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The Journal of Geometric Mechanics (JGM)
 

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

Pages: 445 - 460, Volume 1, Issue 4, December 2009      doi:10.3934/jgm.2009.1.445

 
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Sonia Martínez - Mechanical and Aerospace Engineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0411, United States (email)
Jorge Cortés - Mechanical and Aerospace Engineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0411, United States (email)
Francesco Bullo - Mechanical Engineering, University of California, Santa Barbara, 2338 Engineering Building II, Santa Barbara, CA 9310-5070, United States (email)

Abstract: 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.

Keywords:  mechanical control systems, kinematics, motion planning.
Mathematics Subject Classification:  Primary: 70Q05, 93B05, 70B10; Secondary: 58D19.

Received: April 2009;      Revised: September 2009;      Available Online: January 2010.