TY - GEN
T1 - Trajectory Tracking Control of 3-RPS Parallel Mechanism Based on Udwadia-Kalaba Equation
AU - Li, Duanling
AU - Yin, Xiaoqin
AU - Wei, Yongkang
AU - Mccarthy, Michael
AU - Kong, Xianwen
N1 - Funding Information:
This research is funded by National Natural Science Foundation of China (No. 52175019) and Beijing Municipal Natural Science Foundation (No. 3212009, No. L222038).
Publisher Copyright:
© 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.
PY - 2023/11/4
Y1 - 2023/11/4
N2 - The trajectory tracking control of 3-RPS parallel mechanisms which severs to motion control is widely used in industrial, medical, aerospace and other fields. However, the existing method are troubled by complicated calculation of Lagrange multipliers. To address this problem, we propose a new method for trajectory tracking control of 3-RPS parallel mechanism based on the Udwadia-Kalaba equation (U-K equation). This method allows for the availability of the dynamics equation of the 3-RPS parallel mechanism in analytic form, taking into consideration whether the holonomic and nonholonomic constraints are ideal at the same time. A distinct feature of this method is the division of constrains into structural and kinematic constraints. The dynamics model of 3-RPS parallel mechanism is established by using structural constraints, while 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 determine the constraint force to achieve the desired 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 with accurate tracking of the trajectory.
AB - The trajectory tracking control of 3-RPS parallel mechanisms which severs to motion control is widely used in industrial, medical, aerospace and other fields. However, the existing method are troubled by complicated calculation of Lagrange multipliers. To address this problem, we propose a new method for trajectory tracking control of 3-RPS parallel mechanism based on the Udwadia-Kalaba equation (U-K equation). This method allows for the availability of the dynamics equation of the 3-RPS parallel mechanism in analytic form, taking into consideration whether the holonomic and nonholonomic constraints are ideal at the same time. A distinct feature of this method is the division of constrains into structural and kinematic constraints. The dynamics model of 3-RPS parallel mechanism is established by using structural constraints, while 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 determine the constraint force to achieve the desired 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 with accurate tracking of the trajectory.
KW - 3-RPS parallel mechanism
KW - Mechatronic engineering
KW - Trajectory tracking control
KW - Udwadia-Kalaba equation
UR - http://www.scopus.com/inward/record.url?scp=85177570862&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-45770-8_96
DO - 10.1007/978-3-031-45770-8_96
M3 - Conference contribution
AN - SCOPUS:85177570862
SN - 9783031457692
T3 - Mechanisms and Machine Science
SP - 968
EP - 982
BT - Advances in Mechanism and Machine Science
A2 - Okada, Masafumi
PB - Springer
T2 - 16th International Federation of Theory of Machines and Mechanisms World Congress 2023
Y2 - 5 November 2023 through 9 November 2023
ER -