Finite-time Synchronous Position Control Of Multi-axis Robot Manipulators

Robot manipulator is a very complex multi-input-multi-output nonlinear system with time-varying,strong coupling,and nonlinear dynamic characteristics.In most traditional robot controls,every single actuator does not receive information from others,and there lacks the synchronization and coordination between the actuators.The cross-coupling control technique of multi-axis systems provides a solution for the coordination and synchronization of robotic systems.At present,the synchronous control strategies of most multi-axis robot systems only achieve asymptotic stability.In the practical scenarios,the robot manipulator often needs to reach the control target within finite time,and the finite-time control has faster convergence and higher robustness over the asymptotic stable controls.It is of important theoretical and practical significances to study the finite-time synchronous control of multi-axis robot manipulator.This thesis mainly focuses on the synchronous and coordinated position control of multi-axis robot manipulators within a finite time.Three finite-time stable synchronous position controls are proposed based on the cross-coupling control technique.First,a suitable synchronization function between the two axes is defined to describe the synchronization and coordination of the robotic system,and a finite-time stable nonlinear PD plus gravity compensation(FPD+)synchronous position control with partial model is formulated.Second,taking into account the actuator saturation that the torque provided by the actuator in practical situations is limited,a finite-time stable saturated PD plus gravity compensation(FSPD+)synchronous position control with a definite upper bound is formulated.Third,considering the facts that the robot is a complex and strong coupled nonlinear system and it is hard to obtain its accurate model.To overcome the influence of the uncertainties of gravity,a nonlinear integral action is introduced to replace the gravity vector term in the FPD+ control,and a complete mode-free finite-time stable nonlinear PID(FPID)synchronous position control is proposed.The Lyapunov direct method and geometric homogeneous technique are used to prove the finite-time stability of the closed-loop systems.Numerical simulation comparisons performed on a three-DOF robot manipulator verify the effectiveness and improved performances of the proposed control method.The appealing advantages of the proposed FPID synchronous position control are that it is complete model-free without involvement of modelling information in the control law formulation and has the ability to ensure finite-time stability featuring fast convergences of positioning errors and synchronization errors.The proposed FPID control provides a simple and easy-going improved solution for the synchronous position control of a large class of multi-axis electro-mechanical systems.