Screw-besed Adaptive Fuzzy Sliding-mode Control for Rigid Manipulator Subject to Uncertain Nonlinear Dynamics

The kinematics and dynamics with multiple degrees of freedom(multi-DOF) based on screw theory are established in this paper. The iterative forward and inverse algorithms of the twist and wrench between adjacent joints are completed by using the Lie bracket. At the same time, the exponential product mapping of the screw motion of rigid bodies and the Jacobian matrix of robots are expressed by Lie group and Lie algebra. Moreover, the recursive algorithm and the closed form of the dynamic equation are derived. The multi-DOF manipulator body and its working environment will cause the system to have a certain kind of interference and uncertainty of model parameters. However, The manufacturing error of the manipulator, as well as the disturbance of the external environment, will lead to the uncertainty of the ideal model, which leads to the loss of control accuracy. To this end, an adaptive sliding mode tracking control is designed for improving the control accuracy, in which a fuzzy approximation is employed for estimating the nonlinear uncertainty in the plant. On this basis, a fuzzy-based adaptive sliding mode algorithm is developed to ensure the closed-loop stability and finite-time convergence of the controlled manipulator. The control performance in position and velocity have been demonstrated through tracking errors in the simulation platform which takes a 6-R open-chain manipulator as a simulation model.