A Quasi-Linear Method for Computing and Projecting onto C-Surfaces: Planar Case

George Paul and Katsushi Ikeuchi
tech. report CMU-RI-TR-96-37, Robotics Institute, Carnegie Mellon University, December, 1996


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Abstract
This report presents a general method to compute configuration space (c-space) obstacle surfaces (c-surfaces) in planar quaternion space and for projecting points onto them. We parameterize the general c-surface using the rotational angle and the vector of translation parameters of the individual contacts. Once we compute the domain of the rotation parameter, we can setup the translation parameters in a linear equation. The singular value decomposition of this equation gives us with the exact parameters of the translation. We extend the theory to project a point in c-space onto the c-surface.

We implement our theory on the Assembly Plan from Observation (APO) system. The APO observes discrete instants of an assembly task and reconstructs the compliant motion plan employed in the task. We compute the contacts at each observed instant and the corresponding c-surface. We then interpolate the path on each c-surface to obtain segments of the path. The complete motion plan will be the concatenation of the connected path segments.


Notes
Sponsor: NSF, USAF
Grant ID: F33615-90-C-1465, F33165-93-1-1282
Associated Center(s) / Consortia: Vision and Autonomous Systems Center
Number of pages: 21

Text Reference
George Paul and Katsushi Ikeuchi, "A Quasi-Linear Method for Computing and Projecting onto C-Surfaces: Planar Case," tech. report CMU-RI-TR-96-37, Robotics Institute, Carnegie Mellon University, December, 1996

BibTeX Reference
@techreport{Paul_1996_429,
   author = "George Paul and Katsushi Ikeuchi",
   title = "A Quasi-Linear Method for Computing and Projecting onto C-Surfaces: Planar Case",
   booktitle = "",
   institution = "Robotics Institute",
   month = "December",
   year = "1996",
   number= "CMU-RI-TR-96-37",
   address= "Pittsburgh, PA",
}