A catalog of inverse-kinematics planners for underactuated systems on matrix 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 $\SE{2}\times\real$ classified according to their controllability properties.