Research Papers

Control Constraint of Underactuated Aerospace Systems

[+] Author and Article Information
Pierangelo Masarati

Associate Professor
e-mail: pierangelo.masarati@polimi.it

Marco Morandini

Assistant Professor
e-mail: marco.morandini@polimi.it

Alessandro Fumagalli

e-mail: alessandro.fumagalli@selexgalileo.com
Dipartimento di Scienze e
Tecnologie Aerospaziali,
Politecnico di Milano,
Milano 20156, Italy

For a definition of the differential index of DAEs see for example [20].

See for example [21] for the definitions of A and L stability.

1Corresponding author.

2Now at Selex ES, a Finmeccanica Company, Space Robotics PEM/System Engineering, Milano 20153, Italy.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received July 2, 2012; final manuscript received October 3, 2013; published online January 9, 2014. Assoc. Editor: Jozsef Kovecses.

J. Comput. Nonlinear Dynam 9(2), 021014 (Jan 09, 2014) (9 pages) Paper No: CND-12-1104; doi: 10.1115/1.4025629 History: Received July 02, 2012; Revised October 03, 2013

This paper discusses the problem of control constraint realization applied to the design of maneuvers of complex underactuated systems modeled as multibody problems. Applications of interest in the area of aerospace engineering are presented and discussed. The tangent realization of the control constraint is discussed from a theoretical point of view and is used to determine feedforward control of realistic underactuated systems. The effectiveness of the computed feedforward input is subsequently verified by applying it to more detailed models of the problems, in the presence of disturbances and uncertainties in combination with feedback control. The problems are solved using a free general-purpose multibody software that writes the constrained dynamics of multifield problems formulated as differential-algebraic equations. The equations are integrated using unconditionally stable algorithms with tunable dissipation. The essential extension to the multibody code consisted of the addition of the capability to write arbitrary constraint equations and apply the corresponding reaction multipliers to arbitrary equations of motion. The modeling capabilities of the formulation could be exploited without any undue restriction on the modeling requirements.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Laulusa, A., and Bauchau, O. A., 2008, “Review of Classical Approaches for Constraint Enforcement in Multibody Systems,” ASME J. Comput. Nonlinear Dyn., 3(1), p. 011004. [CrossRef]
Bauchau, O. A., and Laulusa, A., 2008, “Review of Contemporary Approaches for Constraint Enforcement in Multibody Systems,” ASME J. Comput. Nonlinear Dyn., 3(1), p. 011005. [CrossRef]
Chen, Y.-H., 2005, “Mechanical Systems Under Servo Constraints: The Lagrange's Approach,” Mechatronics, 15(3), pp. 317–337. [CrossRef]
Chen, Y.-H., 2008, “Equations of Motion of Mechanical Systems Under Servo Constraints: The Maggi Approach,” Mechatronics, 18(4), pp. 208–217. [CrossRef]
Blajer, W., and Kołodziejczyk, K., 2007, “Control of Underactuated Mechanical Systems With Servo-Constraints,” Nonlinear Dyn., 50(4), pp. 781–791. [CrossRef]
Blajer, W., and Kołodziejczyk, K., 2004, “A Geometric Approach to Solving Problem of Control Constraints: Theory and a DAE Framework,” Multibody Syst. Dyn., 11(4), pp. 343–364. [CrossRef]
Wang, J. T., 1990, “Inverse Dynamics of Constrained Multibody Systems,” J. Appl. Mech., 57(3), pp. 750–757. [CrossRef]
Blajer, W., 1997, “Dynamics and Control of Mechanical Systems in Partly Specified Motion,” J. Franklin Inst., 334(3), pp. 407–426. [CrossRef]
Lam, S., 1998, “On Lagrangian Dynamics and Its Control Formulations,” Appl. Math. Comput., 91(2–3), pp. 259–284. [CrossRef]
Rosen, A., 1999, “Applying the Lagrange Method to Solve Problems of Control Constraints,” J. Appl. Mech., 66(4), pp. 1013–1015. [CrossRef]
Gobulev, Y., 2001, “Mechanical Systems With Servoconstraints,” J. Appl. Math. Mech., 65(2), pp. 205–217. [CrossRef]
Blajer, W., and Kołodziejczyk, K., 2008, “Modeling of Underactuated Mechanical Systems in Partly Specified Motion,” J. Theor. Appl. Mech., 46(2), pp. 383–394.
Blajer, W., and Kołodziejczyk, K., 2011, “Improved DAE Formulation for Inverse Dynamics Simulation of Cranes,” Multibody Syst. Dyn., 25(2), pp. 131–143. [CrossRef]
Fumagalli, A., Masarati, P., Morandini, M., and Mantegazza, P., 2011, “Control Constraint Realization for Multibody Systems,” ASME J. Comput. Nonlinear Dyn., 6(1), p. 011002. [CrossRef]
Singh, R. P., and Likins, P. W., 1985, “Singular Value Decomposition for Constrained Dynamical Systems,” J. Appl. Mech., 52(4), pp. 943–948. [CrossRef]
Mani, N. K., Haug, E. J., and Atkinson, K. E., 1985, “Application of Singular Value Decomposition for Analysis of Mechanical System Dynamics,” ASME J. Mech. Trans. Auto. Design, 107(1), pp. 82–87. [CrossRef]
Kim, S. S., and Vanderploeg, M. J., 1986, “QR Decomposition for State Space Representation of Constrained Mechanical Dynamic Systems,” ASME J. Mech. Trans., 108(2), pp. 183–188. [CrossRef]
Blajer, W., 2001, “A Geometrical Interpretation and Uniform Matrix Formulation of Multibody System Dynamics,” ZAMM J. Appl. Math. Mech., 81(4), pp. 247–259. [CrossRef]
Pennestrì, E., and Vita, L., 2004, “Strategies for the Numerical Integration of DAE Systems in Multibody Dynamics,” Comput. Appl. Eng. Ed., 12(2), pp. 106–116. [CrossRef]
Brenan, K. E., Campbell, S. L. V., and Petzold, L. R., 1989, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, North-Holland, New York.
Lambert, J. D., 1991, Numerical Methods for Ordinary Differential Systems, John Wiley and Sons, Chichester, UK.
Uhlar, S., and Betsch, P., 2008, “Conserving Integrators for Parallel Manipulators,” Parallel Manipulators, J.-H.Ryu, Ed., I-Tech Education and Publishing, Vienna, Austria, pp. 75–108.
Betsch, P., Uhlar, S., Saeger, N., Siebert, R., and Franke, M., 2010, “Benefits of a Rotationless Rigid Body Formulation to Computational Flexible Multibody Dynamics,” 1st ESA Workshop on Multibody Dynamics for Space Applications, ESTEC, Noordwijk, NL.
Panofsky, H. A., and Dutton, J. A., 1984, Atmospheric Turbulence: Models and Methods For Engineering Applications, John Wiley and Sons, New York.


Grahic Jump Location
Fig. 1

Snapshots of planar parallel manipulator at (a) t = 0.0 s, (b) 0.9 s, (c) 1.2 s, and (d) 1.8 s

Grahic Jump Location
Fig. 2

CM trajectory of both platforms

Grahic Jump Location
Fig. 3

CM motion and rotation of both platforms

Grahic Jump Location
Fig. 4

Torque in actuators

Grahic Jump Location
Fig. 5

Rotation of actuators

Grahic Jump Location
Fig. 12

Conventional aircraft: control rotation

Grahic Jump Location
Fig. 14

HAWT: angular velocity

Grahic Jump Location
Fig. 15

HAWT: blade collective pitch

Grahic Jump Location
Fig. 7

Canard vertical motion (top); difference (bottom)

Grahic Jump Location
Fig. 8

Canard pitch rotation (top); difference (bottom)

Grahic Jump Location
Fig. 9

Canard control rotation (top); difference (bottom)

Grahic Jump Location
Fig. 10

Conventional aircraft: sketch

Grahic Jump Location
Fig. 11

Conventional aircraft: vertical motion




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In