Dynamics and Coupling Actuation of Elastic Underactuated Manipulators

This paper investigates the constraint and coupling characteristics of underactuated manipulators by proposing an elastic model of the manipulator and examining the second order constraint equation. A dynamic model and a coupling constraint equation are developed from a Jacobian matrix and the Newton-Euler formulation. The inertia matrix and the Christoffel tensor are analyzed and decomposed into the part concerning actuated joints and the part concerning passive joints. This decomposition is further extended to the dynamic coupling equation and generates an actuation coupling matrix and a dynamic coupling tensor. Two new dynamic coupling indices are hence identified. One is related to an actuation input and the other is related to centrifugal and Coriolis forces. The former reveals the dynamic coupling between the input and the acceleration of passive joints and gives the actuation effect on the passive joints. The latter reveals the dynamic coupling between the centrifugal and Coriolis forces and the acceleration of passive joints and provides the centrifugal and Coriolis effect on the acceleration of passive joints. The study reveals the coupling characteristics of an underactuated manipulator. This is then demonstrated in a three-link manipulator and extended to a serial manipulator with passive prismatic joint. © 2003 Wiley Periodicals, Inc.

[1]  J. R. Jones,et al.  Null–space construction using cofactors from a screw–algebra context , 2002, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[2]  John M. Hollerbach,et al.  A recursive formulation of Lagrangian manipulator dynamics , 1800 .

[3]  Paolo Rocco.  On "Stability and control of elastic-joint robotic manipulators during constrained-motion tasks" , 1997, IEEE Trans. Robotics Autom..

[4]  Yunhui Liu,et al.  Cooperation control of multiple manipulators with passive joints , 1999, IEEE Trans. Robotics Autom..

[5]  C. Barus.  A treatise on the theory of screws , 1998 .

[6]  Jian S. Dai,et al.  Stiffness characteristics and kinematics analysis of two-link elastic underactuated manipulators , 2002, J. Field Robotics.

[7]  John M. Hollerbach,et al.  A Recursive Lagrangian Formulation of Maniputator Dynamics and a Comparative Study of Dynamics Formulation Complexity , 1980, IEEE Transactions on Systems, Man, and Cybernetics.

[8]  J. M. Selig.  Geometrical Foundations of Robotics , 2000 .

[9]  Yoshihiko Nakamura,et al.  Chaos and nonlinear control of a nonholonomic free-joint manipulator , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[10]  Yangsheng Xu,et al.  Robust control of underactuated manipulators: analysis and implementation , 1994, Proceedings of IEEE International Conference on Systems, Man and Cybernetics.

[11]  Giuseppe Oriolo,et al.  Free-joint manipulators: motion control under second-order nonholonomic constraints , 1991, Proceedings IROS '91:IEEE/RSJ International Workshop on Intelligent Robots and Systems '91.

[12]  Abhinandan Jain,et al.  An analysis of the kinematics and dynamics of underactuated manipulators , 1993, IEEE Trans. Robotics Autom..

[13]  Roger W. Brockett,et al.  Dynamics of Kinematic Chains , 1996, Int. J. Robotics Res..

[14]  Mark W. Spong,et al.  Robot dynamics and control , 1989 .

[15]  Roy Featherstone,et al.  Robot Dynamics Algorithms , 1987 .

[16]  Susumu Tachi,et al.  Position control of manipulator with passive joints using dynamic coupling , 1991, IEEE Trans. Robotics Autom..

[17]  Jian S. Dai,et al.  Fine motion control based on constraint criteria under pre-loading configurations , 2000, J. Field Robotics.

[18]  Naoji Shiroma,et al.  Nonholonomic control of a three-DOF planar underactuated manipulator , 1998, IEEE Trans. Robotics Autom..

[19]  Yangsheng Xu,et al.  A dynamic coupling index for underactuated manipulators , 1995, J. Field Robotics.

[20]  Frank Chongwoo Park,et al.  Coordinate-invariant algorithms for robot dynamics , 1999, IEEE Trans. Robotics Autom..

[21]  C. E. Benedict,et al.  Dynamic response analysis of quasi-rigid mechanical systems using kinematic influence coefficients , 1971 .

[22]  Mark W. Spong,et al.  Underactuated mechanical systems , 1998 .

[23]  Frank Chongwoo Park,et al.  A Lie Group Formulation of Robot Dynamics , 1995, Int. J. Robotics Res..

[24]  J. D. Everett.  A Treatise on the Theory of Screws , 1901, Nature.

[25]  Jian S. Dai,et al.  Interrelationship between screw systems and corresponding reciprocal systems and applications , 2001 .

[26]  Rajnikant V. Patel,et al.  Dynamic Analysis of Robot Manipulators , 1991 .

[27]  K. H. Hunt,et al.  Kinematic geometry of mechanisms , 1978 .

[28]  Jean-Jacques E. Slotine,et al.  Robot analysis and control , 1988, Autom..

[29]  Rajnikant V. Patel,et al.  Dynamic analysis of robot manipulators - a Cartesian tensor approach , 1991, The Kluwer international series in engineering and computer science.

[30]  Clément Gosselin,et al.  Simulation and design of underactuated mechanical hands , 1998 .

[31]  Susumu Tachi,et al.  Dynamic control of a manipulator with passive joints in operational space , 1993, IEEE Trans. Robotics Autom..