Pushing Revisited: Differential Flatness, Trajectory Planning and Stabilization

  • Jiaji ZhouEmail author
  • Matthew T. Mason
Conference paper
Part of the Springer Proceedings in Advanced Robotics book series (SPAR, volume 10)


We prove that quasi-static pushing with a sticking contact and ellipsoid approximation of the limit surface is differential flat. Both graphical and algebraic derivations are given. A major conclusion is the pusher-slider system is reducible to the Dubins car problem where the sticking contact constraints translate to bounded curvature. Planning is as easy as computing Dubins curve with the additional benefit of time-optimality. For trajectory stabilization, we design closed-loop control using dynamic feedback linearization or open-loop control using two contact points as a form of mechanical feedback. We conduct robotic experiments using objects with different pressure distributions, shape and contact materials placed at different initial poses that require difficult maneuvers to the goal pose. The average error is within 1.67 mm in translation and 0.5\(^\circ \) in orientation over 60 experimental trials. We also show an example of pushing among obstacles using a RRT planner with exact steering.



The authors would like to thank Guofan Wu, Devin Balkcom, Kevin Lynch and Sanjiban Choudhury for thoughtful discussions.


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Robotics InstituteCarnegie Mellon UniversityPittsburghUSA

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