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General methods for computing hyper-redundant manipulator inverse kinematics

Hyper-redundant robots have a very large or infinite degree of kinematic redundancy. This paper formulates generalized resolved rate methods for solving hyper-redundant manipulator inverse kinematics using a backbone curve. These methods are applicable even when explicit representation of the backbone curve intrinsic geometry cannot be written in closed form. Problems of end-effector trajectory tracking and singularity analysis which were previously intractable can now be handled easily. Examples include configurations generated using the calculus of variations. Also, the method is naturally parallelizable for fast digital and/or analog computation.