Estimation of Inverse Kinematics Model by Forward-Propagation Rule with a High-Order Term

Estimation of an inverse kinematics model is important in robot manipulator control. Multilayered neural networks that can express a nonlinear mapping are applied in order to acquire the inverse kinematics model. Several estimation methods using neural networks have been proposed, and we herein consider the forward-propagation (FP) rule. This method is based on the following steps. First, the goal signal, which corresponds to the supervisor signal at the hidden layer and the output layer, is derived by the Newton-like method. Second, the updating of weights is realized by linear multiple regression. The regression coefficients express the adding correction of the weights. In the FP rule, it is important to realize the goal signal exactly. However, it is difficult to realize this requirement because the correction of the goal signal in the hidden layer, which corresponds to the objective variable, is expressed by the linear combination of the desired trajectory, which corresponds to the describing variable, because the neurons in the input layer are decided by the number of control outputs. In this paper, we propose the FP rule with a high-order term. The layer, which is constructed with the high-order term of the input to the neural network, is inserted between the input layer and the hidden layer. In addition, we derive the goal signal in this scheme. In order to verify the efficacy of the FP rule with a high-order term, we apply this rule to the inverse kinematics problem for the two-link manipulator, which moves on the horizontal plane. The simulation results show that the proposed method obtains a more accurate inverse kinematics model, compared to the FP rule without the high-order term