Trajectory Tracking Control of 3-RPS Parallel Mechanism Based on Udwadia-Kalaba Equation

• 1、Modern Post School, Beijing University of Posts and Telecommunications, Beijing 100876

Abstract：3-RPS parallel mechanisms are widely used in industrial, medical, aerospace and other fields. There are many ways to realize trajectory tracking control. However, the calculation of Lagrange multipliers by these methods is complicated, and relevant researches are not sufficient at present. Based on Udwadia-Kalaba equation (U-K equation), a new method for trajectory tracking control of 3-RPS parallel mechanism is proposed in this paper. By using this method, the dynamics equation of 3-RPS parallel mechanism in analytic form can be obtained, and whether the holonomic and nonholonomic constraints are ideal is considered at the same time. The most important difference with other methods is that the constraints are divided into structural constraints and kinematic constraints. The dynamics model of 3-RPS parallel mechanism is established by using structural constraints, and the kinematic constraints are used to represent the expected motion trajectory. For the nonlinear dynamic system of 3-RPS parallel mechanism, the second order differential form of constraints is used to obtain the constraint force to meet the expected motion. In the whole process of trajectory tracking control, auxiliary variables such as Lagrange multipliers or pseudo-generalized velocity are not needed. Finally, the simulation results show that the 3-RPS parallel mechanism can meet the desired motion, and the tracking trajectory is accurate.

Keywords： Mechatronic Engineering Udwadia-Kalaba equation Trajectory tracking control 3-RPS parallel mechanism