Classification and characterization of inverse kinematics solutions for anthropomorphic manipulators

Topological properties of the kinematics map are exploited to develop a novel method for redundancy parameterization and extremely fast inverse kinematics solutions for 7-DOF anthropomorphic manipulators and animation characters. The method consists of generating joint angles vectors (configurations) and determining their associated hand position/orientation (pose) via the known forward kinematics. The generated data are classified into various inverse kinematics solutions manifolds. These manifolds are subsequently segmented so that the redundancy can be parameterized and the solutions can be represented by simple equations whose parameters are stored for rapid online computation. During the online phase, given the desired hand pose, the appropriate stored parameters are retrieved and various inverse kinematics solutions are computed. The online time to provide various solutions is of the order of several microseconds, which allow real-time inverse kinematics evaluations for fast moving animation characters or manipulators.