Screw-based Nonsingular Terminal Sliding-mode Control For Multi-DOF Manipulator

With the development of robotics technology,the multi-DOF manipulator has become an indispensable part of the manufacturing industry.In the face of danger,heavy work,and complex environments,the manipulator can complete the task well.It has become an inevitable trend in the future that the manipulator will gradually replace human labor.In complex environments,how to accurately track the preset trajectory of the manipulator has become a hot research topic.Therefore,in order to obtain a more accurate multi-DOF dynamic model of the manipulator,this paper describes the position and pose of the rigid body based on the screw theory to avoid the disadvantages of the traditional modeling methods of parameterized rotation matrix.On this basis,the Nonsingular Terminal Sliding Mode(NTSM)controller is designed to ensure that the actual output trajectory is rapidly converged to the expected trajectory with small errors.Firstly,according to the special orthogonal group and special Euclidean group in three-dimensional space,the rigid body rotation matrix and posture matrix are described,and the rigid body motion is described based on the screw theory,thereby establishing the kinematics and dynamics model of a multi-DOF freedom manipulator.Based on the Product of Exponential(Po E)formula,the forward kinematics models of a multi-DOF manipulator in spatial and object coordinate systems are established.Using screw theory to establish a more concise and explicit Jacobian matrix,and using Newton Raphson single point iterative algorithm to solve the inverse kinematics equation of a highly nonlinear multi-DOF manipulator,kinematics simulation is conducted in Linux.At the same time,based on the screw theory,a single rigid body spinor motion spinor equation is established,and the Newton Euler recursive algorithm is used to establish the dynamics equation of a multi-DOF manipulator and give its closed description.Secondly,based on the multi-DOF manipulator model of screw theory,a NTSM algorithm is designed.The sliding mode theory has strong robustness in the nonlinear system,which can suppress the lumped uncertainty and interference suffered by the manipulator system in complex working conditions,and make the space trajectory error of the manipulator joint quickly converge to the small neighborhood of zero.Finally,based on the Lyapunov stability theory,the effectiveness of the proposed NTSM algorithm was demonstrated.The contrast experiment takes the six DOF manipulator as the simulation platform.By comparing the control performance with the existing classical control methods,it is proved that the proposed NTSM control algorithm can achieve faster convergence speed and better overall system performance.The numerical simulation results verify the effectiveness and feasibility of the proposed control method in the joint space trajectory tracking task of the multi-DOF manipulator.