Redundancy parameterization and inverse kinematics of 7-DOF revolute manipulators
arxiv(2023)
摘要
Seven degree-of-freedom (DOF) robot arms have one redundant DOF which does
not change the motion of the end effector. The redundant DOF offers greater
manipulability of the arm configuration to avoid obstacles and singularities,
but it must be parameterized to fully specify the joint angles for a given end
effector pose. For 7-DOF revolute (7R) manipulators, we introduce a new concept
of generalized shoulder-elbow-wrist (SEW) angle, a generalization of the
conventional SEW angle but with an arbitrary choice of the reference direction
function. The SEW angle is widely used and easy for human operators to
visualize as a rotation of the elbow about the shoulder-wrist line. Since other
redundancy parameterizations including the conventional SEW angle encounter an
algorithmic singularity along a line in the workspace, we introduce a special
choice of the reference direction function called the stereographic SEW angle
which has a singularity only along a half-line, which can be placed out of
reach. We prove that such a singularity is unavoidable for any
parameterization. We also include expressions for the SEW angle Jacobian along
with singularity analysis. Finally, we provide efficient and singularity-robust
inverse kinematics solutions for most known 7R manipulators using the general
SEW angle and the subproblem decomposition method. These solutions are often
closed-form but may sometimes involve a 1D or 2D search in the general case.
Search-based solutions may be converted to finding zeros of a high-order
polynomial. Inverse kinematics solutions, examples, and evaluations are
available in a publicly accessible repository.
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