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A catalog of inverse-kinematic planners for underactuated systems on matrix Lie groups
S. Martínez, J. Cortés, F. Bullo
Proceedings of the IEEE/RSJ Conf. Intelligent Robots and Systems, Las Vegas, Nevada, USA, 2003, pp. 625-630

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) x R classified according to their controllability properties.

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