A catalog of inverse-kinematics planners for underactuated systems
on matrix groups
Sonia Martínez - Mechanical and Aerospace Engineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0411, 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.
Received: April 2009; Revised: September 2009; Published: January 2010.
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