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

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  • 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.
    Mathematics Subject Classification: Primary: 70Q05, 93B05, 70B10; Secondary: 58D19.

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