Real-time inverse dynamics control of parallel manipulators using general-purpose multibody software

This work deals with the problem of computing the inverse dynamics of complex constrained mechanical systems for real-time control applications. The main goal is the control of robotic systems using model-based schemes in which the inverse model itself is obtained using a general purpose multibody software, exploiting the redundant coordinate formalism. The resulting control scheme is essentially equivalent to a classical computed torque control, commonly used in robotics applications. This work proposes to use modern general-purpose multibody software to compute the inverse dynamics of complex rigid mechanisms in an efficient way, so that it suits the requirements of realistic real-time applications as well. This task can be very difficult, since it involves a higher number of equations than the relative coordinates approach. The latter is believed to be less general, and may suffer from topology limitations. The use of specialized linear algebra solvers makes this kind of control algorithms usable in real-time for mechanism models of realistic complexity. Numerical results from the simulation of practical applications are presented, consisting in a “delta” robot and a bio-mimetic 11 degrees of freedom manipulator controlled using the same software and the same algorithm.

[1]  Wisama Khalil,et al.  General Solution for the Dynamic Modeling of Parallel Robots , 2007, J. Intell. Robotic Syst..

[2]  Bhaskar Dasgupta,et al.  A Newton-Euler Formulation for the Inverse Dynamics of the Stewart Platform Manipulator , 1998 .

[3]  Javier García de Jalón,et al.  Kinematic and Dynamic Simulation of Multibody Systems: The Real Time Challenge , 1994 .

[4]  Etienne Burdet,et al.  A body-oriented method for finding a linear form of the dynamic equation of fully parallel robots , 1997, Proceedings of International Conference on Robotics and Automation.

[5]  Alain Codourey,et al.  Dynamic Modeling of Parallel Robots for Computed-Torque Control Implementation , 1998, Int. J. Robotics Res..

[6]  Pierangelo Masarati,et al.  A Multibody User-Space Hard Real-Time Environment for the Simulation of Space Robots , 2003 .

[7]  E. J. Haug,et al.  Computer aided kinematics and dynamics of mechanical systems. Vol. 1: basic methods , 1989 .

[8]  Marco Morandini,et al.  Using dense storage to solve small sparse linear systems , 2007, TOMS.

[9]  Rafael Kelly,et al.  PD control with feedforward compensation for robot manipulators: analysis and experimentation , 2001, Robotica.

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

[11]  Marco Morandini,et al.  Open-Source Multibody Analysis Software , 2003 .

[12]  Gilbert Strang,et al.  Introduction to applied mathematics , 1988 .

[13]  Constantinos A. Balafoutis,et al.  A survey of efficient computational methods for manipulator inverse dynamics , 1994, J. Intell. Robotic Syst..

[14]  Ernst Hairer,et al.  The numerical solution of differential-algebraic systems by Runge-Kutta methods , 1989 .

[15]  Linda R. Petzold,et al.  Numerical solution of initial-value problems in differential-algebraic equations , 1996, Classics in applied mathematics.

[16]  T. S. Sankar,et al.  Real-time computational schemes for inverse dynamics of robot manipulators , 1990, 29th IEEE Conference on Decision and Control.

[17]  Werner Schiehlen,et al.  Multibody System Dynamics: Roots and Perspectives , 1997 .

[18]  Marco Morandini,et al.  COMPUTATIONAL ASPECTS AND RECENT IMPROVEMENTS IN THE OPEN-SOURCE MULTIBODY ANALYSIS SOFTWARE "MBDYN" , 2005 .

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

[20]  Timothy A. Davis,et al.  A column pre-ordering strategy for the unsymmetric-pattern multifrontal method , 2004, TOMS.

[21]  Min-Jie Liu,et al.  Dynamics analysis of the Gough-Stewart platform manipulator , 2000, IEEE Trans. Robotics Autom..

[22]  W. Blajer,et al.  Control of underactuated mechanical systems with servo-constraints , 2007 .

[23]  Gabriella Gaias,et al.  A Simple Approach to Kinematic Inversion of Redundant Mechanisms , 2007 .

[24]  O. Brüls,et al.  A Model Reduction Method for the Control of Rigid Mechanisms , 2006 .

[25]  O. Bauchau,et al.  Review of Classical Approaches for Constraint Enforcement in Multibody Systems , 2008 .

[26]  R. Clavel,et al.  A Fast Robot with Parallel Geometry , 1988 .

[27]  D. Stewart,et al.  A Platform with Six Degrees of Freedom , 1965 .

[28]  W. Blajer,et al.  A Geometric Approach to Solving Problems of Control Constraints: Theory and a DAE Framework , 2004 .

[29]  Yacine Amirat,et al.  Analysis and design of a six-DOF parallel manipulator, modeling, singular configurations, and workspace , 1998, IEEE Trans. Robotics Autom..

[30]  Javier García de Jalón,et al.  Kinematic and Dynamic Simulation of Multibody Systems , 1994 .

[31]  François Pierrot,et al.  Towards a fully-parallel 6 DOF robot for high-speed applications , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[32]  G. Hamel.  Tullio Levi‐Civita e Ugo Amaldi, Lezioni di Meccanica Razionale. Volume Secondo. Dinamica dei Sistemi con un numero finito di Gradi di Liberta. Verlag Nicola Zanichelli, Bologna. Parte Prima. IX + 527 S. Parte Seconda. IX + 684 S , 1928 .

[33]  Paolo Mantegazza,et al.  REAL-TIME MULTIBODY ANALYSIS OF WIND-TUNNEL ROTORCRAFT MODELS FOR VIRTUAL EXPERIMENT PURPOSES , 2003 .

[34]  Paolo Mantegazza,et al.  TRAJECTORY OPTIMIZATION AND REAL-TIME SIMULATION FOR ROBOTICS APPLICATIONS , 2005 .