Planning and Control for Cooperative Manipulation and Transportation with Aerial Robots

  • Jonathan Fink
  • Nathan Michael
  • Soonkyum Kim
  • Vijay Kumar
Part of the Springer Tracts in Advanced Robotics book series (STAR, volume 70)


We consider the problem of controlling multiple robots manipulating and transporting a payload in three dimensions via cables. Individual robot control laws and motion plans enable the control of the payload (position and orientation) along a desired trajectory.We address the fact that robot configurations may admit multiple payload equilibrium solutions by developing constraints for the robot configuration that guarantee the existence of a unique payload pose. Further, we formulate individual robot control laws that enforce these constraints and enable the design of non-trivial payload motion plans. Finally, we propose two quality measures for motion plan design that minimize individual robot motion and maximize payload stability along the trajectory. The methods proposed in the work are evaluated on a team of aerial robots in experimentation.


Motion Plan Direct Problem Attachment Point Body Frame Robot Position 
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  1. 1.
    Ascending Technologies, GmbH,
  2. 2.
    Vicon Motion Systems, Inc.,
  3. 3.
    Cottle, R.W., Pang, J., Stone, R.E.: The Linear Complementarity Problem. Academic Press, London (1992)zbMATHGoogle Scholar
  4. 4.
    Fischer, K., Gartner, B., Schonherr, S., Wessendorp, F.: Linear and quadratic programming solver. In: Board, C.E. (ed.) CGAL User and Reference Manual (2007)Google Scholar
  5. 5.
    Hunt, K.: Kinematic Geometry of Mechanisms. Oxford University Press, Oxford (1978)zbMATHGoogle Scholar
  6. 6.
    Lobo, M.S., Vandenberghe, L., Boyd, S., Lebret, H.: Application of second-order cone programming. Linear Algebra and Its Applications 284, 192–228 (1998)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Michael, N., Fink, J., Kumar, V.: Cooperative manipulation and transportation with aerial robots. In: Robotics: Science and Systems, Seattle, WA (2009)Google Scholar
  8. 8.
    Michael, N., Kim, S., Fink, J., Kumar, V.: Kinematics and statics of cooperative multi-robot aerial manipulation with cables. In: ASME Int. Design Engineering Technical Conf. & Computers and Information in Engineering Conf., San Diego, CA (2009) (to appear)Google Scholar
  9. 9.
    Murray, R.M.: Trajectory generation for a towed cable system using differential flatness. In: IFAC World Congress, San Francisco, CA (1996)Google Scholar
  10. 10.
    Phillips, J.: Freedom in Machinery, vol. 1. Cambridge University Press, Cambridge (1990)Google Scholar
  11. 11.
    Selig, J.M.: Geometric Fundamentals of Robotics. Springer, Heidelberg (2005)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Jonathan Fink
    • 1
  • Nathan Michael
    • 1
  • Soonkyum Kim
    • 1
  • Vijay Kumar
    • 1
  1. 1.GRASP LaboratoryUniversity of PennsylvaniaPhiladelphia

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