Autonomous Robots

, Volume 43, Issue 2, pp 327–344 | Cite as

Optimal shape and motion planning for dynamic planar manipulation

  • Orion TaylorEmail author
  • Alberto Rodriguez
Part of the following topical collections:
  1. Special Issue on Robotics: Science and Systems


This paper presents a framework for optimizing both the shape and the motion of a planar rigid end-effector to satisfy a desired manipulation task. Both shape and motion play key roles in determining contact interaction, and while both are commonly seen as design/control freedoms, their synergies are rarely formally explored. In this paper we study quasistatic problems like cam design, or dynamic problems like ball throwing, where both the shape and motion of the surfaces at contact are relevant. We frame this design problem as a nonlinear optimization program, where shape and motion are decision variables represented as splines. The task is represented as a series of constraints, along with a fitness cost, which force the solution to be compatible with the dynamics of frictional hard contact while satisfying the task. We illustrate the approach with the example problem of moving a disk along a desired path or trajectory, and we verify it by applying it to three classical design problems: the rolling brachistochrone, the design of teeth of involute gears, and the pitch curve of rolling cams. We conclude with a case study involving the optimization and real implementation of the shape and motion of a dynamic throwing arm.


Manipulation Optimization Robot end effector design 


Supplementary material

Supplementary material 1 (mp4 20699 KB)


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringMassachusetts Institute of TechnologyCambridgeUSA

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