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

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) /spl times/ /spl Ropf/ classified according to their controllability properties.