Dynamic modeling and analysis of a lightweight robotic manipulator in joint space

• Autorzy: Woliński Ł. , Malczyk P.

Identyfikatory

DOI

10.1515/meceng-2015-0016

Warianty tytułu

PL

Analiza dynamiki manipulatora w przestrzeni współrzędnych złączowych

• Języki publikacji: EN

Abstrakty

EN

The primary importance of the paper is the application of the efficient formulation for the simulation of open-loop lightweight robotic manipulator. The framework employed in the paper makes use of the spatial operator algebra and the associated equations are expressed in joint space. This compact representation of the manipulator dynamics makes it possible to solve the robot forward and inverse dynamics problems in a recursive and fast manner. In the current form, the presented algorithm can be applied for the dynamics simulation of an open-loop chain system possessing any number of joints. Specifically, the formulation has been successfully applied for the analysis of the 7DOF KUKA LWR robot. Results from a number of test cases for the robot demonstrate the verification of the calculations.

PL

W artykule przedstawiono efektywny algorytm do analizy dynamiki manipulatora przestrzennego o otwartym łańcuchu kinematycznym. Równania opisujące dynamikę układu zapisano w formie algebraiczno-macierzowej w przestrzeni współrzędnych złączowych. Wprowadzona zwarta reprezentacja równań opisujących ruch manipulatora pozwoliła na rozwiązanie zadania prostego i odwrotnego dynamiki manipulatora w rekursywny i wydajny sposób. Algorytm uogólniono na przypadki analizy dynamiki otwartych łańcuchów kinematycznych z dowolną liczbą stopni swobody. Opracowane sformułowanie zastosowano do analizy dynamiki manipulatora KUKA LWR o siedmiu stopniach swobody. Zweryfikowano poprawność obliczeń numerycznych dla testowych przypadków ruchu manipulatora, a wyniki porównano z rezultatami otrzymanymi w pakiecie komercyjnym do obliczeń dynamiki układów wieloczłonowych.

Słowa kluczowe

EN

robot dynamics; recursive algorithms; redundant manipulator

PL

dynamika robota; algorytmy rekurencyjne; manipulator redundantny

• Wydawca: Komitet Budowy Maszyn PAN
• Czasopismo: Archive of Mechanical Engineering
• Rocznik: 2015
• Tom: Vol. LXII, nr 2
• Strony: 279--302
• Opis fizyczny: Bibliogr. 50 poz., fot., rys., tab.

Twórcy

autor

Woliński Ł.

• Division of Theory of Machines and Robots, Institute of Aeronautics and Applied Mechanics, Faculty of Power and Aeronautical Engineering, Warsaw University of Technology, Nowowiejska 24, 00-665 Warsaw, Poland

autor

Malczyk P.

• Division of Theory of Machines and Robots, Institute of Aeronautics and Applied Mechanics, Faculty of Power and Aeronautical Engineering, Warsaw University of Technology, Nowowiejska 24, 00-665 Warsaw, Poland

Bibliografia

• [1] Orlandea N., Chace M., and Calahan D.: “A sparcity-oriented approach to the dynamics analysis and design of mechanical systems - parts 1 and 2,” Journal of Engineering for Industry, vol. 43, pp. 773–784, 1977.
• [2] Armstrong W.W.: “Recursive solution to the equations of motion of an n-link manipulator,” in Proceedings of the 5th World Congress on Theory of Machines and Mechanisms, pp. 1343–1346, 1979.
• [3] Hollerbach J.: “A recursive Lagrangian formulation of manipulator dynamics and a comparative study of dynamics formulation complexity,” IEEE Transactions on Systems, Man, and Cybernetics, vol. SMC-10(11), pp. 730–736, 1980.
• [4] Anderson K.: “An order n formulation for the motion simulation of general multi-rigid-body constrained systems,” Computer and Structures, vol. 3, pp. 565–579, 1992.
• [5] Baeand D.S., Haug E.J.: “A recursive formulation for constrained mechanical system dynamics: Part I: Open loop systems,” Mechanics of Structures and Machines, vol. 15, pp. 359–382, 1987.
• [6] Baeand D.S., Haug E.J.: “A recursive formulation for constrained mechanical system dynamics: Part II: Closed loop systems,” Mechanics of Structures and Machines, vol. 15, pp. 481–506, 1988.
• [7] Baraff D.: “Linear-time dynamics using lagrange multipliers,” in SIG-GRAPH 96, Computer Graphics Proceedings, pp. 137–146, 1996.
• [8] Featherstone R.: “The calculation of robot dynamics using articulated-body inertias,” International Journal of Robotics Research, vol. 2, pp. 13–30, 1983.
• [9] Jain A.: “Unified formulation of dynamics for serial rigid multibody systems,” Journal of Guidance, Control, and Dynamics, vol. 14, pp. 531–542, 1991.
• [10] Rodriguez G.: “Kalman filtering, smoothing and recursive robot arm forward and inverse dynamics,” IEEE Journal of Robotics and Automation, vol. 6, pp. 624–639, 1987.
• [11] Rosenthal D.: “An order n formulation for robotic systems,” The Journal of the Astronautical Sciences, vol. 38(4), pp. 511–529, 1990.
• [12] Walkerand M.W., Orin D.E.: “Efficient dynamic computer simulation of robotic mechanisms,” ASME Journal of Dynamic Systems, Measurements, and Control, vol. 104, pp. 205–211, 1982.
• [13] Yamaneand K., Nakamura Y.: “O(N) forward dynamics computation of open kinematic chains based on the principle of virtual work,” in Proceedings of IEEE International Conference on Robotics and Automation, pp. 2824–2831, 2001.
• [14] Anderson K., and Critchley J.: “Improved ’order-n’ performance algorithm for the simulation of constrained multi-rigid-body dynamic systems,” Multi-body System Dynamics, vol. 9, pp. 185–225, 2003.
• [15] Naudet J.: “Forward dynamics of multibody systems: a recursive Hamiltonian approach.” Phd Thesis, Universytet Vrije, Brussels, Belgium, 2005.
• [16] Saha K.S., and Schiehlen W.: ,“Recursive kinematics and dynamics for parallel structured closed-loop multibody systems,” Mechanics of Structures and Machines, vol. 29(2), pp. 143–175, 2001.
• [17] Stejskal V., and Valasek M.: Kinematics and Dynamics of Machinery. Marcel Dekker, NY, 1996.
• [18] Kasahara H., Fujii H., and Iwata M.: “Parallel processing of robot motion simulation,” in Proceedings IFAC World Congress, Munich, 1987.
• [19] Bae D.S., Kuhl J., and Haug E.J.: “A recursive formulation for constrained mechanical system dynamics: Part III. parallel processor implementation,” Mechanics of Structures and Machines, vol. 16, pp. 249–269, 1988.
• [20] Chungand S., Haug E.J.: “Real-time simulation of multibody dynamics on shared memory multiprocessors,” Journal of Dynamic Systems, Measurement, and Control, vol. 115, pp. 627–637, 1993.
• [21] Fijanyand A., Bejczy A.K.: “Techniques for parallel computation of mechanical manipulator dynamics. part II: Forward dynamics,” Control and Dynamics Systems, vol. 40, pp. 357–410, 1991.
• [22] Fijany A., Sharf I., and D’Eleuterio G.: “Parallel O(log n) algorithms for computation of manipulator forward dynamics,” IEEE Transactionson Robotics and Automation, vol. 11, pp. 389–400, 1995.
• [23] Leeand C., Chang P.: “Efficient parallel algorithms for robot forward dynamics,” IEEE Transactions on Systems, Man, and Cybernetics, vol. 18(2), pp. 238–251, 1988.
• [24] Featherstone R.: “A divide-and-conquer articulated body algorithm for parallel O(log n) calculation of rigid body dynamics. Part 1: Basic algorithm,” International Journal of Robotics Research, vol. 18, pp. 867–875, 1999.
• [25] Featherstone R.: “A divide-and-conquer articulated body algorithm for parallel O(log n) calculation of rigid body dynamics. Part 2: Trees, loops, and accuracy,” International Journal of Robotics Research, vol. 18, pp. 876–892, 1999.
• [26] Anderson K.S., and Duan S.: “Highly parallelizable low-order dynamics simulation algorithm for multi-rigid-body systems,” Journal of Guidance, Control, and Dynamics, vol. 23, pp. 355–364, 2000.
• [27] Critchley J., and Anderson K.: “A parallel logarithmic order algorithm for general multibody system dynamics,” Multibody System Dynamics, vol. 12, pp. 75–93, 2004.
• [28] Yamane K., and Nakamura Y.: “Parallel O(log n) algorithm for dynamics simulation of humanoid robots,” in Proceedings of the 6th IEEE-RAS International Conference on Humanoid Robots, (Genova, Italy), pp. 554–559, 2006.
• [29] Mukherjee R., and Anderson K.: “Orthogonal complement based divide-and-conquer algorithm for constrained multibody systems,” Nonlinear Dynamics, vol. 48, pp. 199–215, 2007.
• [30] Malczyk P., and Frączek J.: “Cluster computing of mechanisms dynamics using recursive formulation,” Multibody System Dynamics, vol. 20(2), pp. 177–196, 2008.
• [31] Malczyk P., and Frączek J.: “A divide and conquer algorithm for constrained multibody system dynamics based on augmented lagrangian method with projections-based error correction,” Nonlinear Dynamics, vol. 70(1), pp. 871–889, 2012.
• [32] Yamane K., and Nakamura Y.: “Comparative study on serial and parallel forward dynamics algorithms for kinematic chains,” International Journal of Robotics Research, vol. 28(5), pp. 622–629, 2009.
• [33] Featherstone R.: Rigid Body Dynamics Algorithms. Springer, 2008.
• [34] Jain A.: Robot and Multibody Dynamics: Analysis and Algorithms. Springer; 1st Edition, 2011.
• [35] Rodriguez G., Jain A., and Kreutz-Delgado K.: “Spatial operator algebra for manipulator modelling and control,” International Journal of Robotics Research, vol. 10(4), pp. 371–381, 1991.
• [36] Craig J.: Introduction to Robotics. Mechanics & Control. Addison-Wesley Publishing Company, 1986.
• [37] Bae D.S., and Haug E.J.: “A recursive formulation for constrained mechanical system dynamics: Part I: Open loop systems,” Mechanics of Structures and Machines, vol. 15, pp. 359–382, 1987.
• [38] Jain A.: Robot and Multibody Dynamics: Analysis and Algorithms. Springer, 2011.
• [39] Malczyk P., and Fraczek J.: “Cluster computing of mechanisms dynamics using recursive formulation,” Multibody System Dynamics, vol. 20(2), pp. 177–196, 2008.
• [40] Gaz C., Flacco F., and Luca A.D.: “Identifying the dynamic model used by the kuka lwr: A reverse engineering approach,” in Proceedings of the IEEE International Conference on Robotics and Automation 2014, (Hong Kong, China), pp. 1386–1392, May 31- June 7 2014.
• [41] Jubien A., Gautier M., and Janot A.: “Dynamic identification of the kuka lightweight robot: comparison between actual and confidential kuka’s parameters,” in Proceedings of the IEEE/ASME International Conference on Advanced Intelligent Mechatronics 2014, (Besancon, France), pp. 483–488, July 8-11 2014.
• [42] “Lightweight robot 4+ specification, version: Spez lbr 4+ v2en,” Issued: 06.07.2010, 2010.
• [43] “Adams/solver (c++) statements. integrator,” Adams 2013.1 Help, 2013.
• [44] Scilab Help (https://help.scilab.org/docs/5.5.1/en US/ode.html), 2014.
• [45] Hindmarsh A.: “Serial fortran solvers for ode initial value problems,” http://computation.llnl.gov/casc/odepack/, 2014.
• [46] Malczyk P., Frączek J., and Cuadrado J.: “Parallel index-3 formulation for real-time multibody dynamics simulations,” in Proceedings of the First Joint International Conference on Multibody System Dynamics-IMSD 2010, ISBN978-952-214-778-3, (Lappeenranta, Finland), 25-27 May 2010.
• [47] Critchley J.: “A parallel logarithmic time complexity algorithm for the simulation of general multibody system dynamics.” Praca doktorska, Rensselaer Polytechnic Institute, Troy, New York, USA, 2003.
• [48] Gonzales M., Dopico D., Lugris U., and Cuadrado J.: “A benchmarking system for mbs simulation software: Problem standarization and performance measurement,” Multibody System Dynamics, vol. 16, pp. 179—190, 2006.
• [49] IFToMM: “Library of computational benchmark problems iftomm technical committee for multibody dynamics.” Available online at http://iftomm-multibody.org/benchmark/, May 2015.
• [50] Schreiber G., Stemmer A., and Bischo˙ R.: “The fast research interface for the kuka lightweight robot,” in Proceedings of the IEEE ICRA 2010 Workshop on ICRA 2010 Workshop on Innovative Robot Control Architectures for Demanding (Research) Applications – How to Modify and Enhance Commercial Controllers, (Anchorage), pp. 15–21, May 2010.

Uwagi

EN

This work has been supported by the National Science Center under grant no. DEC-2012/07/B/ST8/03993