Dynamic modeling and robust control of a 3-PRC translational parallel kinematic machine

The dynamic modeling and robust control for a three-prismatic-revolute-cylindrical (3-PRC) parallel kinematic machine (PKM) with translational motion have been investigated in this paper. By introducing a mass distribution factor, the simplified dynamic equations have been derived via the virtual work principle and validated on a virtual prototype with the ADAMS software package. Based upon the established model, three dynamics controllers have been attempted on the 3-PRC PKM. The intuitive co-simulations with the combination of MATLAB/Simulink and ADAMS show that the control performance of neither inverse dynamics control nor robust inverse dynamics control is satisfactory in the presence of parametric uncertainties in PKM dynamics. On the contrary, the controller based on the passivity-based robust control scheme is more suitable for tracking control of the PKM in terms of both control performances and controller design procedures. The results presented in the paper provide a sound base for both the mechanical system design and control system design of a 3-PRC PKM.

[1]  J. Angeles,et al.  Recursive Kinematics and Inverse Dynamics for a Planar 3R Parallel Manipulator , 2005 .

[2]  Jorge Angeles,et al.  Singularity analysis of three-legged parallel robots based on passive-joint velocities , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[3]  M. Spong.  On the robust control of robot manipulators , 1992 .

[4]  V. Parenti-Castelli,et al.  Dynamics of a Class of Parallel Wrists , 2004 .

[5]  H. Lipkin,et al.  Mobility of Overconstrained Parallel Mechanisms , 2006 .

[6]  Qingsong Xu,et al.  Kinematic analysis and design of a new 3-DOF translational parallel manipulator , 2006 .

[7]  G. Feng,et al.  Adaptive control of robot manipulators in task space , 1993, IEEE Transactions on Automatic Control.

[8]  L. Siciliano.  Modelling and Control of Robot Manipulators , 2000 .

[9]  Roberto Brega,et al.  Application of a nonlinear adaptive controller to a 6 DOF parallel manipulator , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[10]  Kyo-Il Lee,et al.  Robust nonlinear task space control for 6 DOF parallel manipulator , 2005, Autom..

[11]  Feng Gao,et al.  Optimum design of 3-DOF spherical parallel manipulators with respect to the conditioning and stiffness indices , 2000 .

[12]  Dan Zhang,et al.  Global kinetostatic modelling of tripod-based parallel kinematic machine , 2004 .

[13]  Qingsong Xu,et al.  Kinematics and inverse dynamics analysis for a general 3-PRS spatial parallel mechanism , 2005, Robotica.

[14]  Liping Wang,et al.  Inverse dynamics and simulation of a 3-DOF spatial parallel manipulator , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[15]  Juan A. Méndez,et al.  On improving the performance in robust controllers for robot manipulators with parametric disturbances , 2007 .

[16]  Alain Codourey,et al.  Dynamic modelling and mass matrix evaluation of the DELTA parallel robot for axes decoupling control , 1996, Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems. IROS '96.

[17]  Clément Gosselin,et al.  A New Approach for the Dynamic Analysis of Parallel Manipulators , 1998 .

[18]  Bin Yao,et al.  Output Feedback Adaptive Robust Control of Uncertain Linear Systems With Disturbances , 2006 .

[19]  Yangmin Li,et al.  Dynamic Modeling and Adaptive Neural-Fuzzy Control for Nonholonomic Mobile Manipulators Moving on a Slope , 2006 .

[20]  Guangjun Liu,et al.  Comparative Study of Robust Saturation-Based Control of Robot Manipulators: Analysis and Experiments , 1996, Int. J. Robotics Res..

[21]  Qingsong Xu,et al.  An investigation on mobility and stiffness of a 3-DOF translational parallel manipulator via screw theory , 2008 .

[22]  L. Tsai.  Solving the Inverse Dynamics of a Stewart-Gough Manipulator by the Principle of Virtual Work , 2000 .

[23]  Massimo Callegari,et al.  Dynamics modelling and control of the 3-RCC translational platform , 2006 .

[24]  Jean-Pierre Merlet.  A Generic Trajectory Verifier for the Motion Planning of Parallel Robots , 2001 .

[25]  Bruno Siciliano,et al.  Modeling and Control of Robot Manipulators , 1995 .