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A catalog of inverse-kinematics planners for underactuated systems on matrix groups
S. Martínez, J. Cortés, F. Bullo
Journal of Geometric Mechanics 1 (4) (2009), 445-460

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 underactuated systems on SE(2), SO(3), and SE(2)xR classified according to their controllability properties.

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