Sensor-based Planning for a Rod-shaped Robot in Three Dimensions: Piecewise Retracts of R3 x S2

Ji Yeong Lee and Howie Choset
Journal Article, Carnegie Mellon University, The International Journal of Robotics Research, Vol. 24, No. 5, pp. 343 - 383, May, 2005

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We present a new roadmap for a rod-shaped robot operating in a three-dimensional workspace, whose configuration space is diffeomorphic to R 3 x S 2. This roadmap is called the rod hierarchical generalized Voronoi graph (rod-HGVG) and can be used to find a path between any two points in an unknown configuration space using only the sensor data. More importantly, the rod-HGVG serves as a basis for an algorithm to explore an unknown configuration space without explicitly constructing it. Once the rod-HGVG is constructed, the planner can use it to plan a path between any two configurations. One of the challenges in defining the roadmap revolves around a homotopy theory result, which asserts that there cannot be a one-dimensional deformation retract of a non-contractible space with dimension greater than two. Instead, we define an exact cellular decomposition on the free configuration space and a deformation retract in each cell (each cell is contractible). Next, we “connect” the deformation retracts of each of the cells using a roadmap of the workspace. We call this roadmap a piecewise retract because it comprises many deformation retracts. Exploiting the fact that the rod-HGVG is defined in terms of workspace distance measurements, we prescribe an incremental procedure to construct the rod-HGVG that uses the distance information that can be obtained from conventional range sensors.

author = {Ji Yeong Lee and Howie Choset},
title = {Sensor-based Planning for a Rod-shaped Robot in Three Dimensions: Piecewise Retracts of R3 x S2},
journal = {The International Journal of Robotics Research},
year = {2005},
month = {May},
volume = {24},
number = {5},
pages = {343 - 383},
} 2017-09-13T10:43:25-04:00