Study On Tracking Control Of Uncertain Manipulator Based On Udwadia-Kalaba

Considering the problem of trajectory tracking control of manipulator in uncertain factors,the trajectory tracking problem is regarded as the constraint of the system,and the servo control force of the manipulator is obtained based on the constrained dynamics Udwadia kalaba(UK)equation.When considering the influence of the uncertainty on the manipulator,the direct application of this method will lead to the deviation of the tracking trajectory.Even if the constraint stabiliztion method is used,there are still problems that are inconsistent with the actual situation and the tracking error is unknown.In order to solve this problem,it is assumed that the uncertainty is unknown,but bounded.By adding additional compensation torque,the tracking error deviation caused by the uncertainty can be compensated.The design of control algorithm can control the tracking error within a given range.Taking UR5 of industrial manipulator as the research object,this paper establishes the kinematic model based on the standard DH method,deduces the positive kinematic equation in the symbolic form,and analyzes and obtains the inverse kinematics solution through the algebra method.In order to obtain the relationship between force and motion,taking into account factors such as computational efficiency,the Newton-Euler method in the form of iteration is used to establish the manipulator.The kinematics/dynamics equations are verified by using the robotics toolbox.In an ideal case,the control moment under the constraint can be obtained directly by using the Udwadia-Kalaba equation.Considering the constraint drift in the process of numerical equation and the incompatibility between the initial condition,the failure of numerical simulation will be caused with the accumulation of errors.This problem uses constraint stabilization method to stabilize the constraint drift,and discusses two methods of stability,parameter selection and their advantages and disadvantages.Because the defect of the stabilization method is that the error is unknown under the given parameters.To solve the problem,based on the nominal model,this paper designs a nonlinear controller.In the control algorithm part,the sliding mode control is used and the continuous function is used instead of the sigum/saturation function,so as to avoid the chattering problem.The error caused by uncertainty is compensated by applying additional control torque.The expression of the additional control torque is given.It is proved by Lyapunov function that under this control torque,in addition,the errors boundary can be controlled within a given range according to the control parameters.The numerical simulation process shows the validity and correctness of the design method.