as a rigid manipulator,and the local joints as flexible joints.Lagrange method is used to derive the expressions of total kinetic energy and potential energy of the manipulator,and the dynamics model of the flexible joint manipulator is established.Finally,physical modeling of the flexible joint manipulator is carried out to verify the validity of the dynamic model.The generalized multichannel uncertain affine system manifold of flexible joints is constructed and a backstepping control strategy based on reduced order extended state observer is proposed.The system model is transformed into Brunovsky form by state space transformation.The multiple uncertainties in the system are bundled into a total disturbance effect.A backstepping controller is designed based on the reduced order extended state observer’s ability to estimate and compensate multiple uncertainties in time and the advantage of Lyapunov redesigning technique to deal with matching uncertainties.It overcomes the problem that the control design depends on model precision,and better restrains model error,external disturbance and variable load.At the same time,higher tracking accuracy and faster response speed are obtained.Simulation and experiment verify the superior performance of the control algorithm.Aiming at the control problem of second-order Brunovsky manifolds of robotic manipulators,a sliding mode strategy based on the asymptotic law of the fastest descending line is proposed.In order to improve the approaching process of sliding mode controller,the brachistochrone reaching law is designed.Make the sliding mode approach the sliding mode surface in the shortest time.The reduced order extended state observer is used to estimate the uncertainty of matching and mismatching precisely,which improves the robustness of the system.A sliding mode controller combined with reduced order extended state observer is designed based on sliding mode principle.On the one hand,the response speed and tracking accuracy of the flexible joint are improved,and on the other hand,the robustness to uncertainties such as disturbance and load changes is enhanced.Simulation and comparison experiments verify the performance of the sliding mode control strategy combined with the reduced order extended state observer.Finally,the proposed control strategy is tested and validated on a flexible joint manipulator.The experimental results agree well with the theoretical analysis.The backstepping control strategy based on reduced order extended state observer has good immunity to multi-channel uncertainties,fast response speed and small tracking error.The novel brachistochrone reaching law has fast response speed has good tracking performance.The reduced order extended state observer estimates and compensates the total disturbance in time,which improves the tracking control accuracy and disturbance suppression ability of the manipulator system. |
