A Unifying Object-oriented Methodology to Consolidate Multibody Dynamics Computations in Robot Control

Modern software-based robot control systems are built upon control schemes relying on descriptions of the robot's dynamical motion. This work develops a general purpose methodology to support the robot control design engineer in the whole modeling process. This comprises robot model specification, automatical generation or manual coding of executable multibody dynamics algorithms and integration of these operational robot models in an evolving robot control software architecture. A new object-oriented paradigm for the precise description of the mechanical robot components and the desired computations, a new extension of the mathematical framework of spatial operators for derivtion of dynamics algorithms and a dataflow-driven model of computation form the basis of a new object-oriented class hierarchy to consolidate all required model computations. Examples of real-world industrial and scientific control applications, e.g., path planning, calibration, and trajectory optimization, motivate the range of possible applications.

[1]  Frédéric Boyer,et al.  An efficient calculation of computed torque control of flexible manipulators , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[2]  Kenneth Kreutz-Delgado,et al.  Multibody dynamical algorithms, numerical optimal control, with detailed studies in the control of jet engine compressors and biped walking , 1999 .

[3]  W. W. Schrader,et al.  Efficient Computation of the Jacobian for Robot Manipulators , 1984 .

[4]  Thomas R. Kane,et al.  The Use of Kane's Dynamical Equations in Robotics , 1983 .

[5]  A. Jain,et al.  Sensitivity Analysis for Mulitbody Dynamics Using Spatial Operators , 1999 .

[6]  Michael A. Saunders,et al.  SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization , 2002, SIAM J. Optim..

[7]  Edward A. Lee,et al.  Ptolemy: A Framework for Simulating and Prototyping Heterogenous Systems , 2001, Int. J. Comput. Simul..

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

[9]  Gilles Kahn,et al.  The Semantics of a Simple Language for Parallel Programming , 1974, IFIP Congress.

[10]  K. Kreutz-Delgado,et al.  A star-topology dynamic model for multipedal locomotion , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[11]  R. Hopler,et al.  Model integrated computing in robot control to synthesize real-time embedded code , 2001, Proceedings of the 2001 IEEE International Conference on Control Applications (CCA'01) (Cat. No.01CH37204).

[12]  Abhinandan Jain,et al.  A Spatial Operator Algebra for Manipulator Modeling and Control , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[13]  Friedrich Pfeiffer,et al.  Multibody Dynamics with Unilateral Contacts , 1996 .

[14]  J. Denavit,et al.  A kinematic notation for lower pair mechanisms based on matrices , 1955 .

[15]  Frédéric Boyer,et al.  Simulation of flexible manipulators using Newton-Euler inverse dynamic model , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[16]  Abhinandan Jain.  Unified formulation of dynamics for serial rigid multibody systems , 1991 .

[17]  Abhinandan Jain,et al.  A reusable, real-time spacecraft dynamics simulator , 1997, 16th DASC. AIAA/IEEE Digital Avionics Systems Conference. Reflections to the Future. Proceedings.

[18]  J. Bobrow,et al.  Time-Optimal Control of Robotic Manipulators Along Specified Paths , 1985 .

[19]  Abhinandan Jain,et al.  A fast recursive algorithm for molecular dynamics simulation , 1993 .

[20]  Hartmut Ehrig,et al.  Computing by Graph Transformation - A Survey and Annotated Bibliography , 1996 .

[21]  Gilmer L. Blankenship,et al.  Symbolic construction of models for multibody dynamics , 1995, IEEE Trans. Robotics Autom..

[22]  Olivier Bruneau,et al.  Dynamic Analysis Tool for Legged Robots , 1998 .

[23]  Abhinandan Jain,et al.  Linearization of manipulator dynamics using spatial operators , 1993, IEEE Trans. Syst. Man Cybern..

[24]  Ralph E. Johnson,et al.  Frameworks = (components + patterns) , 1997, CACM.

[25]  Dieter Bestle.  Analyse und Optimierung von Mehrkörpersystemen , 1994 .

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

[27]  R. Schwertassek,et al.  Dynamik flexibler Mehrkörpersysteme , 1999 .

[28]  Kenneth Kreutz-Delgado,et al.  Approximate dynamic decoupling of multilimbed robotic systems , 1995, Proceedings 1995 IEEE/RSJ International Conference on Intelligent Robots and Systems. Human Robot Interaction and Cooperative Robots.

[29]  Frank Chongwoo Park,et al.  A recursive algorithm for robot dynamics using Lie groups , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[30]  Peter I. Corke,et al.  A robotics toolbox for MATLAB , 1996, IEEE Robotics Autom. Mag..

[31]  Laurian M. Chirica,et al.  The entity-relationship model: toward a unified view of data , 1975, SIGF.

[32]  Alessandro De Luca.  Feedforward/Feedback Laws for the Control of Flexible Robots , 2000, ICRA.

[33]  Guillermo Rodríguez-Ortiz,et al.  Spatial operator factorization and inversion of the manipulator mass matrix , 1992, IEEE Trans. Robotics Autom..

[34]  Gabor Karsai,et al.  Self-adaptive software for signal processing , 1998, CACM.

[35]  Bran Selic,et al.  Using UML for Modeling Complex Real-Time Systems , 1998, LCTES.

[36]  H. Vangheluwe,et al.  Meta-Models are models too , 2002, Proceedings of the Winter Simulation Conference.

[37]  Edward A. Lee,et al.  Overview of the Ptolemy project , 2001 .

[38]  Oskar von Stryk,et al.  Efficient dynamic modeling, numerical optimal control and experimental results for various gaits of a quadruped robot , 2003 .

[39]  L. Sweet,et al.  Redefinition of the robot motion-control problem , 1985, IEEE Control Systems Magazine.

[40]  Delbert Tesar,et al.  A reusable operational software architecture for advanced robotics , 1996 .

[41]  Martin Otter.  Objektorientierte Modellierung mechatronischer Systeme am Beispiel geregelter Roboter , 1994 .

[42]  John J. Murray,et al.  Linearization and sensitivity functions of dynamic robot models , 1984, IEEE Transactions on Systems, Man, and Cybernetics.

[43]  Andrés Kecskeméthy,et al.  Objektorientierte Modellierung der Dynamik von Mehrkörpersystemen mit Hilfe von Übertragungselementen , 1993 .

[44]  A. Albu-Schäffer.  Regelung von Robotern mit elastischen Gelenken am Beispiel der DLR-Leichtbauarme , 2002 .

[45]  Alin Albu-Schäffer,et al.  On a new generation of torque controlled light-weight robots , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[46]  C. A. Balafoutis.  A New Lagrangian Formulation of Dynamics for Robot Manipulators , 2007 .

[47]  Ralph Johnson,et al.  design patterns elements of reusable object oriented software , 2019 .

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

[49]  M. Spong.  Modeling and Control of Elastic Joint Robots , 1987 .

[50]  Pascal Raymond,et al.  The synchronous data flow programming language LUSTRE , 1991, Proc. IEEE.

[51]  Derek J. Hatley,et al.  Strategies for Real-Time System Specification , 1987 .

[52]  Friedrich Pfeiffer,et al.  A concept for manipulator trajectory planning , 1987, IEEE J. Robotics Autom..

[53]  R. Featherstone.  The Calculation of Robot Dynamics Using Articulated-Body Inertias , 1983 .

[54]  Martín Abadi,et al.  A Theory of Objects , 1996, Monographs in Computer Science.

[55]  David Notkin,et al.  Language Support for Connector Abstractions , 2003, ECOOP.

[56]  Edward A. Lee,et al.  Dataflow process networks , 1995, Proc. IEEE.

[57]  J. Y. S. Luh,et al.  On-Line Computational Scheme for Mechanical Manipulators , 1980 .

[58]  Alessandro De Luca,et al.  A general algorithm for dynamic feedback linearization of robots with elastic joints , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[59]  Scott McMillan,et al.  Efficient computation of articulated-body inertias using successive axial screws , 1995, IEEE Trans. Robotics Autom..

[60]  Martin Buss,et al.  Towards an autonomous, humanoid, and dynamically walking robot: modeling, optimal trajectory planning, hardware architecture, and experiments , 2003 .

[61]  Heiko Dörr,et al.  Efficient Graph Rewriting and Its Implementation , 1995, Lecture Notes in Computer Science.

[62]  J. Craig Cleaveland,et al.  Building application generators , 1988, IEEE Software.

[63]  Johann Bals,et al.  Control of robots with elastic joints based on automatic generation of inverse dynamics models , 2001, Proceedings 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems. Expanding the Societal Role of Robotics in the the Next Millennium (Cat. No.01CH37180).

[64]  Oskar Wallrapp,et al.  Standardization of flexible body modeling in multibody system codes , 1994 .

[65]  Dinesh K. Pai,et al.  Forward dynamics algorithms for multibody chains and contact , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[66]  Abhinandan Jain,et al.  Spatial Operator Algebra for multibody system dynamics , 1992 .

[67]  O. V. Stryk,et al.  Optimal control of the industrial robot Manutec r3 , 1994 .

[68]  O. von Stryk,et al.  Dynamic modeling in the simulation, optimization, and control of bipedal and quadrupedal robots , 2003 .

[69]  N. V. Orlandea,et al.  ADAMS THEORY AND APPLICATION , 1987 .

[70]  David A. Levinson,et al.  Interactive Computerized Symbolic Dynamics for the Dynamicist , 1988, 1988 American Control Conference.

[71]  Robert E. Tarjan,et al.  Depth-First Search and Linear Graph Algorithms , 1972, SIAM J. Comput..

[72]  Robert Höpler,et al.  Symbolic computation of the inverse dynamics of elastic joint robots , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[73]  Robert J. Anderson.  SMART: a modular architecture for robotics and teleoperation , 1993, [1993] Proceedings IEEE International Conference on Robotics and Automation.

[74]  K. Beck,et al.  Extreme Programming Explained , 2002 .

[75]  Guilin Yang,et al.  Automatic Model Generation for Modular Reconfigurable Robot Dynamics , 1998 .

[76]  Richard Gourdeau,et al.  Object-oriented programming for robotic manipulator simulation , 1997, IEEE Robotics Autom. Mag..

[77]  Abhinandan Jain,et al.  RECURSIVE FLEXIBLE MULTIBODY SYSTEM DYNAMICS USING SPATIAL OPERATORS , 1992 .

[78]  Dinesh K. Pai,et al.  Forward Dynamics, Elimination Methods, and Formulation Stiffness in Robot Simulation , 1997, Int. J. Robotics Res..

[79]  David J. Miller,et al.  An object-oriented environment for robot system architectures , 1991, IEEE Control Systems.

[80]  J. Wittenburg,et al.  Dynamics of systems of rigid bodies , 1977 .

[81]  F. W. Carter.  Discussion on Paper , 1903 .

[82]  John Stuart Lakos,et al.  Large-Scale C++ Software Design , 1996 .

[83]  Reiko Heckel,et al.  A view-oriented approach to system modelling based on graph transformation , 1997, ESEC '97/FSE-5.

[84]  Oussama Khatib,et al.  A unified approach for motion and force control of robot manipulators: The operational space formulation , 1987, IEEE J. Robotics Autom..

[85]  Gabor Karsai,et al.  Model-Integrated Computing , 1997, Computer.

[86]  C. Pantelides.  The consistent intialization of differential-algebraic systems , 1988 .

[87]  David W. Binkley.  C++ in safety critical systems , 1997, Ann. Softw. Eng..

[88]  Abhinandan Jain,et al.  Diagonalized Lagrangian robot dynamics , 1995, IEEE Trans. Robotics Autom..

[89]  Roy Featherstone,et al.  The Acceleration Vector of a Rigid Body , 2001, Int. J. Robotics Res..

[90]  Alin Albu-Schäffer,et al.  State feedback controller for flexible joint robots: a globally stable approach implemented on DLR's light-weight robots , 2000, Proceedings. 2000 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2000) (Cat. No.00CH37113).

[91]  Gregor Engels,et al.  Object-oriented modeling: a roadmap , 2000, ICSE '00.

[92]  Alfred V. Aho,et al.  The Design and Analysis of Computer Algorithms , 1974 .

[93]  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.

[94]  Kenneth Kreutz-Delgado,et al.  A star topology dynamic model for efficient simulation of multilimbed robotic systems , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[95]  G. Sohl,et al.  A Recursive Multibody Dynamics and Sensitivity Algorithm for Branched Kinematic Chains , 2001 .

[96]  Ahmed A. Shabana,et al.  Dynamics of Multibody Systems , 2020 .

[97]  R. McN. Alexander,et al.  The Gaits of Bipedal and Quadrupedal Animals , 1984 .

[98]  William M. Silver.  On the equivalence of Lagrangian and Newton-Euler dynamics for manipulators , 1981 .

[99]  John T. Wen,et al.  Simulation and analysis of flexibly jointed manipulators , 1990, 29th IEEE Conference on Decision and Control.

[100]  Martin Otter,et al.  A versatile C++ toolbox for model based, real time control systems of robotic manipulators , 2001, Proceedings 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems. Expanding the Societal Role of Robotics in the the Next Millennium (Cat. No.01CH37180).

[101]  Brian Foote,et al.  Designing Reusable Classes , 2001 .

[102]  Edward A. Lee,et al.  What's Ahead for Embedded Software? , 2000, Computer.

[103]  Wolfgang Rulka,et al.  SIMPACK — A Computer Program for Simulation of Large-motion Multibody Systems , 1990 .

[104]  John M. Hollerbach,et al.  A Recursive Lagrangian Formulation of Manipulator Dynamics , 1980 .

[105]  K. Anderson,et al.  Improved `Order-N' Performance Algorithm for the Simulation of Constrained Multi-Rigid-Body Dynamic Systems , 2003 .

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

[107]  Bran Selic,et al.  Real-time object-oriented modeling , 1994, Wiley professional computing.

[108]  Herman Bruyninckx,et al.  Open robot control software: the OROCOS project , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[109]  Wisama Khalil,et al.  Minimum operations and minimum parameters of the dynamic models of tree structure robots , 1987, IEEE Journal on Robotics and Automation.

[110]  Scott McMillan,et al.  Computational dynamics for robotic systems on land and under water , 1995 .

[111]  Francis L. Merat,et al.  Introduction to robotics: Mechanics and control , 1987, IEEE J. Robotics Autom..

[112]  David E. Orin,et al.  Efficient Dynamic Computer Simulation of Robotic Mechanisms , 1982 .

[113]  R. Schwertassek,et al.  Representation of Joints in Multibody Systems , 1988 .

[114]  M. Hiller,et al.  A comparative study of recursive methods , 1995 .

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

[116]  Wisama Khalil,et al.  A new geometric notation for open and closed-loop robots , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

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

[118]  R. Roberson,et al.  A dynamical formalism for an arbitrary number of interconnected rigid bodies, with reference to the problem of satellite attitude control. , 1966 .

[119]  D. M. Douglas.  Elastic Joints , 1971 .