-Neural Network Model with Hierarchical Objective Functions - Abstract:This paper propose a new parallel-hierarchical neural network model to enable motor learning for simultaneous control of both trajectory and force, by integrating Hogan's control method and our previous neural network control model using a feedback-error-learning scheme. Furthermore, two hierarchical control laws which apply to the model are derived by using the Moore- Penrose pseudo-inverse matrix: one is related to the minimum muscle-tension-change trajectory; and the other is related to the minimum motor-command-change trajectory. The human arm is redundant at the dynamics level since joint torque is generated by agonist and antagonist muscles. Therefore, acquisition of the inverse model is an ill-posed problem. However, the combination of these control laws and feedback-error-learning resolves the ill-posed problem. Finally, the efficiency of the parallel-hierarchical neural network model is shown by learning experiments using an artificial muscle arm and computer simulations.