Screw-based Adaptive Fuzzy Sliding-mode Control For Rigid Manipulator Subject To Uncertain Nonlinear Dynamics

The kinematics and dynamics model of the multi-DOF manipulator are established based on the screw theory in this paper,with a fuzzy control system designed to approximate the uncertainty in the dynamics model of the manipulator.At the same time,the adaptive sliding mode control law is designed to track expected behavior and the stability of the control system is proved.Taking the 6-DOF UR5 manipulator as the simulation object,the desired position and velocity tracking of each joint is realized.Starting from the Lie groups and Lie algebra,the two most important Lie groups in the motion of rigid body special orthogonal group and special Euclidean group are elaborated,as same as lie algebra,by giving their definitions,properties,etc.For the inverse kinematics algorithm,combining the physical meaning of screw motion and using the Jacobian matrix and adjoint matrix defined under the screw theory,the Newton-Raphson single-point iteration method is adopted,by selecting the appropriate iteration initial value to solve the nonlinear kinematics equation and to obtain the inverse solution within the allowable error.Based on single rigid body dynamics and Lie group theory,a Newton Euler recursive algorithm for multi rigid body inverse dynamics is established,by which the closed form dynamic equation is established and the forward dynamic operation is completed by numerical integration.The multi-DOF manipulator is highly nonlinear,and its working environment will make the system produce certain disturbance and uncertainty to the model parameters.Therefore,an adaptive sliding mode control with fuzzy approximation adopted to estimate the dynamic state of the uncertain controlled object is proposed.The sliding surface and an adaptive control law can be adjusted for tracking the nonlinear system better.The closed-loop system has been proven to be stable.At the same time,the tracking error of expected behavior has met the requirements.Finally,The 6-DOF manipulator UR5 is selected as the simulation object.The simulation experiment of fuzzy adaptive sliding mode control algorithm is completed and the tracking effect of joint angle error is given.