Reachable Distance Space: Efficient Sampling-Based Planning for Spatially Constrained Systems

Xinyu Tang, S. Thomas, P. Coleman, N. M. Amato

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


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 number of the robot's degrees of freedom. In addition to supporting efficient sampling of configurations, 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 1,000 links in time comparable to open chain sampling, and we can generate samples for 1,000-link multi-loop systems of varying topologies in less than a second. © 2010 The Author(s).
Original languageEnglish (US)
Pages (from-to)916-934
Number of pages19
JournalThe International Journal of Robotics Research
Issue number7
StatePublished - Jan 25 2010
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: This research supported in part by NSF Grants EIA-0103742, ACR-0113971, CCR-0113974, ACI-0326350, CRI-0551685, CCF-0833199, CCF-0830753, by Chevron, IBM, Intel, HP, and by King Abdullah University of Science and Technology (KAUST) Award KUS-C1-016-04. S. Thomas was supported in part by a NSF Graduate Research Fellowship, a PEO Scholarship, a Department of Education Graduate Fellowship (GAANN), and an IBM T.J. Watson PhD Fellowship. The work of X. Tang was performed when he was a PhD student in the Department of Computer Science and Engineering at Texas A&M University.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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