# American Institute of Mathematical Sciences

December  2009, 1(4): 445-460. doi: 10.3934/jgm.2009.1.445

## A catalog of inverse-kinematics planners for underactuated systems on matrix groups

 1 Mechanical and Aerospace Engineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0411, United States, United States 2 Mechanical Engineering, University of California, Santa Barbara, 2338 Engineering Building II, Santa Barbara, CA 9310-5070, United States

Received  April 2009 Revised  September 2009 Published  January 2010

This paper presents motion planning algorithms for underactuated systems evolving on rigid rotation and displacement groups. Motion planning is transcribed into (low-dimensional) combinatorial selection and inverse-kinematics problems. We present a catalog of solutions for all left-invariant underactuated systems on SE(2), SO(3), and SE(2)$\times$ R classified according to their controllability properties.
Citation: Sonia Martínez, Jorge Cortés, Francesco Bullo. A catalog of inverse-kinematics planners for underactuated systems on matrix groups. Journal of Geometric Mechanics, 2009, 1 (4) : 445-460. doi: 10.3934/jgm.2009.1.445
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