Solving inverse problems by decomposition, classification and simple modeling

Inverse problems appear in many areas ranging from microwave circuits to environmental studies and to robotics, just to mention a few. In this paper we propose a new approach to solving inverse problems based on decomposition of output space into cells, with the corresponding regions in the input space. Solutions are identified using a clustering method and the relationship between data in an output cell and the corresponding input region is modeled by a simple polynomial. It is shown that the proposed method achieves very high accuracy even with relatively high number of inputs and outputs. It is also extremely fast and is suitable for real-time control, where needed. The method is applied to a highly complex inverse problem in robot kinematics and its performance is demonstrated.