Closed-form dynamic model of planar multilink lightweight robots

Closed-form equations of motion are presented for planar lightweight robot arms with multiple flexible links. The kinematic model is based on standard frame transformation matrices describing both rigid rotation and flexible displacement, under small deflection assumption. The Lagrangian approach is used to derive the dynamic model of the structure. Links are modeled as Euler-Bernoulli beams with proper clamped-mass boundary conditions. The assumed modes method is adopted in order to obtain a finite-dimensional model. Explicit equations of motion are detailed for two-link case assuming two modes of vibration for each link. The associated eigenvalue problem is discussed in relation with the problem of time-varying mass boundary conditions for the first link. The model is cast in a compact form that is linear with respect to a suitable set of constant parameters. Extensive simulation results that validate the theoretical derivation are included. >

[1]  Robert P. Judd,et al.  Dynamics of Nonrigid Articulated Robot Linkages , 1983, 1983 American Control Conference.

[2]  Wayne J. Book,et al.  Symbolic modeling and dynamic simulation of robotic manipulators with compliant links and joints , 1989 .

[3]  Antonio Tornambè,et al.  Approximate modeling of robots having elastic links , 1988, IEEE Trans. Syst. Man Cybern..

[4]  Steven Dubowsky,et al.  The Application of Finite Element Methods to the Dynamic Analysis of Flexible Spatial and Co-Planar Linkage Systems , 1981 .

[5]  R. Ravindran,et al.  STRUCTURAL FLEXIBILITY OF THE SHUTTLE REMOTE MANIPULATOR SYSTEM MECHANICAL ARM , 1982 .

[6]  Wayne J. Book,et al.  A linear dynamic model for flexible robotic manipulators , 1987 .

[7]  Eduardo Bayo,et al.  On trajectory generation for flexible robots , 1987, J. Field Robotics.

[8]  Celia M. Oakley,et al.  Initial Experiments on the Control of a Two-Link Manipulator with a Very Flexible Forearm , 1988, 1988 American Control Conference.

[9]  R. Nadira,et al.  A Finite Element/Lagrange Approach to Modeling Lightweight Flexible Manipulators , 1986 .

[10]  W. Book.  Recursive Lagrangian Dynamics of Flexible Manipulator Arms , 1984 .

[11]  Bruno Siciliano,et al.  Trajectory control of a non-linear one-link flexible arm , 1989 .

[12]  E. Barbieri,et al.  Unconstrained and Constrained Mode Expansions for a Flexible Slewing Link , 1988, 1988 American Control Conference.

[13]  R. H. Cannon,et al.  Initial Experiments on the End-Point Control of a Flexible One-Link Robot , 1984 .

[14]  Sabri Cetinkunt,et al.  Closed-Loop Behavior of a Feedback-Controlled Flexible Arm: A Comparative Study , 1991, Int. J. Robotics Res..

[15]  E. Barbieri,et al.  Unconstrained and constrained mode expansions for a flexible slewing link , 1988 .

[16]  Alessandro De Luca,et al.  Dynamic Modelling of Multi-Link Flexible Robot Arms , 1990, Modelling the Innovation.

[17]  M. Benati,et al.  Dynamics of Chain of Flexible Links , 1988 .

[18]  Leonardo Lanari,et al.  Output regulation of a flexible robot arm , 1990 .

[19]  J. Slotine,et al.  On the Adaptive Control of Robot Manipulators , 1987 .

[20]  Celia M. Oakley,et al.  End-Point Control of a Two-Link Manipulator with a Very Flexible Forearm: Issues and Experiments , 1989, 1989 American Control Conference.

[21]  R. Judd,et al.  Dynamics of nonrigid articulated robot linkages , 1985 .

[22]  Antonio Tornambè,et al.  Dynamic modelling of flexible robot manipulators , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[23]  E. Schmitz,et al.  Modeling and control of a planar manipulator with an elastic forearm , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[24]  B. Siciliano,et al.  Explicit dynamic modeling of a planar two-link flexible manipulator , 1990, 29th IEEE Conference on Decision and Control.

[25]  Giovanni Ulivi,et al.  Exact modeling of the flexible slewing link , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[26]  L. Meirovitch.  Analytical Methods in Vibrations , 1967 .