Fixed-Time Sliding Mode Control of the Slave Manipulator Based on Lagrange Equation

Minimally invasive surgical robot gets a lot of attention in the medical field because of their advantages such as fine stability, minimal trauma, and fast recovery. However, the large mass of the slave manipulator results in low positioning accuracy. To solve this problem, we design a fixed-time sliding mode controller which is by using Lagrangian dynamics equation. To begin with, the dynamic equation of the slave manipulator is established and the accuracy of the model is verified using Adams. Then, a novel non-singular fixed-time sliding mode controller based on the fixed-time stability theory is constructed by combining the dynamic model. The system stability is proved using the Lyapunov stability criterion. The performance of the controller can be clearly demonstrated that it is useful to cut down the influence of joints gravity and inertia on all of the active joints' moving accuracy of the slave manipulator of minimally invasive surgical robots and achieve faster convergence speed and good robustness.