Modeling of robot inverse kinematics by spatial decomposition and functional approximation

A novel method is proposed for extremely fast inverse kinematics computation suitable for anthropomorphic limbs, and manipulators with seven or fewer degrees of freedoms. The method consist of two phases, an off-line phase where the workspace of the robot is decomposed into small cells, and joint angle vectors and end-effector position/orientation data sets are generated in each cell using the forward kinematics. This data is used to determine the parameters of a simple linear or quadratic model that closely approximates the inverse kinematics within a cell. These parameters are stored in lookup file ordered by an index number that gives the address of the cell. During the online phase, given the desired position/orientation, 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 much faster than even using closed-form inverse kinematics solutions, if such solutions exist. A case study is reported to demonstrate the feasibility of the method, and to evaluate its performance.