A case study of inverse dynamics control of manipulators with passive joints

• Autorzy: Blajer W. , Kołodziejczyk K.
• Języki publikacji: EN

Abstrakty

EN

Manipulators with both active and passive joints are examples of underactuated systems, featured by less control inputs than degrees of freedom. Due to the underactuation, in the trajectory tracking (servo-constraint) problem, the feed-forward control obtained from an inverse model is influenced by internal dynamics of the system, leading to a more involved control design than in the fully actuated case. It is demonstrated that a convenient approach to the problem solution is to formulate the underactuated system dynamics in the input-output normal form, with the arising governing equations formulated either as ODEs (ordinary differential equations) or DAEs (differential-algebraic equations). The interrelationship between the inverse dynamics control and the associated internal dynamics is then studied and illustrated using a planar manipulator with two active and one passive joint. Some simulation results for the sample case study are reported.

Słowa kluczowe

EN

inverse dynamics; underactuated manipulators; passive joints; servo-constraints

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2014
• Tom: Vol. 52 nr 3
• Strony: 793--801
• Opis fizyczny: Bibliogr. 18 poz., rys.

Twórcy

autor

Blajer W.

• University of Technology and Humanities in Radom, Faculty of Mechanical Engineering, Radom, Poland

autor

Kołodziejczyk K.

• University of Technology and Humanities in Radom, Faculty of Mechanical Engineering, Radom, Poland

Bibliografia

• 1. Ascher U.M., Petzold L.R., 1998, Computer Methods for Ordinary Differential Equations and Differential–Algebraic Equations, SIAM, Philadelphia
• 2. Bajodah A.H., Hodges D.H., Chen Y.-H., 2005, Inverse dynamics of servo-constraints based on the generalized inverse, Nonlinear Dynamics, 39, 1/2, 179-196
• 3. Benosman M., Le Vey G., 2004, Control of flexible manipulators: a survey, Robotica, 22, 5, 533-545
• 4. Blajer W., Kołodziejczyk K., 2007, Control of underactuated mechanical systems with servoconstraints, Nonlinear Dynamics, 50, 4, 781-791
• 5. Blajer W., Kołodziejczyk K., 2008, Modeling of underactuated mechanical systems in party specified motion, Journal of Theoretical and Applied Mechanics, 46, 2, 383-394
• 6. Blajer W., Seifried R., 2012, From orthogonal to tangential control of underactuated mechanical systems in partly specified motion – a cases study illustration, International Journal of Applied Mechanics and Engineering, 17, 3, 689-706
• 7. De Luca A., Oriolo G., 2002, Trajectory planning and control for planar robots with passive last joint, The International Journal of Robotics Research, 21, 5/6, 575-590
• 8. Fantoni I., Lozano R., 2002, Non-linear Control for Underactuated Mechanical Systems, Springer, London
• 9. Fliess M., L´evine J., Martin P., Rouchon P., 1995, Flatness and defect of nonlinear systems: introductory theory and examples, International Journal of Control, 61, 6, 1327-1361
• 10. Kirgetov V.I., 1967, The motion of controlled mechanical systems with prescribed constraints (servoconstraints), Journal of Applied Mathematics and Mechanics, 31, 3, 433-466
• 11. Kov´acs L.L., Bencsik L., 2012, Stability case study of the ACROBOTER underactuated service robot, Theoretical and Applied Mechanics Letters, 2, 4, paper ID: 043004 (7 pages)
• 12. Paul R.P., 1981, Robot Manipulators: Mathematics, Programming, and Control, MIT Press, Cambridge, MA
• 13. R. Seifried R., 2011, Optimization-based design of minimum phase underactuated multibody systems, [In:] Multibody Dynamics: Computational Methods and Applications, Arczewski K., Blajer W., Frączek J., Wojtyra M. (Eds.), Springer, Dordrecht, 261-282
• 14. Seifried R., 2012a, Integrated mechanical and control design of underactuated multibody systems, Nonlinear Dynamics, 67, 2, 1539-1557
• 15. Seifried R., 2012b, Two approaches for feedforward control and optimal design of underactuated multibody systems, Multibody System Dynamics, 27, 1, 75-93
• 16. Seifried R., Blajer W., 2013, Analysis of servo-constraint problems for underactuated multibody systems, Mechanical Sciences, 4, 1, 113-129
• 17. Spong M.W., 1987, Modeling and control of elastic joint robots, Transactions of the ASME, Journal of Dynamic Systems, Measurements, and Control, 109, 4, 310-319
• 18. Spong M.W., 1998, Underactuated mechanical systems, [In:] Control Problems in Robotics and Automation, Siciliano B., Valavanis K.P. (Eds.), Springer, London, 135-150