Improving tracking accuracy of a novel 3-DOF redundant planar parallel kinematic machine

Abstract Improving the accuracy of parallel kinematic machines (PKMs) for practical applications remains a significant challenge. This paper focuses on reducing the PKM's tracking error caused by the deformations in its kinematic chains by introducing redundancy. A novel 3-DOF planar redundant PKM, which has a redundant chain with both actuation and kinematic redundancies, is designed and serves as the object of study. Regarding the deformations of PKM kinematic chains as the structural errors, the general tracking error model is first established on the basis of kinematic analysis. The concise PKM dynamic model is then derived by using the Newton-Euler method to obtain the constraint forces and inertial loads of each kinematic chain for calculating their deformations. The redundant force applied by the redundant chain can be controlled actively and its size and direction are all optimized to reduce the PKM tracking error with consideration of the mechanical constraint and the limitation on the maximum angular velocity of the redundant chain. Finally, simulation results are provided to verify the effectiveness of the redundant force optimization method in improving the tracking accuracy of the redundant PKM.

[1]  Xin-Jun Liu,et al.  Step kinematic calibration of a 3-DOF planar parallel kinematic machine tool , 2008 .

[2]  Shuang Cong,et al.  Motion Control of Parallel Manipulators Using Acceleration Feedback , 2014, IEEE Transactions on Control Systems Technology.

[3]  John T. Wen,et al.  Redundant actuation for improving kinematic manipulability , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[4]  Bin Yao,et al.  An Orthogonal Global Task Coordinate Frame for Contouring Control of Biaxial Systems , 2012, IEEE/ASME Transactions on Mechatronics.

[5]  Liping Wang,et al.  Running accuracy analysis of a 3-RRR parallel kinematic machine considering the deformations of the links , 2014 .

[6]  Scott B. Nokleby,et al.  Wrench capability analysis of redundantly actuated spatial parallel manipulators , 2009 .

[7]  O Company,et al.  Simplified dynamic modelling and improvement of a four-degree-of-freedom pick-and-place manipulator with articulated moving platform , 2009 .

[8]  S. Nokleby,et al.  Force capabilities of redundantly-actuated parallel manipulators , 2005 .

[9]  Jung Hyun Choi,et al.  Singularity analysis of a planar parallel mechanism with revolute joints based on a geometric approach , 2013 .

[10]  Bo Hu,et al.  Kinematics, dynamics and stiffness analysis of a novel 3-DOF kinematically/actuation redundant planar parallel mechanism , 2017 .

[11]  Jih-Hua Chin,et al.  System structure and contour tracking for a hybrid motion platform , 2005 .

[12]  Vigen Arakelian,et al.  Design of planar 3-DOF 3-RRR reactionless parallel manipulators , 2008 .

[13]  Dong Liang,et al.  Optimum design of a novel redundantly actuated parallel manipulator with multiple actuation modes for high kinematic and dynamic performance , 2016 .

[14]  C. Gosselin,et al.  Kinematic Analysis and Design of Kinematically Redundant Parallel Mechanisms , 2004 .

[15]  Clément Gosselin,et al.  Kinematic Analysis and Optimization of a New Three Degree-of-Freedom Spatial Parallel Manipulator , 2000 .

[16]  Han Ding,et al.  A generalized online estimation algorithm of multi-axis contouring errors for CNC machine tools with rotary axes , 2015 .

[17]  Warren E. Dixon,et al.  Adaptive nonlinear contour coupling control for a machine tool system , 2012 .

[18]  Faa-Jeng Lin,et al.  DSP-Based Cross-Coupled Synchronous Control for Dual Linear Motors via Intelligent Complementary Sliding Mode Control , 2012, IEEE Transactions on Industrial Electronics.

[19]  François Pierrot,et al.  Dual-space adaptive control of redundantly actuated parallel manipulators for extremely fast operations with load changes , 2012, 2012 IEEE International Conference on Robotics and Automation.

[20]  Jun Wu,et al.  Dynamic model and force control of the redundantly actuated parallel manipulator of a 5-DOF hybrid machine tool , 2009, Robotica.

[21]  Jianhe Lei,et al.  Kinematic analysis of a novel 3-DOF actuation redundant parallel manipulator using artificial intelligence approach , 2011 .

[22]  Guilherme Sartori Natal,et al.  Dual-Space Control of Extremely Fast Parallel Manipulators: Payload Changes and the 100G Experiment , 2015, IEEE Transactions on Control Systems Technology.

[23]  Yao Jiang,et al.  The dynamic modeling, redundant-force optimization, and dynamic performance analyses of a parallel kinematic machine with actuation redundancy , 2015, Robotica.

[24]  J. A. Carretero,et al.  A Family of Kinematically Redundant Planar Parallel Manipulators , 2008 .

[25]  Gang Cheng,et al.  Dynamics analysis of a parallel hip joint simulator with four degree of freedoms (3R1T) , 2012 .

[26]  Joohn-Sheok Kim,et al.  A Feasible Approach for the Unified PID Position Controller Including Zero-Phase Error Tracking Performance for Direct Drive Rotation Motor , 2009 .

[27]  Frank Chongwoo Park,et al.  Design and analysis of a redundantly actuated parallel mechanism for rapid machining , 2001, IEEE Trans. Robotics Autom..

[28]  Chinedum E. Okwudire,et al.  Pre-compensation of servo contour errors using a model predictive control framework , 2015 .

[29]  Yundou Xu,et al.  Dynamic analysis and driving force optimization of a 5-DOF parallel manipulator with redundant actuation , 2017 .

[30]  Juan A. Carretero,et al.  Kinematic analysis and path planning of a new kinematically redundant planar parallel manipulator , 2008, Robotica.

[31]  Z. M. Bi,et al.  Dynamic modeling and validation of a tripod-based machine tool , 2008 .

[32]  Yao Jiang,et al.  Stiffness modeling of compliant parallel mechanisms and applications in the performance analysis of a decoupled parallel compliant stage. , 2015, The Review of scientific instruments.

[33]  Yixin Chen,et al.  Fault tolerance of parallel manipulators using task space and kinematic redundancy , 2006, IEEE Transactions on Robotics.

[34]  Zexiang Li,et al.  Task Polar Coordinate Frame-Based Contouring Control of Biaxial Systems , 2014, IEEE Transactions on Industrial Electronics.

[35]  Xin-Jun Liu,et al.  A new methodology for optimal kinematic design of parallel mechanisms , 2007 .

[36]  Aria Alasty,et al.  Experimental kinematic calibration of parallel manipulators using a relative position error measurement system , 2010 .

[37]  Yueming Hu,et al.  Robust design of feedback feed-forward iterative learning control based on 2D system theory for linear uncertain systems , 2016, Int. J. Syst. Sci..

[38]  Ty A. Lasky,et al.  Kinematically-Redundant Variations of the 3-RRR Mechanism and Local Optimization-Based Singularity Avoidance , 2007 .

[39]  Jean-Pierre Merlet.  Redundant parallel manipulators , 1996 .

[40]  Liping Wang,et al.  Dynamic modeling and redundant force optimization of a 2-DOF parallel kinematic machine with kinematic redundancy , 2015 .

[41]  Fengfeng Xi,et al.  Tripod stiffening using clamping plates with no increase of moving mass , 2012 .

[42]  S. Staicu,et al.  Inverse dynamics of a 3-PRC parallel kinematic machine , 2012 .

[43]  Aun-Neow Poo,et al.  Improving contouring accuracy by using generalized cross-coupled control , 2012 .

[44]  Xin-Jun Liu,et al.  Inverse dynamics of the HALF parallel manipulator with revolute actuators , 2007 .

[45]  Fengfeng Xi,et al.  Nonstationary Vibration of a Fully Flexible Parallel Kinematic Machine , 2007 .

[46]  Y. F. Zheng,et al.  Optimal Load Distribution for Two Industrial Robots Handling a Single Object , 1989 .

[47]  Shyh-Leh Chen,et al.  Contouring Control of Multi-Axis Motion Systems for NURBS Paths , 2016, IEEE Transactions on Automation Science and Engineering.

[48]  M. Bergamasco,et al.  Dynamics of parallel manipulators by means of screw theory , 2003 .