Inverse kinematics solutions of anthropomorphic limbs by decomposition and fuzzy classification

The paper proposes a novel method for extremely fast inverse kinematics computation suitable for anthropomorphic limbs. The forward kinematics formulation and decomposition of the workspace into cells are described. In a preprocessing phase, the workspace of the robot is decomposed into small cells, and joint angle vectors (configurations) and end-effector position/orientation (posture) data sets are generated randomly in each cell using the forward kinematics. Due to the existence of multiple solutions for a desired posture, the generated configurations form a cluster in the joint space. A method involving classification and fuzzy rule base reasoning is described to separate the cluster into appropriate solutions. After classification, the data belonging to each solution is used to determine the parameters of a simple linear model that closely approximates the inverse kinematics within a cell. These parameters are stored in lookup file. During the online phase, given the desired posture the index of the appropriate cell is found, the model parameters are retrieved, and the joint angle vectors are computed. The advantages of the proposed method over the existing approaches are discussed. In particular, the method is complete (provides all solutions), and is very fast. Statistical analysis is provided to demonstrate the performance of the proposed method.