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Planning with Reachable Distances

  • Chapter
Book cover Algorithmic Foundation of Robotics VIII

Part of the book series: Springer Tracts in Advanced Robotics ((STAR,volume 57))

Abstract

Motion planning for spatially constrained robots is difficult due to additional constraints placed on the robot, such as closure constraints for closed chains or requirements on end effector placement for articulated linkages. It is usually computationally too expensive to apply sampling-based planners to these problems since it is difficult to generate valid configurations. We overcome this challenge by redefining the robot’s degrees of freedom and constraints into a new set of parameters, called reachable distance space (RD-space), in which all configurations lie in the set of constraint-satisfying subspaces. This enables us to directly sample the constrained subspaces with complexity linear in the robot’s number of degrees of freedom. In addition to supporting efficient sampling, we show that the RD-space formulation naturally supports planning, and in particular, we design a local planner suitable for use by sampling-based planners. We demonstrate the effectiveness and efficiency of our approach for several systems including closed chain planning with multiple loops, restricted end effector sampling, and on-line planning for drawing/sculpting. We can sample single-loop closed chain systems with 1000 links in time comparable to open chain sampling, and we can generate samples for 1000-link multi-loop systems of varying topology in less than a second.

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Author information

Authors and Affiliations

  1. Google, 1600 Amphitheatre Parkway, Mountain View, CA, 94043, USA

    Xinyu Tang

  2. Department of Computer Science and Engineering, Texas A&M University, College Station, TX, 77843, USA

    Shawna Thomas & Nancy M. Amato

Authors
  1. Xinyu Tang
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  2. Shawna Thomas
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  3. Nancy M. Amato
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Editor information

Editors and Affiliations

  1. Department of Mechanical Engineering, The Johns Hopkins University, 21218, Baltimore, Maryland, USA

    Gregory S. Chirikjian

  2. Carnegie Mellon University, 5000 Forbes Ave., Newell-Simon Hall 3211, 15213, Pittsburgh, PA, USA

    Howie Choset

  3. Sistemas Digitales, Instituto Tecnológico, Autónomo de México, Rio Hondo 1, Progreso Tizapán, 01080, México, D.F., México

    Marco Morales

  4. Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, 60208, Evanston, IL, USA

    Todd Murphey

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© 2009 Springer-Verlag Berlin Heidelberg

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Tang, X., Thomas, S., Amato, N.M. (2009). Planning with Reachable Distances. In: Chirikjian, G.S., Choset, H., Morales, M., Murphey, T. (eds) Algorithmic Foundation of Robotics VIII. Springer Tracts in Advanced Robotics, vol 57. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00312-7_32

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  • DOI: https://doi.org/10.1007/978-3-642-00312-7_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00311-0

  • Online ISBN: 978-3-642-00312-7

  • eBook Packages: EngineeringEngineering (R0)

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