On the terminology and geometric aspects of redundant parallel manipulators

Parallel kinematics machines (PKMs) can exhibit kinematics as well as actuation redundancy. While the meaning of kinematic redundancy has been already clarified for serial manipulators, actuation redundancy, which is only possible in PKMs, is differently classified in the literature. In this paper a consistent terminology for general redundant PKM is proposed. A kinematic model is introduced with the configuration space (c-space) as central part. The notion of kinematic redundancy is recalled for PKM. C-space, output, and input singularities are distinguished. The significance of the c-space geometry is emphasized, and it is pointed out geometrically that input singularities can be avoided by redundant actuation schemes. In order to distinguish different actuation schemes of PKM, a nonlinear control system is introduced whose dynamics evolves on c-space. The degree of actuation (DOA) is introduced as the number of independent control vector fields, and PKMs are classified as full-actuated and underactuated machines. Relating this DOA to degree of freedom allows to classify the actuation redundancy.

[1]  A. D. Lewis,et al.  Geometric Control of Mechanical Systems , 2004, IEEE Transactions on Automatic Control.

[2]  Andreas Müller,et al.  Mobility and Higher Order Local Analysis of the Configuration Space of Single-Loop Mechanisms , 2008 .

[3]  S. Jain,et al.  Forward and Inverse Kinematic Solution of the Variable Geometry Truss Robot Based on an N-Celled Tetrahedron-Tetrahedron Truss , 1990 .

[4]  Andreas Müller,et al.  Internal Preload Control of Redundantly Actuated Parallel Manipulators—Its Application to Backlash Avoiding Control , 2005, IEEE Transactions on Robotics.

[5]  C. Gosselin,et al.  Constraint Singularities as C-Space Singularities , 2002 .

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

[7]  Jorge Angeles,et al.  Force optimization in redundantly-actuated closed kinematic chains , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[8]  Y. K. Yiu,et al.  Auto-calibration for a parallel manipulator with sensor redundancy , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[9]  Yoshihiko Nakamura,et al.  Dynamics computation of closed-link robot mechanisms with nonredundant and redundant actuators , 1989, IEEE Trans. Robotics Autom..

[10]  Tsuneo Yoshikawa,et al.  Manipulability of Robotic Mechanisms , 1985 .

[11]  Charles F. Reinholtz,et al.  Closed-Form Inverse Kinematic Analysis of Variable-Geometry Truss Manipulators , 1992 .

[12]  J. Jeong,et al.  Kinematic Calibration for Redundantly Actuated Parallel Mechanisms , 2004 .

[13]  Zexiang Li,et al.  Singularities of parallel manipulators: a geometric treatment , 2003, IEEE Trans. Robotics Autom..

[14]  L. W. Tsai,et al.  Robot Analysis: The Mechanics of Serial and Parallel Ma-nipulators , 1999 .

[15]  Jinliang Gong,et al.  Singularity elimination of parallel mechanisms by means of redundant actuation , 2007 .

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

[17]  Parviz E. Nikravesh,et al.  Generalized co-ordinate partitioning in static equilibrium analysis of large-scale mechanical systems , 1985 .

[18]  Gaël Écorchard,et al.  Elasto-geometrical modeling and calibration of redundantly actuated PKMs , 2010 .

[19]  Ron P. Podhorodeski,et al.  Force-unconstrained poses for a redundantly-actuated planar parallel manipulator , 2004 .

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

[21]  Shuang Cong,et al.  Modeling, Identification and Control of a Redundant Planar 2-DOF Parallel Manipulator , 2007 .

[22]  Frank Chongwoo Park,et al.  Simulation-based actuator selection for redundantly actuated robot mechanisms , 2002, J. Field Robotics.

[23]  Feng Gao,et al.  The joint velocity, torque, and power capability evaluation of a redundant parallel manipulator , 2011, Robotica.

[24]  M. Abedinnasab,et al.  Analysis of a 6-DOF redundantly actuated 4-legged parallel mechanism , 2009 .

[25]  T. Mruthyunjaya,et al.  Force redundancy in parallel manipulators: Theoretical and practical issues , 1998 .

[26]  Carl D. Crane,et al.  Stiffness mapping of planar compliant parallel mechanisms in a serial arrangement , 2006, ARK.

[27]  Hiroshi Furuya,et al.  Variable geometry truss and its application to deployable truss and space crane arm , 1985 .

[28]  Dimitar Chakarov,et al.  Study of the antagonistic stiffness of parallel manipulators with actuation redundancy , 2004 .

[29]  Andreas Müller,et al.  Generic mobility of rigid body mechanisms , 2009 .

[30]  J. Burdick.  On the inverse kinematics of redundant manipulators: characterization of the self-motion manifolds , 1989 .

[31]  Walter Schumacher,et al.  A parallel x-y manipulator with actuation redundancy for high-speed and active-stiffness applications , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[32]  Philippe Wenger,et al.  Cuspidal and noncuspidal robot manipulators , 2007, Robotica.

[33]  Masao Tanaka,et al.  Dynamic Analysis of a Truss-Type Flexible Robot Arm , 1990 .

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

[35]  John F. Gardner,et al.  Kinematics and control of redundantly actuated closed chains , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[36]  Andreas Müller,et al.  A projection method for the elimination of contradicting control forces in redundantly actuated PKM , 2011, 2011 IEEE International Conference on Robotics and Automation.

[37]  F. Park,et al.  Manipulability of Closed Kinematic Chains , 1998 .

[38]  Alain Liégeois,et al.  A study of multiple manipulator inverse kinematic solutions with applications to trajectory planning and workspace determination , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[39]  Walter Schumacher,et al.  Redundant Parallel Kinematic Structures and Their Control , 2011, Robotic Systems for Handling and Assembly.

[40]  Sungchul Lee,et al.  Kinematic Optimization of a Redundantly Actuated Parallel Mechanism for Maximizing Stiffness and Workspace Using , 2011 .

[41]  Il Hong Suh,et al.  Optimal design of a five-bar finger with redundant actuation , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[42]  Zexiang Li,et al.  Dynamics and control of redundantly actuated parallel manipulators , 2003 .

[43]  Jun Wu,et al.  An Experimental Study of a Redundantly Actuated Parallel Manipulator for a 5-DOF Hybrid Machine Tool , 2009 .

[44]  Erdinc Sahin Conkur,et al.  Clarifying the definition of redundancy as used in robotics , 1997, Robotica.

[45]  Damien Chablat,et al.  Working modes and aspects in fully parallel manipulators , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[46]  Gregory S. Chirikjian,et al.  Hyper-redundant manipulator dynamics: a continuum approximation , 1994, Adv. Robotics.

[47]  Vincent Hayward,et al.  Multiple-goal kinematic optimization of a parallel spherical mechanism with actuator redundancy , 1992, IEEE Trans. Robotics Autom..

[48]  Yongjie Zhao,et al.  Dynamic performance comparison of the 8PSS redundant parallel manipulator and its non-redundant counterpart—the 6PSS parallel manipulator , 2009 .

[49]  Blake Hannaford,et al.  Advantages of actuation redundancy for the design of haptic displays , 1995 .

[50]  F. Amirouche.  Fundamentals Of Multibody Dynamics. Theory And Applications , 2005 .

[51]  Grigore Gogu.  Fully-Isotropic Redundantly-Actuated Parallel Wrists With Three Degrees of Freedom , 2007 .

[52]  Nikolaos G. Tsagarakis,et al.  A High-performance Redundantly Actuated Parallel Mechanism for Ankle Rehabilitation , 2009, Int. J. Robotics Res..

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

[54]  R. G. Fenton,et al.  Identification and classification of the singular configurations of mechanisms , 1998 .

[55]  Richard M. Murray,et al.  A Mathematical Introduction to Robotic Manipulation , 1994 .

[56]  Xiaoqiang Tang,et al.  Singularity analysis of redundant parallel manipulators , 2004, 2004 IEEE International Conference on Systems, Man and Cybernetics (IEEE Cat. No.04CH37583).

[57]  Jens Kotlarski,et al.  On the inverse dynamics problem of general parallel robots , 2009, 2009 IEEE International Conference on Mechatronics.

[58]  Andreas Müller,et al.  Stiffness Control of Redundantly Actuated Parallel Manipulators , 2006, ICRA.

[59]  Clément Gosselin,et al.  Singularity analysis of closed-loop kinematic chains , 1990, IEEE Trans. Robotics Autom..

[60]  Arjan van der Schaft,et al.  Non-linear dynamical control systems , 1990 .

[61]  Damien Chablat,et al.  Uniqueness domains and non singular assembly mode changing trajectories , 2011, 2011 IEEE International Conference on Robotics and Automation.

[62]  Dieter Schramm,et al.  Consequences of the Use of Decentralized Controllers for Redundantly Actuated Parallel Manipulators , 2011 .

[63]  Andreas Müller,et al.  Consequences of Geometric Imperfections for the Control of Redundantly Actuated Parallel Manipulators , 2010, IEEE Transactions on Robotics.

[64]  Jun Wu,et al.  Workspace and singularity analysis of a 3-DOF planar parallel manipulator with actuation redundancy , 2009, Robotica.